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Core Connections Algebra 2

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for<br />

<strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 1.1.1<br />

1-4. a: 1 2 b: 3<br />

1-5. a: h(x) then g(x) b: Yes, g(x) then h(x).<br />

1-6. See graph above right.<br />

# of Buses<br />

4<br />

3<br />

2<br />

1<br />

45 90 135 180<br />

# of Students<br />

1-7. a: y<br />

b: c: y<br />

d:<br />

y<br />

x<br />

1-8. a: Not linear. b: The exponent. c: A parabola.<br />

1-9. Answers will vary.<br />

Lesson 1.1.2 (Day 1)<br />

1-12. y = 2x + 10<br />

See graph and table at right.<br />

x 0 1 2 3 4<br />

y 10 12 14 16 18<br />

1-13. a: x = –13 or 17 b: x = – 3 2 or 7 3<br />

c: x = 0 or 3 d: x = 0 or 5<br />

e: x = 7 or –5 f: x = 1 3<br />

or –5<br />

1-14. a: 14, –4, 3x – 1 b: f(x) = 3x – 1<br />

1-15. a: y = 5x – 2 b: x = 2 5<br />

1-16. a: 21, 15, (0, 15) b: –3, 3, (0, 3)<br />

1-17. a: 16 b: 9 c: 478.38<br />

Temperature<br />

1-18. a: y depends on x; x is independent. Explanations will vary.<br />

b: Temperature is dependent; time is independent.<br />

c: See graph above right.<br />

Time<br />

2 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 1.1.2 (Day 2)<br />

1-19. y = 30 – x<br />

Graph and table shown at right.<br />

Answers will vary.<br />

x 0 1 6 20<br />

y 30 29 24 10<br />

1-20. See graph below. Possible inputs: x –4 –2 0 1 6<br />

all real numbers; possible outputs: y 8 2 0 0.5 18<br />

any number greater than or equal to zero.<br />

1-21. a: 1 b: x = 12<br />

c: 13 d: no solution<br />

e: x = ± 13 2<br />

≈ ± 2.55 f: x = ± 7 ≈ ± 2.65<br />

1-22. Cube each input: f (x) = x 3<br />

1-23. a: The more gas you buy, the more money you spend. I: gallons, D: dollars<br />

b: People grow a lot in their early years and then their growing slows down.<br />

I: age, D: height<br />

c: As time goes by, the ozone concentration goes down, although the effect is slowing.<br />

I: year, D: ozone<br />

d: As the number of students grows, more classrooms are used and each classroom holds<br />

30 students. I: students, D: classrooms<br />

e: Possible inputs: x can be any number between and including 0 and 120,<br />

possible outputs: y = 1, 2, 3, 4<br />

1-24. They are similar by AA.<br />

a: n m b: m x<br />

1-25. Error in line 2: It should be –14, not +14; x = –37.<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 3

Lesson 1.1.3<br />

1-34. a: The numbers between –2 and 4 inclusive.<br />

b: The numbers between –1 and 3 inclusive.<br />

c: No. He is missing all the values between those<br />

numbers. The curve is continuous, so the description<br />

needs to include all real numbers, not just integers.<br />

(–2,3)<br />

(4,–1)<br />

d: See graph at right.<br />

1-35. a: 70 b: 2 c: 43 d: undefined<br />

e: 3x 2 = x – 5 – 3 f: 3x 2 = x – 5 + 7<br />

g: all real numbers h: all real numbers greater than or equal to 5.<br />

i: They are different because the square root of a negative is undefined, whereas any real<br />

number can be squared.<br />

1-36. Chelita is correct about how to find the intercepts, but she makes an error with signs<br />

while factoring. The correct equation is (x − 7)(x − 3) = 0 and the x-intercepts are<br />

7 and 3.<br />

1-37. a: y = x–6<br />

b: y =<br />

x+10<br />

5<br />

c: y = ± x<br />

d: y = ± x+4<br />

e: y = ± x + 5<br />

1-38. a: –7 b: 3.5 c: The x- and y-intercepts.<br />

1-39. a: y = 3x + 24; Table and graph shown at right.<br />

1-40. a: x = 13 b: x = 8<br />

0<br />

24<br />

27<br />

30<br />

33<br />

36<br />

39<br />

Height (in inches)<br />

Time (in weeks)<br />

4 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 1.1.4<br />

1-46. (2, 1)<br />

1-47. a: 2 b: 10 c: 100 d: ≈ 142.86<br />

1-48. a: x = 5, 3 b: x ≈ 3.39, –0.89 or x =<br />

5± 73<br />

1-49. a: 34 ≈ 5.83 units b: 3 5<br />

1-50. a: 1 52<br />

b:<br />

51<br />

52<br />

1-51. The error is in line 3. It should be: 0 = 5.4x + 23.7, x ≈ –4.39<br />

1-52. a: x ≈ –7.37 b: x = 2.8<br />

Lesson 1.2.1 (Day 1)<br />

1-59. Table and graph shown below right.<br />

D: −∞ < x < ∞ ; R: −∞ < y < ∞<br />

intercepts (0, –4) and<br />

4, 0<br />

1-60. a: ≈ 5.18 b: ≈18.66<br />

( ) or (≈ 1.59, 0)<br />

–3<br />

–2<br />

–1<br />

h(x)<br />

–31<br />

–12<br />

–5<br />

–4<br />

23<br />

c: ≈ 24.62º d: 180 ≈ 13.42<br />

1-61. a: A line, no variables are raised to a power.<br />

b: y = 2 3<br />

x – 2 , graph shown at right.<br />

c: Substitute x = 0 and solve for y, substitute<br />

y = 0 and solve for x. (3, 0) and (0, –2)<br />

d: Answers will vary.<br />

e: The intercepts are (–9, 0) and (0, 6),<br />

graph shown at right.<br />

1-62. a: D: x = –1, 1, 2 b: D: –1 ≤ x < 1 c: D: x ≥ –1 d: D: −∞ < x < ∞<br />

R: y = –2, 1, 2 R: –1 ≤ y < 2 R: y ≥ –1 R: y ≥ –2<br />

1-63. There is an error in line 2. Both sides need to be multiplied by x: 5 = x 2 – 4x,<br />

0 = x 2 –4 –5 = (x –5)(x + 1), x = –1, 5.<br />

1-64. a: x = 3, –2 b: x = 3, –3<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 5

Lesson 1.2.1 (Day 2)<br />

1-65. a: 2 b: –4 c: 1 0<br />

is undefined d: Answers will vary.<br />

1-66. a: (0, 3) and ( –<br />

2 3 , 0 ) , see graph at right.<br />

b: These equations are equivalent, they just have different<br />

notation.<br />

1-67. x ≈ 2.72 feet, y ≈ 1.27 feet<br />

1-68. a: D: –2, –1, 2 b: D: –1< x ≤ 1 c: D: x > –1 d: D: −∞ < x < ∞<br />

R: –1, 0, 1 R: –1< y ≤ 2 R: y > –1 R: −∞ < y < ∞<br />

1-69. l = 4w and l + w = 22 or w + 4w = 22<br />

The length is 17.6 cm, and the width is 4.4 cm.<br />

1-70. a: x = −<br />

17 1 ≈ −0.059 b: x =<br />

66<br />

13<br />

≈ 5.08 c: x = –1, 3<br />

1-71. a: (–1, 9) and (5, 21) b: x 2 +17 c: x 2 – 4x – 5<br />

Lesson 1.2.1 (Day 3)<br />

1-72. a: x = 5(y–1)<br />

b: x = –2y+6<br />

c: x = ± y d: x = ± y +100<br />

1-73. y = π x 2 , table and graph shown at right.<br />

1-74. a: 58 ≈ 7.62<br />

y 0 π 4π 9π 16π radius<br />

b: –<br />

7<br />

1-75. Solve x 2 + 2x +1 = 1 ; 0 or –2.<br />

1-76. a: (0, 6) b: (0, 2) c: (0, 0)<br />

d: (0, –4) e: (0, 25) f: (0, 13)<br />

-3<br />

-1 -1<br />

area<br />

6 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 1.2.2 (Day 1)<br />

1-84. (1, 3) and (7, 81)<br />

1-85. a: x = –6 b: x = 38<br />

13 ≈ 2.92<br />

1-86. Graph shown at right. intercepts: (0, –2) and (4, 0),<br />

domain: x ≥ 0, range: y ≥ –2<br />

f(x)<br />

1-87. x +(x + 18) or x + y = 84 and y = x +18; 33 and 51 meters long.<br />

1-88. a: Table and graph shown at right, y = 2x + 26.<br />

b: 37 weeks after his birthday.<br />

1-89. y = 0<br />

a: (–2, 0) b: (–10, 0) c: (0, 0)<br />

( ) e: (5, 0) f:<br />

( 13, 0)<br />

d: ± 2, 0<br />

1-90. Graph shown at right. domain: −∞ < x < ∞ , range: y ≥ –8<br />

26<br />

28<br />

32<br />

34<br />

-2<br />

4 x<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 7

Lesson 1.2.2 (Day 2)<br />

1-91. a: x = y–b<br />

m b: r = ± A π<br />

c: W = V<br />

LH d: y = 1<br />

3–2x<br />

1-92. See table and graph at right. Answers will vary.<br />

1-93. a: Answers will vary.<br />

b: When the y-values are the same, they must be equal.<br />

c: 3x + 15 = 3 – 3x, x = –2<br />

d: y = 9<br />

–2 –1<br />

–1 –2<br />

–0.5 –4<br />

0 undef.<br />

0.5 4<br />

1 2<br />

2 1<br />

e: They cross at the point (–2, 9).<br />

1-94. 7.5 feet<br />

1-95. ( ± 5, 0) ; Graph shown at right.<br />

1-96. a: y<br />

b: y c: y-intercept (0, 3) for both, x-intercept<br />

1-97. a: 4 b: 2 c: 3 d: 1<br />

( –<br />

2 3 , 0 ) for (a) and none for (b).<br />

d: (0, 3) and (2, 7), solve 2x + 3 = x 2 + 3 to<br />

get x = 0<br />

or x = 2<br />

8 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 1.2.3<br />

1-104. m = –<br />

4 3 , (4, 0), (0, 3), graph shown at right.<br />

1-105. y = 3 2 x – 3<br />

1-106. x =<br />

−3± 21<br />

7± 193<br />

≈ –3.79, 0.79 b: x =<br />

6<br />

≈ 3.48, –1.15<br />

1-107. $12.00<br />

(Schools with an open campus)<br />

1-108. Sample graphs.<br />

# of People<br />

or<br />

= 2<br />

1-110. a: 1, 2, 3, 4, 5 or 6 b: 1 6 c: 4 6<br />

1-109. a: D: –3≤ x ≤ 3 b: D: x = 2 c: D: x ≥ −2<br />

R: y = –2, 1, 3 R: −∞ < y < ∞ R: −∞ < y < ∞<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 9

Lesson 1.2.4<br />

1-112. a: A portion of the trip at a specific speed.<br />

b: About 400 miles. It is the total distance on the graph.<br />

c: Graph shown below – a speed of approximately 30 mph for 1 hour, approximately<br />

80 mph for the next 3 hours, 0 mph for 2 hours, approximately 40 mph for 2 hours,<br />

and then approximately 20 mph for the last 2 hours. Note that the step graph assumes<br />

instantaneous change of speed, which is not technically possible.<br />

1-113. a: x = 2 b: x = 4<br />

1-114. mB = 39.8° , 244 ≈ 15.62<br />

1-115. 56 inches<br />

Speed (mph)<br />

Time (hours)<br />

1-116. The independent variable is the volume of<br />

water; the dependent variable is the height<br />

C<br />

of the liquid. The graph is 3 line segments<br />

A<br />

starting at the origin. C is the steepest, and<br />

B is the least steep.<br />

Volume of Water<br />

Added<br />

1-117. Diagrams vary; graph and table below, y = 3x.<br />

1-118. a:<br />

26 1 b: 25 1 x y<br />

1 3<br />

Height of Liquid<br />

2 6<br />

3 9<br />

B<br />

10 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 2.1.1<br />

2-4. a: See graph at right.<br />

b: Yes, for every possible amount of water usage,<br />

there is only one possible cost.<br />

c: Domain: 0 to 1,000 cubic feet; range: discrete<br />

values including: $12.70, $16.60, $20.50, $24.40,<br />

$29.60, $34.80, $40, $45.20, $50.40, $55.60,<br />

$60.80<br />

Cost ($)<br />

Water Used (ft 3 )<br />

2-5. Smallest: a: 2; b: 0; c: –3; d: none.<br />

Largest: a: none. b: none. c: none. d: 0. e: At the vertex.<br />

2-6. The negative coefficient causes parabolas to open<br />

downward, without changing the vertex. See graph at right.<br />

2-7. a: Parabola with vertex (3, 0), see graph at right.<br />

b: Shifted to the right three units.<br />

2-8. a: 4, 1, 0.25; t(n) = 256(0.25) n – 1<br />

b: They get smaller, but are never negative.<br />

c: See graph at right. They get very close to zero.<br />

d: The domain is n integers greater than or equal to zero.<br />

The domain of the function is all real numbers.<br />

t(n)<br />

2-9. a: y = − 2 3 x − 4 b: y = 2<br />

n<br />

c: x = 2 d: y = 2 3 x − 8 3<br />

2-10. n = 24; 650 = 5 26<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 11

Lesson 2.1.2<br />

2-16. Answers will vary.<br />

2-17. a: (0, –6)<br />

b: (–6, 0) and (1, 0)<br />

c: x-intercepts at (0, 0) and (–5, 0) and y-intercept at (0, 0); the graph of p(x) is 6 units<br />

lower than q(x)<br />

d: –6<br />

2-18. a: z = 1.5 b: z = – 18 5<br />

c: z = 8 d: z = –3, 2<br />

2-19. a: 3 b:<br />

x 2 y 4 c: y<br />

2-20. a: 3p + 3d = 22.50 and p + 3d + 3(8) = 37.5, so popcorn costs $4.50 and a soft drink costs<br />

$3.00.<br />

b: Answers will vary.<br />

2-21. a: 146 ≈ 12.1 b: 145 ≈ 12.0 c: 50 ≈ 7.1 d: 5 2<br />

2-22. Maximum profit is $25 million when n = 5 million.<br />

2-23. a: vertex at (–3, –8), opens up, vertically stretched.<br />

b: x-intercepts (–5, 0) and (–1, 0); y-intercept (0, 10)<br />

2-24. a, b, and c: Answers will vary.<br />

2-25. a: y = (x – 8) 2 – 5 b: y = 10(x + 6) 2 c: y = –0.6x(x + 7) 2 – 2<br />

2-26. Answers will vary.<br />

2-27. a: 5 2 b: 6 2 c: 3 5<br />

2-28. a: x = 46.71 b: x = 8.19<br />

2-29. About $ 365.00. b: y = 300(1.04) x<br />

12 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 2.1.3<br />

2-35. a: y = 0 or 6 b: n = 0 or –5 c: t = 0 or 7 d: x = 0 or –9<br />

2-36. a: (7, −16), y = (x − 7) 2 −16 b: (2, −16), y = (x − 2) 2 −16<br />

c: (7, −9), y = (x − 7) 2 − 9 d: (2, –1)<br />

2-37. a: (2, –1)<br />

b: When x = 2, (x – 2) 2 will equal zero and y = –1, the smallest possible value for y in<br />

the equation. So the y-value of the vertex is the minimum value in the range of the<br />

function.<br />

2-38. a: 9.015 gigatons<br />

b: C(x) = 8(1.01) (x+2) if x represents years since 2000 or 8.16(1.01) x .<br />

2-39. a: 2 b: 1 c: 1 d: 2 e: 2 f: 1<br />

h: If the factored version includes a perfect-square binomial factor, the parabola will<br />

touch at one point only.<br />

2-40. a: 4 b:<br />

16x 4 y 10<br />

c: 6xy3<br />

2-41. a: 8 27<br />

12<br />

27 c: 6<br />

27 d: 1<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 13

Lesson 2.1.4<br />

2-50. a: f (x) = (x + 3) 2 + 6 (–3, 6), x = –3<br />

b: y = (x − 2) 2 + 5 , (2, 5) x = 2<br />

c: f (x) = (x − 4) 2 −16 , (4, –16), x = 4<br />

d: y = (x + 3.5) 2 −14.25 , (–3.5, –14.25), x = –13.5<br />

2-51.<br />

b 2 a<br />

2-52. The second graph is a reflection of the first<br />

across the x-axis. See graph at right.<br />

2-53. a: 45 = 3 5 ≈ 6.71; y = 1 2<br />

x + 5 b: 5; x = 3<br />

c: 725 ≈ 26.93; y = − 5 2 x + 5 2<br />

d: 4; y = –2<br />

2-54. After x is factored out, the other factor is a quadratic equation. After using the<br />

Quadratic Formula the solutions are x =<br />

−23± 561<br />

8<br />

or 0.<br />

2-55. a: x = 21 b: x = 10 5 ≈ 22.4 c: x = 50<br />

2-56. a: 1 4 b: 1 3<br />

2-57. B<br />

2-58. a: A cylinder b: 45π = 141.37 cubic units<br />

2-59. a and b: Answers will vary. c: A circle.<br />

2-60. (5, 14)<br />

2-61. a: 0.625 hours or about 37.5 minutes.<br />

b: 0.77 hours or about 46.2 minutes.<br />

c: About $22.99 per minute.<br />

2-62. a: 61 b: 30º c: tan −1 ( 4 5 ) d: 5 3<br />

2-63. a: Years; 1.06; 120,000; 120000(1.06) x<br />

b: Hours; 1.22; 180; 180(1.22) x<br />

14 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 2.1.5<br />

2-69. Answers will vary.<br />

2-70. See graph at right.<br />

a: It is the slope.<br />

b: No, because only lines have (constant) slopes.<br />

This 2 is the stretch factor.<br />

2-71. a and b: No. Answers will vary.<br />

2-72. a: y = 0.25 ⋅6 x b: y = 12 ⋅0.3 x<br />

2-73. a: x: (1, 0), ( – 5 2 , 0 ), y : (0, –5) b: x: (2, 0), y: none<br />

2-74. See graphs at right.<br />

a: stretched parabola, vertex (0, 5)<br />

b: inverted parabola, vertex (3, –7)<br />

2-75. a: x = ± 5 b: x = ± 11<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 15

Lesson 2.2.1 (Day 1)<br />

2-81. Possible equation: y = − 4 25 (x − 5)2 + 8 , standing at (0, 0)<br />

domain: 0 ≤ x ≤ 10; range: 4 ≤ y ≤ 8<br />

2-82. a: x : (− 1 2 , 0), (−1, 0); y : (0, 1) b: x = – 3 4<br />

( ) or (–0.75, –0.125)<br />

c: – 3 4 , – 1 8<br />

2-83. Move it up 0.125 units: y = 2x 2 + 3x +1.125<br />

2-84. a: 2 6 b: 3 2 c: 2 3 d: 5 3<br />

2-85. a: Years; 0.89; 12250; 12250(0.89) x b: Months; 1.005; 1000; 1000(1.005) x<br />

2-86. a: 32 b: x 2 y 2 x c: x2 y<br />

2-87. c + m = 18 and $4.89c + $5.43m = $92.07<br />

10.5 lbs. of Colombian and 7.5 lbs. of Mocha Java.<br />

Lesson 2.2.1 (Day 2)<br />

2-88. a: 15 ft<br />

b: Surface area of concrete: 793.14 sq. ft.; 528.76 cu. ft.; $1,263.74<br />

2-89. a: See graph at right. b: y = 3x +2 c: 2, 5, 8, 11<br />

d: One is continuous and one is discrete. They have<br />

the same slope so the “lines” are parallel, but they<br />

have different intercepts.<br />

2-90. a: 4.116 ⋅10 12 b: y = 1.665(10 12 )(1.0317) t<br />

c: Answers will vary.<br />

2-91. a: 6 x + 3 y b: 32 c: 5 d:<br />

2-92. a: 6x 3 + 8x 4 y b: x 14 y 9<br />

2-93. See graph at right. line of symmetry x = 4<br />

2-94. a: 4π + 4 3 π ≈ 16.755 m 3 b: No; r, r 2 , r 3 relationship; V = 80π<br />

3 ≈ 83.776 m 3<br />

c: V = 4 3 π r3 + 4π r 2<br />

16 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 2.2.1 (Day 3)<br />

2-95. a: y = 1<br />

x+2 b: y = x2 – 5 c: y = (x – 3) 3 d: y = 2 x – 3<br />

e: y = 3x – 6 f: y = (x + 2) 3 + 3 g: y = (x + 3) 2 – 6 h: y = –(x – 3) 2 + 6<br />

i: y = (x + 3) 3 – 2<br />

2-96. He should move it up 6 units or redraw the axes 6 units lower.<br />

2-97. a: 18 b: 3 2 c: 1 3 or 3<br />

d: 11+ 6 2<br />

2-98. a: (2x – 3y)(2x + 3y) b: 2x 3 (2 + x 2 )(2 − x 2 )<br />

c: (x 2 + 9y 2 )(x − 3y)(x + 3y) d: 2x 3 (4 + x 4 )<br />

2-99. x = −by3 +c+7<br />

a<br />

2-100. a: t(n) = –6n + 26 b: t(n) = −1.5(4) n or − 6(4) n−1<br />

2-101. a: See graph at right. b: 2<br />

c: –1 d:<br />

–13<br />

e: no solution f: Three because the graphs cross three times.<br />

g: x 3 – x 2 – 2x<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 17

Lesson 2.2.2 (Day 1)<br />

2-107. a: y = (x – 2) 2 + 3 b: y = (x – 2) 3 + 3 c: y = –2(x + 6) 2<br />

2-108. a: D: all real numbers, R: y ≥ 3 b: D and R: all real numbers<br />

c: D: all real numbers, R: y ≤ 0<br />

2-109. a: compresses or stretches b: shifts up or down<br />

c: shifts left or right d: shifts up or down<br />

2-110. a: y = 0.4 ⋅0.5 x b: y = 8 ⋅2 x<br />

2-111. a: 2 25 b: 3x2 y 3<br />

z 4 c: 54m 4 n d: y 5x 2 z<br />

2-112. a: See table and graph at right.<br />

b: He had 28,900 miles in May.<br />

c: 5600 miles<br />

d: No, he will not be able to go in<br />

December, he will only have<br />

24,200 miles.<br />

Miles<br />

2-113. a: x = ± y 2 +17 b: x = (y + 7)3 − 5<br />

Month<br />

Month Miles<br />

1 15,000<br />

2 18,000<br />

3 22,900<br />

4 25,900<br />

5 28,900<br />

6 8,800<br />

7 11,800<br />

8 14,800<br />

9 19,700<br />

10 22,700<br />

11 25,700<br />

12 5,600<br />

18 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 2.2.2 (Day 2)<br />

2-114. a: (10, 48) b:<br />

29<br />

( 5<br />

, 9 5 )<br />

2-115. a: 8 3 b: 3 x c: 12 d: 108<br />

2-116. a: g ( 1 2 = –4.75 ) b: g(h +1) = h 2 + 2h − 4<br />

2-117. See graph at right.<br />

a: y = 2x : (0, 0), y = – 1 2<br />

x + 6 : (0, 6), (12, 0)<br />

b: It should be a triangle with vertices<br />

(0, 0), (12, 0), and (2.4, 4.8).<br />

c: Domain 0 ≤ x < 12, Range 0 ≤ y ≤ 4.8<br />

d: A = 1 2<br />

(12)(4.8) = 28.8 square units<br />

2-118. y ≈ 2(x − 5) 2 + 2 and y ≈ − 1 2 (x − 5)2 + 2<br />

2-119. See graph at right.<br />

y = (x +1) 2 − 81; x-intercepts: (–10, 0), (8, 0),<br />

y-intercept: (0, –80); vertex: (–1, –81)<br />

2-120. Yes, when n = 117.<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 19

Lesson 2.2.3<br />

2-125. a and : Neither c: Even<br />

2-126. a: b: c: Neither function is odd nor even.<br />

2-127. y = − 3 4 (x − 2)2 + 3<br />

2-128. a: x: (–1, 0), y: (0, 2) b: x: (0, 0), (2, 0), y: (0, 0)<br />

V: (–1, 0), y = 2(x +1) 2 V: (1, 1), y = –(x –1) 2 +1<br />

2-129. a: y = x b:<br />

( 2<br />

, 1 3 ) c:<br />

, 1 3 )<br />

d: The solution to the system is the point at which the lines intersect.<br />

2-130. a: t(n) = 40( 1 4 )n or 10( 1 4 )n−1 b: t(n) = −6n + 4<br />

2-131. a: x: (2, 0), (6, 0) y: (0, 2) vertex (4, –2), D: all real numbers; R: y ≥ –2<br />

b: x: (–4, 0), (2, 0) y: (0, 2) vertex (–1, 3), D: all real numbers; R: y ≤ 3<br />

20 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 2.2.4<br />

2-139. y = (x + 3.5) 2 − 20.25<br />

2-140. a: See graph at right.<br />

b: Loudness depends on distance.<br />

2-141. See graph at right. The domain is all positive<br />

numbers (or d > 0). The range is all real<br />

numbers greater than or equal to 3 and that<br />

are multiples of 0.25.<br />

$5.00<br />

$4.00<br />

Loudness<br />

Distance<br />

2-142. Answers will vary.<br />

$3.00<br />

2-143. The second graph shifts the first 5 units left and<br />

7 units up and stretches it by a factor of 4.<br />

2-144. a: x 2 –1 b: 2x 3 + 4x 2 + 2x<br />

c: x 3 − 2x 2 − x + 2 d: y: (0, 2), x: (1, 0), (–1, 0), (2, 0)<br />

2-145. a: (a, b) = ( 2, ± 1 2 ) b: (a, b) = ( 1 2 , ± 2 )<br />

2-146. a: y = − 5 9 (x − 3)2 + 5 b: x = − 3<br />

25 (y − 5)2 + 3<br />

0.2 0.4 0.6 0.8<br />

Distance (miles)<br />

2-147. See graph at right.<br />

a: y = 2x 2 − 4x + 6<br />

b: There is no difference, but the explanations vary.<br />

c: y = x 2<br />

d: y = x 2<br />

2-148. a: The graph will be a circle with a center at (5, 8) and a radius of 7.<br />

b: See graph at right.<br />

2-149. a: –2 b: –2 c: 1 2<br />

d: –1<br />

e: The product of the slopes of any two perpendicular lines is –1.<br />

2-150. Answers will vary.<br />

2-151. a: (0, 0), (–24, 0), and (0, 0) b: (6, 0), (10, 0), and (0, 60)<br />

2-152. (3, 2)<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 21

Lesson 2.2.5<br />

2-162. x < 2, y = –(x – 2) 2 ; x ≥ 2, y = x + 2<br />

2-163. Any function for which f (x) = f (−x). On a graph, the function will have the y-axis as its<br />

line of symmetry.<br />

2-164. y = −2 x + 3 + 4<br />

2-165. a: (x + 2) 2 + (y − 3) 2 = 4 b: (x −12) 2 + (y +15) 2 = 81<br />

2-166. y = (x − 2.5) 2 + 0.75 , vertex (2.5, 0.75)<br />

2-167. He is incorrect. Answers will vary.<br />

2-168. f (x) = x 2 +1<br />

2-169. ± 11, ± 9, ±19<br />

Lesson 3.1.1<br />

3-5. a: 4x 2 –12x +14 b: 81y4<br />

x 4<br />

3-6. a: 3 b: 4 c: 1 d: 5 e: 2<br />

3-7. They are both correct: x12 y 3<br />

64<br />

.<br />

3-8. a: Horizontal line through (0, 3), domain: all real numbers, range: 3<br />

b: Vertical line through (–2, 0), domain: –2, range: all real numbers<br />

c: (–2, 3)<br />

3-9. m = 15, b = –3<br />

3-10. a: (4, 8, 4 3 ), (5, 10, 5 3 )<br />

b: The long leg is n 3 units long, and the hypotenuse is 2n units long.<br />

3-11. a: 15, 21, 27, 33, t(n) = 6n –3<br />

b: 27, 81, 243, 729, t(n) = 3 n<br />

3-12. a: 1 5 b: 3 c: 27 d: 1 8<br />

22 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 3.1.2<br />

3-23. a: not equivalent b: equivalent c: equivalent<br />

d: equivalent e: not equivalent f: not equivalent<br />

3-24. a: equal if x = 0 e: equal if x = 0 or x = 1 f: equal if a = 1 or a = 0<br />

3-25. a: Possibilities include x – 2 = 4 or 2x – 4 = 8.<br />

b: They have the solution x = 6.<br />

c: 3 – x = 7, x = –4<br />

3-26. a: t (n) = –3n + 17, points along a line with y-intercept (0, 17) and slope –3;<br />

b: t(n) = 50(0.8) n , points along a decreasing exponential curve with<br />

y-intercept (0, 50)<br />

3-27. a: 4 b: –30 c: 12 d: –2 1 4 e: x = –4, 1 3<br />

3-28. (0, 0) and (–6, 0)<br />

3-29. a: 2x 2 + 6x b: x 2 – 2x –15 c: 2x 2 – 5x – 3 d: x 2 + 6x + 9<br />

3-30. The first graph opens downward, is stretched, and has its vertex at (–1, –3).<br />

The second is the parent graph.<br />

3-31. a: (1, –4) b: (1, –4) c: (–2.5, –4.25)<br />

3-32. a: y8<br />

x 12<br />

d: Domain: −∞ < x < ∞ , Range: y ≥ –4.25<br />

b: −18x3 y + 6x 5 y 2 z<br />

3-33. a: odd b: even c: even<br />

3-34. a: $4.00 b: $4.00<br />

c: $4.00. $5.00 d: See graph above right.<br />

e: No, it is a step function. f: The graph will shift (translate) upward by $2.00.<br />

3-35. a: (x + 2) 2 + (y −13) 2 = 144 b: (x +1) 2 + (y + 4) 2 = 1<br />

c: (x − 3) 2 + (y + 8) 2 = 16<br />

-1 -1 1 2 3 4 5 6 7 8<br />

Hours<br />

3-36. a: 24 blocks per hr. b: 18 blocks per hr. c: 11.08 blocks per hr.<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 23

Lesson 3.1.3<br />

3-45. a: n = –2 b: x = –4, 1<br />

3-46. a: equivalent b: equivalent c: equivalent<br />

d: not equivalent e: not equivalent f: not equivalent<br />

3-47. d: equal if a = 0 or b = 0 e: equal if x = 1 f: equal if x = 5 and y = 2<br />

3-48. 10 = 15m + b and 106 = 63m + b; m = 2, b = –20, t (n) = 2n –20<br />

3-49. a: t(n) = 450000 (1.03) n<br />

b: They will make $154,762.37 or 34.39% profit.<br />

3-50. 5xy(x + 2)(x + 5)<br />

3-51. a: They both have the solution x = 2.<br />

b: She divided both sides of the equation by 150 and used the Distributive Property.<br />

3-52. a: –6, –14, –22, –30, t(n) = 18 – 8n<br />

b: 2 5 , 25 2 , 2<br />

125 , 2<br />

625 , t(n) = 50 ( 1 5 ) n<br />

3-53. a: 5 1/2 b: 9 1/3 or 3 2/3 c: 17 x/8 d: 7x 3/4<br />

3-54. a: x 2 + y 2 = 36<br />

b: (x − 2) 2 + (y + 3) 2 = 36<br />

c: (x − 4) 2 + (y + 5) 2 = 36<br />

3-55.<br />

741.8−25<br />

1800−0<br />

= 0.4 ºF/sec<br />

3-56. a: b: Shift the graph up $11.<br />

Price ($)<br />

100<br />

50<br />

Duration (days)<br />

24 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 3.2.1<br />

3-63. odd numbers; 46 th term: 91; n th term: 2n – 1<br />

3-64. after 44 minutes<br />

3-65. a: 1.03 b: f (n) = 10.25(1.03) n c: $13.78<br />

3-66. (y –2)(y – 2)(y –2)<br />

3-67. a: x 1/5 b: x –3 3<br />

c: x 2<br />

d: x –1/2<br />

e:<br />

xy 8 f: 1<br />

m 3 g: xy3 x h:<br />

81x 6 y 12<br />

3-68. Yes, he can. a: x = 2 b: Divide both sides by 100.<br />

3-69. a: 5m 2 + 9m – 2 b: –x 2 + 4x +12<br />

c: 25x 2 –10xy + y 2 d: 6x 2 –15xy +12x<br />

Lesson 3.2.2<br />

3-78. a: x–4<br />

3x+2 b: 5<br />

x–3<br />

c: 2<br />

3-79. a: 1 b: none c: 2 d: 1<br />

3-80. a: x – 2 = 4 b: For each, x = 6. c: x + 3 = 8, x = 5<br />

3-81. a: x < 0 b: x ≤ –4<br />

3-82. a: 3 7 b: 5 4<br />

3-83. Graph shown at right.<br />

a: y = x 3 ; The vertex has been shifted up 4 and left 2.<br />

b: It would not differ.<br />

3-84. See graph at right.<br />

a: all real numbers<br />

b: See graph at far right.<br />

c: f(x) is a continuous function with<br />

range y > 0 while t(n) is a discrete<br />

sequence with positive integer inputs.<br />

15<br />

10<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 25

Lesson 3.2.3<br />

3-90.<br />

2x<br />

3(2x–1) = 2x<br />

6x–3<br />

3-91. a: x ≠ –4 or 2, x+4<br />

x–2<br />

x–4<br />

x+4<br />

b: x ≠ –2 or 3,<br />

2(x+2)<br />

(x–3) 2<br />

3-92. Answers will vary.<br />

3-93. a:<br />

( 3<br />

, –2) b: (4, –9)<br />

3-94. n ⋅ 3 15 = 72 million, n = 5; There were 5 bacteria at first.<br />

3-95. The function is even. A reflection across the y-axis results in the same graph.<br />

3-96. a: m = 6 b: x = 5.5 c: k = 4 d: x = 90<br />

Lesson 3.2.4<br />

3-102. a: Because if x = 4, then the denominator is zero. Since dividing by zero makes the<br />

expression undefined, x ≠ 4.<br />

b: a: x ≠ – 1 3<br />

and x ≠ 5; b: x ≠ 3 or –3<br />

3-103. a:<br />

8x+8<br />

(x–4)(x+2) b: 1<br />

x+2<br />

3-104. a: all real numbers b: –5 < x < 4<br />

c: no solution d: x = 1 3<br />

3-105. a: x – 4 b: 7m–1<br />

3m+2<br />

c:<br />

(4z–1)2<br />

z+2<br />

d: x–3<br />

3-106. a: 1722 b: 1368 c: y = 1500(1.047) n+3<br />

3-107. a: 5(3x–1)<br />

2(4x+1)<br />

b: 1 c: 3 d: –m2<br />

3-108. See graph at right; x-intercept: (–2, 0), y-intercept: (0, –2);<br />

there is no value for f(1), which creates a break in the graph.<br />

3-109. a: –15 b: –4 c: 3 d: –m 2<br />

26 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 3.2.5<br />

3-113. a:<br />

3x+1<br />

x–7<br />

x–3 c: x–2<br />

2x+12 d: 1<br />

3-114. a: 1 b: 4 c: 2 d: 5<br />

3-115. a: x = 3 b: 0 ≤ x ≤ 6 c: x = 1 or 5 d: x < 2 or x > 4<br />

3-116. Domain: all real numbers; Range y ≥ 0; g(–5) = 8<br />

g(a + 1) = 2a 2 +16a + 32 , x = 1 or x = 7, x = –3<br />

3-117. x = –3 or –11<br />

3-118. a: 1 b: 3 c: 2<br />

3-119. (–3, 8) and (1, –12)<br />

3-120. a:<br />

x+1<br />

x 2 −4<br />

x+6<br />

2(x+2) 2 c: 1 x d: – 1 2<br />

3-121. x = 62<br />

3-122. a: y = – 1 2 x +12 b: y = 2 3 x –15<br />

3-123. The width is 1.5 meters, and the outer dimensions are 8 m by 5 m.<br />

3-124. 80x + 0.5 = 100x, so x = 1 40<br />

of an hour or 1.5 minutes.<br />

3-125. 6 7<br />

3-126. a: (5x –1)(5x +1) b: 5x(x + 5)(x − 5)<br />

c: (x +9)(x –8) d: x(x –6)(x +3)<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 27

Lesson 4.1.1<br />

4-7. See graph at right. x = 0 and x = 4<br />

4-8. a: x = 5 or x = –3 b: m = 35<br />

c: no solution d: x = 7<br />

4-9. a: y = 0 b: x = 0<br />

4-10. a: Combining the equations leads to an impossible result,<br />

so there is no solution.<br />

c: There can be no intersection because the lines are parallel.<br />

When assuming there is an intersection, students will find that their work results in a<br />

false statement.<br />

4-11. This is a scalene triangle, because the sides have lengths 29 , 17 and 20 .<br />

4-12. a: 63 b: 0 c: n 3 –1 d: Neither; answers will vary.<br />

4-13. a: (x−2)(x+6)<br />

(x+4)(2x+3)<br />

2x+1<br />

x−5<br />

9m+27<br />

m+3<br />

= 9 d:<br />

n+3<br />

n–1<br />

4-14. a: 0-2 times<br />

b: 0-4 times<br />

c: 0-4 times<br />

d: 1-3 times if you consider parabolas that open up or down. 0-4 times if you consider<br />

rotated parabolas.<br />

28 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 4.1.2<br />

4-22. Graph y = (x − 3) 2 − 2 and y = x +1 and find the x-values of the points of intersection.<br />

Or, graph y = x 2 − 7x + 6 and find the x-intercepts. x = 1 or x = 6<br />

4-23. See graph at right. x = 3 or x = 6<br />

4-24. a: x = 15 b: x = 7 3<br />

or x = –5<br />

4-25. The lines intersect at the point (2, 6).<br />

Ted will solve the system algebraically by setting 18x – 30 = –22x + 50.<br />

4-26. a = 18.5, b = 5.5<br />

4-27. x = 13, x = 5 is extraneous<br />

4-28. x = 36 b: x = 20 2 or x ≈ 28.28<br />

4-29. See graph at right. x = 1 and x = 3; No.<br />

4-30. a: 1 2 (x − 2)3 +1 = 2x 2 − 6x − 3, x = 0 or x = 4<br />

b: x = 6 is also a solution.<br />

c: 1 2 (x − 2)3 +1 = 0 , x ≈ 0.74<br />

d: Domain and range of f(x): all real numbers, domain of g(x): all real numbers,<br />

range of g(x): y ≥ –7.5<br />

4-31. a: x = –3 b: x = 1 or x = 3 c: x = –8 or x = 13 d: x = 1.2<br />

4-32. a: y = 5 3 x – 4 b: m 2 = Fr2<br />

Gm 1<br />

c: m = 2E<br />

v 2 d: y = ± 10 − (x − 4)2 +1<br />

4-33. (a + b) 2 = a 2 + 2ab + b 2 , substitute numbers, etc.<br />

4-34. a: See graph at top right.<br />

b: See graph at bottom right.<br />

c: Graph (b) is similar to graph (a), but is rotated<br />

90º clockwise.<br />

d: (a) D: all real numbers, R: y ≥ 0; (b) D: x ≥ 0, R: all real numbers<br />

4-35. a: 21.00 b: 117.58<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 29

Lesson 4.1.3<br />

4-40. a: (–2, –11); The lines intersect at one point.<br />

b: infinite solutions; The equations are equivalent.<br />

c: (2, 45), and(–1, 3); The line and parabola intersect twice.<br />

d: (3, 6); The line is tangent to the parabola.<br />

4-41. a: y = 3 or y = –5 b: x = – 99 4<br />

c: y = 1 d: x = –13<br />

4-42. a: E t(n) = −2 + 3n ; R t(0) = −2, t(n +1) = t(n) + 3<br />

b: E t(n) = 6( 1 2 )n ; R t(0) = 6, t(n +1) = 1 2 t(n)<br />

c: t(n) = 10 – 7 d: t(n) = 5(1.2) n e: t(n) = 1620<br />

4-43. 19.79 feet<br />

4-44. a: m = – 6 5 , b = (0, –7) b: m = 2 3 , b = (0, –5) c: m = 2, b = (0, –12)<br />

4-45. a: not a function; D: –3 ≤ x ≤ 3; R: –3 ≤ y ≤ 3<br />

b: a function; D: –2 ≤ x ≤ 3; R: –2 ≤ y ≤ 2<br />

4-46. (–7, 11)<br />

Lesson 4.1.4<br />

4-51. 4c + 5p = 32, c + 8p = 35, cylinders weigh 3 oz. and prisms weigh 4 oz.<br />

4-52. Yes. No. Any value of x such that –3 ≤ x ≤ 2 is a solution.<br />

4-53. a: x = 4 b: x = 6 c: x = 6 d: x = 3 2<br />

4-54. a: (4, –6) b: (4, –6) c:<br />

, – 9 4 )<br />

4-55. a: b:<br />

4-56. B<br />

4-57. a: See graph at right. b: x ≈ 0.71<br />

30 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 4.2.1<br />

4-65. a: boundary point x = –4 b: boundary points x = 4, – 3 2<br />

4-66. a: –4 < x < 1 b: x ≤ –4 or x ≥ 1 c: –1 < x < 4<br />

d: x ≤ –1 or x ≥ 4 e: –1 < x < 4 f: x ≤ –1 or x ≥ 4<br />

4-67. a: y = –3x + 8 b: y = –x – 1 2<br />

4-68. a: No real solutions b: y = 7, y = 13 3<br />

is extraneous<br />

4-69. a:<br />

3x 2 +x−3<br />

2x 3 +9x 2 −5x<br />

b: 3x−5<br />

2x+3<br />

4-70. x = −6 + 4 6 or x = –6 – 4 6<br />

4 x−3<br />

m+5<br />

m+4<br />

4-71. a: x(b + a) b: x(1 + a) c:<br />

d: x–b<br />

4-72. See graph at right.<br />

a: Rectangle; perpendicular lines or slopes.<br />

b: (1, 4), (–3, –3), (–5, 1), (3, 0)<br />

4-78. a: y = 1 2 x – 2 b: y = 2x + 2<br />

4-73. a: –5 < x < 13 b: x ≥ 250 or x ≤ –70 c:<br />

2 3 ≤ x ≤ 2<br />

4-74. a: C = 800 + 60m b: C = 1200 + 40m c: 20 months d: 5 years<br />

4-75. a: input x, output x<br />

b: Replace x with c in first function machine resulting in c – 5 , then substitute this<br />

expression for x in the second function machine, yielding 6(c−5)+8<br />

= 3c −11 .<br />

Substitute this a third time in the final machine, giving (3c−11)+11<br />

= c .<br />

4-76. a:<br />

3x–14<br />

2x–1<br />

4-77. (1, 12) and (–5, 42)<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 31

Lesson 4.2.2<br />

4-83. x = –2, y = 3, z = –5; Solve the system to two equations with x and y, then substitute these<br />

values into the third equation to find z.<br />

4-84. a: x ≤ 4 b: x < –6 or x > 6<br />

4-85. red = 10 cm, blue = 14 cm<br />

–5 0 5 –6<br />

0 6<br />

4-86. The points on the line y = 2x – 2 are excluded from the solution region of y < 2x –2.<br />

4-87. a: y = 1 3 x – 4 b: y = 6 5 x – 1 5 c: y = (x + 1) 2 + 4 d: y = x 2 + 4x<br />

4-88. y = 0, x = 0<br />

4-89. 2.11 feet<br />

Lesson 4.2.3<br />

4-92. There is no solution, so the lines are parallel.<br />

4-93. See graph at right.<br />

a: A square, justifications will vary.<br />

b: (0, –3), (4, 1), (–4, 1), (0, 5)<br />

c: 32 square units.<br />

4-94. a: x < 13 b:<br />

5− 57 5+ 57<br />

≤ x ≤<br />

or −0.637 ≤ x ≤ 3.137<br />

13 –1 0 3<br />

4-95. a: no solution b: y ≈ 4.3 or 10.7<br />

4-96. (25, –3)<br />

a: x 2 + 3y = 16 and x 2 − 2y = 31<br />

b: The solutions to the new system are (5, –3) and (–5, –3).<br />

4-97. a: See graph at right; y = –2x +8<br />

b: 63.43º or 116.57º<br />

32 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 4.2.4<br />

4-99. a: y = 1 2 (x + 3)2 − 2 b: y = x +5 c: x = 1 or x = –5<br />

d: (1, 6) and (–5, 0) e: x < –5 and x > 1 f: x = –1 or x = –5<br />

g: x = –1 h: Answers will vary.<br />

4-100. y ≤ 3x + 3, y ≥ 0.5x − 2 , y ≤ −0.75x + 3<br />

4-101. a: x ≤ 1 or x ≥ 7 3 b: x < 3<br />

0 1 2 x 1 2 3 x<br />

4-102. a: y b: y c:<br />

4-103. 60º<br />

4-104. a: y > 3x –3 b: y < 3 c: y ≥ 3 2 x – 3 d: y ≥ x2 – 9<br />

4-105. a: w = 0 or w = –4 b: w = 0 or w = 2 5<br />

c: w = 0 or w = 6<br />

Lesson 5.1.1<br />

5-8. a: y = 2(x +3) b: Yes, y = x. See graph at right.<br />

5-9. a: 9 b: 4 c: x ≈ 1.89<br />

5-10. x = sin −1 (0.75) ≈ 48.59° ; to check: sin(48.59 ) ≈ 0.75<br />

5-11. x must equal y.<br />

5-12. a: x = 12 5 b: x = 5 2 c: x = 8 d: x = 80 3<br />

5-13. The area between an upward parabola with vertex (0, –5)<br />

and the downward parabola with vertex (1, 7). See graph at right.<br />

5-14. a and b: See graph at right.<br />

c: Possible equation: y = 10x – 5<br />

d: For this equation, approximately $495.<br />

5-15. ≈ 17.74 feet<br />

Weight (ounces)<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 33<br />

Cost (dollars)<br />

Lesson 5.1.2<br />

5-26. See graph at right.<br />

5-27. a: y = 1 3<br />

(x + 8) b: y = 2(x – 6) c: y = 2x – 6<br />

5-28. x ≈ 0.53<br />

5-29. a: x 2 – 5x –14 b: 6m 2 +11m – 7 c: x 2 – 6x + 9 d: 4y 2 – 9<br />

5-30. (x + 3) 2 + (y − 5) 2 = 9 . See graph at right.<br />

5-31. a:<br />

x−3<br />

x(x−4) b: 4<br />

c: 2 d: x–1<br />

5-32. a: f (x) ≈ 1.5(1.048) x<br />

b: ≈ $425.04<br />

5-33. See graph at right.<br />

For f(x), domain: –2≤ x ≤ 5, range: –3 ≤ y ≤ 3<br />

For f –1 (x), domain: –3 ≤ x ≤ 3, range: –2≤ y ≤ 5<br />

-4<br />

5-34. a: L(x) = x 2 −1, R(x) = 3(x + 2)<br />

b: 30<br />

c: Order does matter – show by substituting numbers; output is 224 if x = 3 for L(R(x)).<br />

5-35. a: The system has no solution.<br />

b: The graphs do not intersect, they are parallel lines.<br />

5-36. If she adds nothing else to the account and it just sits there making interest, she will have<br />

$440.13 on her eighteenth birthday.<br />

5-37. a: x 2 –10x – 56 b: 4m 2 + 8m – 5<br />

c: x 2 – 81 d: 9y 2 +12y + 4<br />

5-38. a: (2, 0), (–1, 0) b: (–5, 0), (–3, 0)<br />

5-39. x = 2.5<br />

34 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 5.1.3<br />

5-48. 121 b: 17<br />

5-49. a: 2x 3 + 2x 2 − 3x − 3 b: x 3 − x 2 + x + 3<br />

c: 2x 2 +12x +18 d: 4x 3 − 8x 2 − 3x + 9<br />

5-50. a: x = – 10 7 b: x = 1 3 or x = 1<br />

c: x = 115 d: x = 0 or x = 4<br />

5-51. a: y = ± x − 3 b:<br />

y = 4 ( x − 6)<br />

c: y = x2 +6<br />

5-52. (x − 2) 2 + y 2 = 20 ; circle, x 2 + y 2 = r 2 , center (2, 0)<br />

and radius ≈ 4.5; See graph at right.<br />

5-53. 70<br />

5-54. a: 3 b: y – 4 c: 1 3x d: x<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 35

Lesson 5.2.1<br />

5-60. Domain: x > 0; Range: −∞ < y < ∞ ; x-intercept: (1, 0) no y-intercept;<br />

asymptote at x = 0<br />

5-61. a: undefined b: x ≠ 7 c: g(3) = 11 d: f (g(3)) = − 1 2<br />

5-62. a: e(x) = (x −1) 2 − 5<br />

b: One machine undoes the other so e( f (−4)) = −4.<br />

c: They would be reflections of each other across the line y = x.<br />

5-63. See graph at right.<br />

a: Domain: all real numbers, range: y > –3<br />

b: No<br />

c: (0, –2), (1.585, 0)<br />

d: Sample: y +a = 2 x , where a ≤ 0.<br />

5-64. a: x ≈ 36.78 b: x ≈ 31.43<br />

5-65. a: B = 0.07(0.3x) or B = 0.021x<br />

b: S = 0.09(0.7x) or S = 0.063x<br />

c: 0.084x = 5000; $59,523.81<br />

5-66. a: (x + 7)(x – 7) b: 6x(x + 8)<br />

c: (x – 9)(x + 8) d: 2x(x + 2)(x – 2)<br />

5-67. The region between the two parabolas, see graph at right.<br />

-5<br />

36 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 5.2.2<br />

5-73. x = 2 y , no, yes, yes; They have the same graph or give the same table of (x, y) values,<br />

or one is just a rewritten equation of the other.<br />

5-74. a: x = log 5 (y) b: x = 7 y c: x = log 8 (y)<br />

d: K = log A (C) e: C = A K f: K = ( 1 2 ) N<br />

5-75. a: $1.90, 1.38, 0.96, 0.94, 0.90, 0.88<br />

b: decrease<br />

c: Smaller size. Note: Sketching a graph of rate with respect to<br />

bag size like the one at right may help here.<br />

Rate<br />

5-76. Answers will vary. Possible answers:<br />

5-77. x = –4<br />

a: Factor and use the Zero b: Take the square root (undo)<br />

Product Property (rewrite), (–8, 0) and (1, 0)<br />

c: Quadratic Formula d: Complete the square (rewrite)<br />

Bag size (pounds)<br />

5-78. a: x = 17 3 ≈ 29.44 b: x = 4 2 ≈ 5.66<br />

5-79. See graph at right. domain: x ≥ 0, range: y ≥ 0, x- and y-intercept: (0, 0),<br />

no asymptotes, half of parabola: y = πx 2<br />

5-80. a: A good sketch would be a parabola opening upwards with a locator<br />

point at (–6, –7).<br />

b: Shift the graph up 9 units.<br />

c: The graph is the same except the region below the x-axis is reflected across the axis so<br />

that the graph is entirely above the x-axis.<br />

e: y = x + 7 − 6<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 37

Lesson 5.2.3<br />

5-84. Possible answer: y = 2 x +15 5-85. y = log 7 x<br />

5-86. n ≈ 3.66 5-87. (x + 2) 2 + (y − 3) 2 = 4r 2<br />

5-88. $0.66<br />

5-89. See graphs at right.<br />

a: The second is just the first shifted up ten units.<br />

b: y = km x + b<br />

5-90. a: x = 10 or x = –8 b: x = 2 or x –4<br />

c: –2 < x < 4 d: x ≥ 3 or x ≤ –13<br />

5-91. a: x(x + 8) b: (xy + 9z)(xy – 9z)<br />

c: 2(x +8)(x –1) d: (3x + 1)(x – 4)<br />

5-92. a: 2 b:<br />

x+2 c: x−4<br />

(x−2)(x−1)<br />

4 x+16<br />

x(x+2)<br />

Lesson 5.2.4<br />

5-96. a: 12 because 12 .926628408 = 10 b: Answers will vary<br />

5-97. a: x = 25 b: x = 2 c: x = 343 d: x = 3 e: x = 3 f: x = 4<br />

5-98. Less than one; Answers will vary.<br />

5-99. x ≈ 17.973<br />

5-100. a: (2x + 1)(2x – 1) b: (2x +1) 2 c: (2y + 1)(y + 2) d: (3m + 1)(m – 2)<br />

5-101. a: –1 < x < 3 b: x ≤ 1 or x ≥ 2<br />

5-102. No; log 3 2 < 1and log 2 3 > 1<br />

5-103. a: a = y<br />

b x<br />

b: b is the x th root of y a , or b = x y a<br />

5-104. See graphs at right.<br />

38 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2<br />

Lesson 5.2.5<br />

5-112. f (g(x)) = g( f (x)) = x ; They are inverses.<br />

5-113. No. For f (x) = mx + b, f (a) + f (b) = ma + b + mb + b = m(a + b) + 2b and<br />

f (a + b) = m(a + b) + b .<br />

5-114. x ≈ 1.585<br />

5-115. a: t(n) is arithmetic, h(n) is geometric, q(n) is neither<br />

b: No, because h(n) is increasing much faster than the other two.<br />

c: h(1) = q(1) = 12 and t(2) = h(2) = 36 ; continuous graphs for t(n) and q(n) intersect but<br />

not for an integer n. h(n) is increasing much faster than q(n).<br />

5-116. s(n) = (50 + 7n) 2 − 6(50 − 7n) +17 , neither, it is quadratic and there is no common<br />

difference or multiplier.<br />

5-117. a: 1<br />

5-118. See graph at right.<br />

b: 10x+m<br />

5-119. (–3, 0, 5)<br />

5-120. m ≈ 2.19<br />

-5 5<br />

5-121. a and b: g( f (x)) = log x or f (g(x)) = log x ,<br />

see graphs at right.<br />

c: The log of an absolute value is very different<br />

from the absolute value of a log.<br />

d: See graph at right. Note that x = 0 is an asymptote<br />

5-122. 1 2<br />

no matter where X is placed.<br />

5-123. x ≈ 1.68<br />

5-124. a:<br />

6x−21<br />

(x−4)(x+1)<br />

5+6x<br />

2(x−5) c: 1<br />

x 2 −9<br />

5-125. a: b + a b: 3d + 2c 2 c: x – 1 d: xy<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 39

Lesson 6.1.1<br />

6-8. a: Their y- and z-coordinates are zero. b: Answers will vary.<br />

6-9. x = –2, y = 5<br />

6-10. a: 9 b: 4N – 3, arithmetic<br />

6-11. a: x ≈ 1.204 b: x ≈ 1.613 c: x = 6 d: x ≈ 2.004<br />

6-12. a:<br />

25 1 b: x<br />

y 2 c: 1<br />

x 2 y 2 d: b10<br />

6-13. a: x b:<br />

x 2 −3x+2<br />

6-14. a: 1 2<br />

b: –2<br />

c: The product of the slopes is –1, or they are negative reciprocals of each other.<br />

6-15. Heather is correct, because a 4% decrease does not “undo” a 4% increase.<br />

40 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 6.1.2<br />

6-21. a: (0, 10, 0), (0, 0, 4) b: (8, 0, 0), (0, 6, 0), (0, 0, 12)<br />

c: (0, 0, 4), (0, 0, –4), (2, 0, 0) d: (0, 0, 6)<br />

6-22. A line b: They do not intersect. c: They do not intersect.<br />

6-23. a: y = −2(x + 4) 2 + 2 b: y = 1<br />

x−2 c: y = −x3 + 3<br />

6-24. It is not the parent. The second equation does not have a vertical asymptote, and it has a<br />

maximum value, while y = 1 x<br />

does not.<br />

6-25. a: x = b 3 b: x = b<br />

5a<br />

c: x = b<br />

1+a<br />

6-26. a: No, input equals output only if x ≥ 0.<br />

b: The output is the absolute value of the input value.<br />

c: n + 2, n 2 − 4 , n<br />

d: Because x 2 = x .<br />

6-27. It is the log 5 (x) graph shifted 2 units to the right.<br />

See graph at right.<br />

6-28. a: 254,000 people/year b: 1,574,000 people/year c: 1960 to 2010<br />

6-29. a: –7 b: –102 c: –102 d: –132<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 41

Lesson 6.1.3<br />

6-35. See graph at right.<br />

6-36. Yes.<br />

6-37. Answers will vary.<br />

6-38. y ≤ −x + 4, y ≥ 1 3 x<br />

6-39. a: x+3<br />

2x−1 b: 1<br />

(x−3)<br />

• • • • • • • • • • • • • • • •<br />

• • • • • • • • • • • • • • • • •<br />

z<br />

6-40. a: Most solving strategies will yield x = 8 or x = 1.<br />

b: x = 1 does not check, so it is extraneous.<br />

6-41. a: x = –4 or x = 5 2<br />

b: x = –4, 2, or 3<br />

6-42. a: Neither b: Even<br />

6-43. x = 3, y = 1, z = 3<br />

Lesson 6.1.4<br />

6-51. (1, –2, 4)<br />

6-52. a: ≈ $140,809.30 b: ≈ 24.2 years c: ≈ $164,706.25<br />

6-53. x = 7<br />

6-54. a: They both equal 16, but this is a special case (for example, 5 3 ≠ 3 5 ).<br />

6-55. a: x = 6.5 b: x = –3.75 or x = 5<br />

6-56. a: y = 1 3 x + 5 b: y = 2x + 5 c: y = − 1 2 x + 15 2<br />

d: y = 2x<br />

6-57. a: y = −x 2 + 4x b: y = 5 ± x − 3<br />

6-58. a: See graph right.<br />

b: See graph far right.<br />

6-59. 384 feet<br />

42 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 6.1.5<br />

6-71. x = –1, y = 3, z = 5<br />

6-72. y = 3x 2 − 5x + 7<br />

6-73. a: x+3<br />

x−4 b: 1<br />

6-74. a: y + x 2 b: 2b + 4a2 c: 6x – 1 d: xy<br />

6-75. a: x = 12 y b: y x = 17 c: 2x = log 1.75 y d: 7 = log x 3y<br />

6-76. x = 14<br />

6-77. a: ≈ 0.0488 grams<br />

b: Roughly between 4600 and 6700 depending on how the base is rounded.<br />

c: Never<br />

6-78. a: See graph at right.<br />

b: x > −2; y = x + 2 and x ≤ −2; y = (x + 2) 3<br />

6-79. a: 2 4 b: 2 –3 c: 2 1/2 d: 2 2/3<br />

6-80. x = –1, y = 3, z = 6<br />

6-81. y = 2x 2 − 3x + 5<br />

6-82. a: 24 = b a b: 7 = (2y) 3x c: 5x = log 2 3y d: 6 = log 2q 4 p<br />

6-83. a:<br />

x−4<br />

6-84. Yes, Hannah is correct; 4(x − 3) 2 − 29 = 4x 2 − 24x + 7 and 4(x − 3) 2 − 2 = 4x 2 − 24 + 34<br />

6-85. a: y = 2(x − 2) 2 −1, vertex (2, –1), axis of symmetry x = 2<br />

b: y = 5(x −1) 2 −12 , vertex (1, –12), axis of symmetry x = 1<br />

6-86. See graph at right. y = log(x − 6) + 3<br />

6-87. a: 2a 2 − 4 b: 18a 2 − 4 c: 2a 2 + 4ab + 2b 2 − 4<br />

d: 2x 2 + 28x + 94 e: 50x 2 + 60x +14 f: 10x 2 −17<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 43

Lesson 6.2.1<br />

6-95. y = 3 x<br />

6-96. In 2 = 1.04 x the variable is the exponent, but in 56 = x 8 the exponent is known so<br />

you can take the 8 th root.<br />

6-97. x > 100, because 10 2 = 100<br />

6-98. Answers will vary.<br />

6-99. a: 1 8 b: 1 x<br />

c: m ≈ 1.586 d: n ≈ 2.587<br />

e: Answers will vary. x = b 1/a<br />

6-100. 2 1/2 = 2 and 2 −1 = 1 2<br />

6-101. a: –3 < x < 3 b: –2 < x < 1 c: x ≤ –2 or x ≥ 1<br />

6-102. a: Yes<br />

b: See graph at right, (it is not a function).<br />

c: Not necessarily.<br />

d: Functions that have inverse functions have no<br />

repeated outputs; a horizontal line can intersect<br />

the graph in no more than one place.<br />

e: Yes; for example, a sleeping parabola is not a function,<br />

but its inverse is a function.<br />

6-103. a: x = –3, y = 5, z = 10<br />

b: There are infinitely many solutions.<br />

c: The planes intersect in a line.<br />

44 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 6.2.2<br />

6-113. a: 5.717 b: 11.228<br />

6-114. a: x2<br />

x−1<br />

b: b+a<br />

a−a 2 b<br />

6-115. log 5 7<br />

log5 2<br />

6-116. It is the log 3 (x) graph shifted 4 units to the left. See graph at right.<br />

6-117. 16.5 months; 99.2 months<br />

6-118. They are correct. Vertex: (2.5, –23.75), line of symmetry: x = 2.5.<br />

6-119. a: f (x) = 4(x −1.5) 2 − 3, vertex (1.5, –3), line of symmetry x = 1.5<br />

b: g(x) = 2(x + 3.5) 2 − 20.5 , vertex (–3.5, –20.5), line of symmetry x = –3.5<br />

6-120. a: Consider only x ≥ –2 or x ≤ –2.<br />

b: Depending on the original domain restriction, y = x+7<br />

− 2 or y = − x+7<br />

− 2 .<br />

c: x ≥ –7 and y ≥ –2 or x ≥ –7 and y ≤ –2.<br />

6-121. a:<br />

x 2 −3x−4<br />

6-122. a: 20, 100, 500 b: n = 7<br />

c: No, because there are no terms between the 6 th term (62,500) and the 7 th term<br />

(312,500).<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 45

Lesson 6.2.3<br />

6-127. a: y = 40(1.5) x<br />

b: When x = –9, or 9 days before the last day of October (October 22).<br />

6-128. Possible answer: 4 (x+1) = 6<br />

6-129. Answers will vary.<br />

6-130. The graph should show a decreasing exponential function which will have an asymptote<br />

at room temperature.<br />

6-131. y = x 2 − 6x + 8<br />

6-132. a: x ≥ 1 2 and y ≥ 3 b: g(x) = (x−3)2 +1<br />

c: x ≥ 3 and y ≥ 1 2<br />

d: x e: x (They are the same, because f and g are inverses.)<br />

6-133. a: x ≈ 6.24 b: x = 5<br />

6-134. a: (x −1) 2 + y 2 = 9 b: (x + 3) 2 + (y − 4) 2 = 4<br />

6-135. a: x + 5 b: a + 5 c: x – y d: x2 +1<br />

x 2 −1<br />

6-136. a: p −1 (x) = 3 ( x 3 − 6) b: k −1 (x) = 3 ( x−6<br />

3 )<br />

c: h −1 (x) = x+1<br />

d: j−1 (x) = 3x−2<br />

= − 2 x + 3<br />

46 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 6.2.4<br />

6-138. a: Decreasing by 20% means you multiply by 0.8 each time, and the presence of a<br />

multiplier implies exponential.<br />

b: y = 23500(0.8 x ) c: $9625.60<br />

d: ≈ 6.12 years e: $42,926.44<br />

6-139. a: x = 1 2<br />

b: x > 0 c: x = 1023<br />

6-140. a: x = 2.236 b: x = 4.230 c: x = 0.316<br />

d: x = 2.021 e: x = 3.673<br />

6-141. a: 16 b: 12 c: 12 4 = 20736 d: 54<br />

e: No, they are not inverses (if they were, then the answers to parts (c) and (d) would<br />

have to be 2).<br />

6-143. c(x) = x 2 − 5<br />

6-144. x = 17<br />

6-145. a: 2(x+1)<br />

x+3 b: 3x2 −5x−3<br />

(2x+1) 2<br />

6-146. a: 30° b: 22.6°<br />

6-147. y ≤ −<br />

4 3 x + 3, y ≥ − 4 3 x − 3, x ≤ 3, x ≥ −3<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 47

Lesson 7.1.1<br />

7-3. a: The shape would be stretched vertically. In other words, there would be a larger<br />

distance between the lowest and highest points of each cycle.<br />

b: Each cycle would be longer horizontally. Fewer cycles would fit on a page of the<br />

same length.<br />

7-4. See graph at right. domain: x ≠ 3, range: y ≠ 0,<br />

asymptotes at x = 3 and y = 0 f −1 (x) = 2 x + 3<br />

7-5. a: ≈ 27.04 feet b: ≈ 176.88 cm c: ≈ 28.94 meters<br />

7-6. 30º - 60º: 1 2 , 3<br />

2 ; 45º - 45º: 1 , 1 or 2<br />

2 2 2 , 2<br />

7-7. y = 6x − x 2<br />

7-8. x = 5, x ≈ 19.69 does not check.<br />

7-9. a: y = ( x + 5 2 ) 2 +<br />

4 3 , vertex ( − 5 2 , 4<br />

3 ) b: (0, 7)<br />

c: (–5, 7); See graph at right.<br />

7-10. No x-intercepts, y-intercept: (0, 88)<br />

7-11. (x −1) 2 + y 2 = 30 ; See graph at right.<br />

center: (1, 0), intercepts: (± 30 +1, 0) and (0, ± 29)<br />

48 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 7.1.2 (Day 1)<br />

7-15. a: 30 – 60: hypotenuse: 2, leg: 3 ; isosceles: hypotenuse: 2 , leg: 1<br />

b: See diagram at right.<br />

7-16. ≈ 17.46°<br />

60°<br />

60° 60°<br />

7-17. x = 2 , − 5 2 , y = –10<br />

7-18. a: 0 b: 3 c: 4 d: 64<br />

7-19. y : 3; 4; 5; undefined; 7; 8<br />

a: See graph at right. It is linear. The data does not all<br />

connect because f (1) is undefined.<br />

b: y = x + 5, f (0.9) = 5.9, f (1.1) = 6.1, no asymptote.<br />

c: The complete graph is the line y = x +5 with a hole at (1, 6).<br />

7-20. a: An exponential function b: y = 60000 +12000(0.93) t<br />

7-21. If he drives down the center of the road, the height of the tunnel at the edge of the house<br />

is only approximately 23.56 feet. The house will not fit.<br />

7-22. a: x ≈ 33.752 b: x ≈ 9.663<br />

7-23. x = 18, y = 13, z = 9<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 49

Lesson 7.1.2 (Day 2)<br />

7-24. −∞ < θ < ∞<br />

7-25. ≈ 40.5º or 139.5º<br />

7-26. She should have subtracted 3⋅16 = 48 to<br />

account for the factor of three. The vertex is (4, 7).<br />

7-27.<br />

7-28. See graph above right.<br />

7-29. a: b: c: d:<br />

7-30. x = 3 2 or − 1 4 , y = –3<br />

W -1 (x)<br />

7-31. a: See graph at right.<br />

b: No; when the points are interchanged, the<br />

input x = 0 has two outputs.<br />

7-32. R + B + G = 40, R = B + 5, R = 2G ; 18 red, 13 blue and 9 green<br />

50 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 7.1.3<br />

7-36. See graph at right.<br />

7-37. (a): Above ground just past the highest point.<br />

(b): Just below ground.<br />

(c): Back to the starting point.<br />

See diagram at right.<br />

7-38. ≈ 82.4 feet<br />

(a)<br />

-1<br />

(c) (c) (c)<br />

(c)<br />

90 270 450 630<br />

(b)<br />

7-39. a: log 6 = log 3+ log 2 ≈ 0.7781 b: log15 = log 3+ log 5 ≈ 1.1761<br />

c: log 9 = 2 log 3 ≈ 0.9542 d: log 50 = 2 log 5 + log 2 ≈ 1.6990<br />

7-40. x = −3± 6<br />

, y = 1<br />

7-41. y = 3(x +1) 2 − 2 ; See graph at right.<br />

7-42. x ≤ –5<br />

7-43. No real solution.<br />

7-44. C + W + P = 40 , W = C − 5 , C = 2P ; 18 from California, 13 from Washington, and<br />

9 from Pennsylvania<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 51

Lesson 7.1.4 (Day 1)<br />

7-53.<br />

( 4 , 1 4 )<br />

or ( −<br />

4 , 1 4 )<br />

7-54. P: (cos 50º , sin 50º ) or (~0.643, ~0.766); Q: (cos110º , sin110º ) or (~ –0.342, ~0.940)<br />

( 2 )<br />

7-55. a: 300° b: 1 2 , 3<br />

2 c: 1<br />

, − 3<br />

7-56. a: 30° b: 60 ° c: 67° d: 23 °<br />

7-57. x = 11<br />

7-58. a: downward parabola, vertex (2, 3), see graph above right.<br />

b: cubic, point of inflection (1, 3), see graph below right.<br />

7-59. Solving graphically: x ≈ –3.2<br />

7-60. a: y = 25d + 0.50m and y = 0.03(2) m−1<br />

b: R vs. T: $55 vs. $15.36, $60 vs. $15,728.64, $100 vs. ~ $1.901×10 28<br />

7-61. All of these problems could be solved using the same system of equations.<br />

52 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 7.1.4 (Day 2)<br />

7-62. 58º, 122º, 238º, or 302º<br />

7-63. a: An angle in the 4 th quadrant. b: 270 ° or –90°<br />

c: An angle in the 3 rd quadrant. d: Approximately 160°<br />

e: No, an angle with sine equal to 0.9 has cosine equal to ±0.4359, so the point (0.8, 0.9)<br />

is not on the unit circle.<br />

7-64. a: (0.3420, 0.9397) b: (cos70° , sin70 ° )<br />

c: (cos 70°) 2 + (sin 70°) 2 = 0.1170 + 0.8830 = 1<br />

7-65. Graph 2 is sine, while graph 1 is cosine. Answers will vary.<br />

7-66. a: All yes.<br />

c: x = (−180° + 360°n) for all integers n<br />

7-67. y-intercept: (0, –17), x-intercepts: (−2 + 21, 0) and (−2 − 21, 0)<br />

7-68. a: x = –4 b: x =<br />

7-69. 7.07 '<br />

5± 57<br />

c: no solution<br />

d: If a =<br />

x+2 3 , then a + 5 ≠ a. Or, solving yields x = –2, but when substituted, –2 gives a<br />

zero denominator.<br />

7-70. Tess is correct: A sequence has no more than one output for each input. A sequence is a<br />

function with domain limited to positive integers.<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 53

Lesson 7.1.5<br />

7-77. a: Same; π 3<br />

and 60° are measures of the same angle.<br />

b: 45º, 135º, 405º, etc.<br />

7-78. a:<br />

2 ≈ 0.707 b: 3<br />

2 ≈ 0.866<br />

7-79. a: Set each factor equal to zero to get x = 0, 1 2<br />

, or 3.<br />

b: Factor to get x(x – 1)(2x + 3) = 0. x = 0, 1, – 3 2<br />

7-80. a: x ≈ 2.657 b: x ≈ 0.936 c: x ≈ –0.711<br />

7-81. He should have subtracted 2 ⋅ 9 4 = 9 2 to account for the factor of 2. The vertex is 3<br />

, − 5 2 )<br />

7-82. a: y = 3(x − 3) 2 −1, vertex: (3, –1), axis of symmetry x = 3<br />

b: y = 3( x − 2 3 ) 2 − 37 3 , vertex: 2<br />

, − 37 3 ) , axis of symmetry: x = 2 3<br />

7-83. a: x = 2.5121 b: x = 5 57y<br />

7-84. See graph at right.<br />

a: No<br />

b: –10 ≤ x ≤ 10, –10 ≤ y ≤ 10<br />

c: 200π<br />

≈ 209.44 sq. units<br />

7-85. f −1 (x) = (x −1) 2 + 3 for x ≥ 1; See graph at right.<br />

54 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 7.1.6<br />

7-90. a: –0.76 b: – 3<br />

7-91.<br />

π<br />

, 5π 6<br />

7-92.<br />

, π 3 , π 2 , 2π 3 , 3π 4 , 5π 6 , π, 7π 6 , 5π 4 , 4π 3 , 3π 2 , 5π 3 , 7π 4 , 11π<br />

6 , 2π<br />

7-93. See diagram at right.<br />

a: A little less than 360° (almost 344° ).<br />

b: sin6 ≈ –0.3<br />

7-94. a: 1 b: 1 2<br />

c: undefined d: 9<br />

7-95. ~ 4.73% annual interest<br />

7-96.<br />

sin A<br />

cos A = 3<br />

91<br />

≈ −0.3145<br />

7-97. a: f −1 (x) = x3 +1<br />

b: g −1 (x) = 7 x<br />

7-98. a: x = 4 or x = –2 b: x ≈ 2.81<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 55

Lesson 7.1.7<br />

7-104. 420°<br />

a: π 3 ± 2π n<br />

2 , 1 2 , 3<br />

7-105. a: 0 b: 0 c: –1<br />

d: 0.5 e: 0 f: undefined<br />

0 1 x<br />

7-106. Some may set up a proportion, others may use<br />

180<br />

7-107. a: 210° b: 300 ° c: π 4 radians<br />

d: 5π 9 radians e: 9π 2<br />

radians f: 630 °<br />

7-108. See graph at right.<br />

7-109. f (x) = 2(x − 4) 2 + 2<br />

f -1 (x)<br />

7-110. a: – 5<br />

13 b: 5<br />

7-111. a: a + b b: 2c c: a + 2b d: 3a + c<br />

7-112. a: See graph at right.<br />

b: Yes, the pizza will never get below room temperature.<br />

temperature<br />

time<br />

56 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 7.2.1<br />

7-116. a: See graph at right.<br />

b: y = 1+ sin x<br />

c: y : (0, 1), x : ( −<br />

2 π , 0 3π<br />

), ( 2<br />

, 0<br />

7π<br />

, 0), ...<br />

d: Yes, there are infinitely many, at intervals of 2π .<br />

7-117. a: π b: y = sin(x + π )<br />

7-118. a: This may go up and down, but the cycles are probably of differing length.<br />

b: This may or may not be periodic.<br />

c: This is probably approximately periodic.<br />

7-119. y = 100 sin ( x +<br />

π ) − 50 or y = 100 cos x − 50<br />

7-120. Only one needs to be a parent, since y = sin(x + 90°) is the same as y = cos x.<br />

7-121. a: y = 3⋅6 x b: y = −2(0.5) x<br />

7-122. a: x = ± 3 5 = ± 15<br />

b: x = 4, –1 c: x = 4<br />

7-123. a: – 3 b:<br />

7-124. a = −<br />

3125 3 = −0.00096 , possible equation: y = −<br />

3125 (x −125)2 +15<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 57

Lesson 7.2.2<br />

7-129. a: y = sin x − π 4<br />

( ) + 2<br />

( ) + 0.5<br />

( ) + 2 or y = sin ( x + 5π 6 ) + 2<br />

( ) −1 or y = −3sin ( x +<br />

π ) −1<br />

b: y = 1.5 sin x + π 2<br />

c: y = − sin x − π 6<br />

d: y = 3sin x − 2π 3<br />

7-130. 360° is the period of y = cosθ , so shifting it 360° left lines up the cycles perfectly.<br />

7-131. Graphing form: y = 2(x −1) 2 + 3 ; vertex (1, 3);<br />

7-132. a: x = (0, 0),<br />

5±3 3<br />

, 0) and y = (0, 0)<br />

7-133. 17.67 years<br />

7-134. a: y = −2 ( x + 1 4 ) 2 + 105<br />

8 , x = all real numbers, y = −∞ < y < 25 8<br />

; Yes it is a function.<br />

b: y = −3(x +1) 2 +15 , domain: all real numbers, range: −∞ < y < 15 ; Yes it is a function.<br />

7-135. 64.16 ° , unsafe<br />

7-136. a: 5,000,000 bytes b: ≈ 12.3 minutes<br />

c: According to the equation, technically never, but for all practical purposes, after<br />

23 minutes.<br />

7-137. See graph at right.<br />

a: The vertex of the graph is at (6, –4) with<br />

two rays emanating at slopes of ±1.<br />

b: See graph at right. Flip all parts of the graph<br />

that are below the x-axis above the x-axis.<br />

58 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 7.2.3<br />

7-144. a: Amplitude 3, period 4π<br />

c: The differences are the period and<br />

amplitude, and therefore some of the<br />

x-intercepts. They have the same basic shape.<br />

7-145. 1, 2π<br />

2π<br />

= 1 or 2π (1) = 2π<br />

7-146. Colleen’s calculator was in radian mode, while Jolleen’s calculator was in degree mode.<br />

Colleen’s calculation is wrong.<br />

7-147. y = sin 2(x −1) is correct. To shift the graph one unit to the right, subtract 1 from x<br />

before multiplying by anything.<br />

7-148. They are both wrong. The equation needs to be set equal to zero before the Zero Product<br />

Property can be applied. 2x 2 + 5x − 3 = 4 is equivalent to (2x + 7)(x −1) = 0 .<br />

x = 1 or x = − 7 2<br />

7-149. a: 3 b: 1.5 c: 2 d: 12<br />

7-150. a: y = 20 ( 1 2 ) x + 5 b: w = 5.078<br />

7-151. a: Answers vary, if g(x) is linear, tangent lines only.<br />

b: Any line y = b such that b < –8.<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 59

Lesson 7.2.4<br />

7-158. a: Yes b: y = cos ( x +<br />

π ) c: y = –sin x<br />

7-159. 6 cycles, period: π 3<br />

7-160. Answers will vary.<br />

7-161. a: 180º b: 540º c: π 6 radians<br />

d: 45º e: 5π 4<br />

radians f: 270º<br />

7-162. a: − 2<br />

b: 3 c: – 1 2 d: 2<br />

e: 1 f: − 1 3<br />

g: π 4 or 5π 4 h: 3π 4 or 7π 4<br />

7-163. ( –1, 1 2 , 2 )<br />

7-164. a: x = 0, x = – 1 2 , or x = 5 3<br />

b: x = 6 or x = –1<br />

7-165. a, b, and c: Answers will vary.<br />

7-166. a: About $564,240 b: In 2025 c: About $36,585<br />

60 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 8.1.1 (Day 1)<br />

8-8. See graphs and tables below. Parent functions:<br />

a: y = x 3 b: y = x 4 c: y = x 3<br />

x y<br />

–2 –9<br />

–1 0<br />

0 1<br />

1 0<br />

2 3<br />

–2 9<br />

2 9<br />

–2 0<br />

–1 3<br />

0 0<br />

1 –3<br />

2 0<br />

8-9. Functions in parts (a), (b), and (e) are polynomial functions; explanations vary.<br />

8-10. Graphs will vary.<br />

a: 0, 1, or ∞ b: 0. 1, or 2 c: 0, 1, 2, 3<br />

d: 0, 1, 2, 3, or 4 (1 and 3 require the parabola to be tangent to the circle.)<br />

8-11. (–2, –1) and (3, 4)<br />

8-12. a: adds 2; multiplies by 3; ; subtracts 1<br />

b: f −1 (x) = ( x−3<br />

2 )2 +1, g −1 (x) = 3(x + 2) −1<br />

8-13. The second graph is shifted up 5 from the first.<br />

8-14. a: b: c:<br />

8-15. a: 4n– 27 b: At least 2507 times.<br />

8-16. a: 60º, 300º b: 135º, 315º c: 60º, 120º d: 150º, 210º<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 61

Lesson 8.1.1 (Day 2)<br />

8-17. The functions in parts (a), (b), (d), (e), (h), (i), and (j) are polynomial functions.<br />

8-18. They are not equivalent. Explanations vary. Students may substitute numbers to check.<br />

Also, the second equation can be written y = – x + 12, which is a line, not a circle.<br />

8-19. a: x = 2 or x = 4 b: x = 3 c: x = –2, x = 0, or x = 2<br />

8-20. See graph at right.<br />

a: 2 b: x = 7, – 7<br />

8-21. x = –1± 6<br />

a: 2 b: At x ≈ 1.45 and x ≈ –3.45<br />

8-22. See graph at right.<br />

8-23. x = –1 or 5<br />

8-24. a: y = ( 3 x ) – 4 b: y = 3 (x–7)<br />

8-25. y: –21.2' ; 0'; 21.2'; 30'; 21.2'; 0'; …; –30'<br />

a: Repeat the pattern for several cycles.<br />

b: 30'<br />

c: y = 30 sin x<br />

62 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 8.1.2<br />

8-36. At (−3 ± 5, 0) .<br />

8-37. At (74, 0), a double root, and at (–29, 0).<br />

8-38. Possible Answers: a: y = x 2 + x – 6 b: y = 2x 2 + 5x – 3<br />

8-39. a: 2 b: 5 c: 3 d: 6<br />

8-40. Lines, parabolas (vertically oriented), and cubics are polynomial functions because they<br />

can be written in the form y = ax n . Exponentials are not polynomial functions because<br />

“x” is the exponent. Circles are not functions.<br />

8-41. a: y<br />

8-42. a: (x − 2) 2 + (y − 6) 2 = 4 b: (x − 3) 2 + (y − 9) 2 = 9<br />

8-43. See graph at right.<br />

8-44. a: 30º, 150º b: 60º, 240º<br />

c: 30º, 330º d: 225º, 315º<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 63

Lesson 8.1.3<br />

8-54. Stretch factor is –2. f (x) = −2(x + 2) 2 (x −1)<br />

8-55. a: degree 4, a 4 = 6 , a 3 = –3 , a 2 = 5 , a 1 = 1, a 0 = 8<br />

b: degree 3, a 3 = −5 , a 2 = 10 , a 1 = 0 , a 0 = 8 ,<br />

c: degree 2, a 2 = –1, a 1 = 1, a 0 = 0<br />

d: degree 3, a 3 = 1, a 2 = –8 , a 1 = 15 , a 0 = 0<br />

e: degree 1, a 1 = 1<br />

f: degree 0, a 0 = 10<br />

8-56. Possible equation: p(x) = 2.5(x + 4)(x −1)(x − 3)<br />

8-57. a: y = 4x 2 + 5x − 6 b: y = x 2 − 5<br />

8-58. There is no real solution, because a radical cannot be equal to a negative value.<br />

8-59. a: C: (3, 7), r: 5 b: C: (0, –5), r: 4<br />

c: x = 4 d: x = 7<br />

8-60. a: x = log17<br />

log 2<br />

b: x = 242 c: x = 4 d: x = 7<br />

8-61. a: –3 < x < 2 b: x ≤ –1 or x ≥ 7 3<br />

8-62. y = 2 + 4sinx<br />

64 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 8.2.1<br />

8-70. a: –18 – 5i b: 1± 2i c: 5 + i 6<br />

8-71. i 3 = i 2 i = −1i = −i ; 1<br />

8-72. a: –21 b: –10 + 7i c: –22 + i<br />

8-73. Yes, substitute it into the equation to check.<br />

8-74. x = –8<br />

8-75. Yes; both are equivalent to x 2 –10x + 25 .<br />

8-76. a: 7i b: 2i or i 2 c: –16 d: –27i<br />

8-77. a: x+3<br />

2 b: x − 2 + 3<br />

8-78. a: x ≈ 2.24 b: x ≈ ± 2.25<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 65

Lesson 8.2.2<br />

8-87. Possible Functions:<br />

a: f (x) = x 2 + 6x +10 b: g(x) = x 2 −10x + 22<br />

c: h(x) = x 3 + 2x 2 − 7x −14 d: p(x) = x 3 + 2x 2 −14x − 40<br />

8-88. a: b 2 − 4ac = −7 , complex b: b 2 − 4ac = 49 , real<br />

8-89. See graph at right. Area = 25 sq. units<br />

8-90. a: Repeat 1, i, –1, –i, etc. b: 1, i, –i, 1<br />

c: 1 d: i, –1, –i<br />

e: 1, i, –1, –i<br />

8-91. a: 1 b: i c: –1<br />

8-92. If n is a multiple of 4, the value is 1; if it is 1 more than a multiple of 4, the value is i; if it<br />

is 2 more than a multiple of 4, the value is –1; if it 3 more than a multiple of 4, the value<br />

is –i.<br />

8-93. a: x =<br />

log 17<br />

log 3<br />

x = 17<br />

8-94. a: 2 b: 4 c: 5 d: 3 e: 1<br />

8-95. a: Standard form for y-intercept at (0, 400) and graphing form for vertex at (0.5, 404).<br />

b: 400 ft; 404 ft<br />

8-96. a: y = log x b: x = 2 c: y = log 2 (x − 2) is one possibility.<br />

66 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 8.2.3<br />

8-104. a: three real linear factors (one repeated), therefore two real (one single, one double) and<br />

zero complex (non-real) roots<br />

b: one linear and one quadratic factor, therefore one real and two complex (non-real)<br />

roots<br />

c: four linear factors, therefore four real and zero complex (non-real) roots<br />

d: two linear and one quadratic factor, therefore two real and two complex (non-real)<br />

8-105. a: b: c: d:<br />

8-106. a: (3, 0), (0, 0), and (–3, 0) b: See graph at right.<br />

8-107. See graphs below.<br />

a: x-intercepts ( − 5 2 , 0 ), (0, 0) , and<br />

, 0), y-intercept (0, 0)<br />

b: x-intercepts (−3, 0) and<br />

a: b:<br />

( ) (double root), y-intercept (0, 675)<br />

8-108. See graph at far right.<br />

8-109. a: Platform is 11.27 meters off the ground. h = −4.9(t − 5) 2 +133.77 ;<br />

Therefore, the maximum height is 133.77 meters. Time when h = 0 is 10.22 sec.<br />

b: h ≈ −4.9(t −10.22)(t + 0.22) ; Factored form reveals the intercepts, or how long it took<br />

the firework to reach the ground.)<br />

8-110. b ≥ 20 or b ≤ –20<br />

8-111. a: (i − 3) 2 = i 2 − 6i + 9 = −1− 6i + 9 = 8 − 6i<br />

b: (2i −1)(3i +1) = 6i 2 − 3i + 2i −1 = −6 − i −1 = −7 − i<br />

c: (3− 2i)(2i + 3) = 6i − 4i 2 − 6i + 9 = 4 + 9 = 13<br />

8-112. ( ±6, 1 2 )<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 67

Lesson 8.3.1<br />

8-120. a: –7 c: (x + 7) d: (x 2 − 2x − 2) f: −7, 1± 3<br />

8-122. Part (c), because (–2)(3)(–5) = 30 and (x)(x)(x) = x 3 not 2x 3 .<br />

8-123. Part (b), because 5 is a factor of the last term, but 2 and 3 are not.<br />

8-124. (x − 5)(x 2 − 4x −1); zeros: 5, 2 ± 5<br />

8-125. a: (x − 2)(5x + 3) b: −<br />

5 3 , 2 c: Explanations will vary.<br />

d: 3 and 2 are factors of 6, while 5 is a factor of the lead coefficient.<br />

8-126. a: See the combination histogram boxplot at right.<br />

The five number summary (for the box plot) is<br />

0, 2.75, 8, 15.7, 36.5.<br />

b: The distribution has a right skew and an outlier at<br />

36.5 pounds so the center is best described by the<br />

median of 8.0 pounds and the spread by the IQR<br />

of 12.95 pounds.<br />

c: The median is better in this case because it is not<br />

affected by skewing and outliers.<br />

d: The IQR is better in this case because it is less affected by skewing and outliers than<br />

the standard deviation.<br />

e: If you remove the outlier from the data the mean drops to 8.7 pounds which is below<br />

the profitable minimum. You could suggest running the test a few more weeks<br />

because perhaps as people get used to the composting program they will participate<br />

even more.<br />

0 6 12 18 24 32 36 42<br />

8-127. a: b:<br />

8-128. a: See graph below.<br />

b: Yes, it is a solution to the equation.<br />

68 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 8.3.2 (Day 1)<br />

8-138. a: It shows that (x – 3) is a double factor and 3 is a double root.<br />

b: p(x) = (x − 3) 2 (x 2 + 2x −1) ; x = 3, −1± 2<br />

8-139. a: x 2 − 6x + 25 = 0 b: x 2 − 6x + 25 = 0 c: Answers will vary.<br />

8-140. a: 3+2i<br />

−4+7i ⋅ −4−7i<br />

−4−7i = 2−29i<br />

65<br />

b: 2<br />

65 − 29<br />

65 i<br />

8-141. a: 12 5 − 1 5 i b: − 3<br />

13 + 11<br />

13 i<br />

8-142. See graph at right; x + 3 −1; x ≥ −3, y ≥ −1<br />

8-143. a: See graph below left. −1, 1± 3 i<br />

b: See graph below right. 2, −1± 3 i<br />

8-144. (3, 4, –1)<br />

8-145. x = 1 2<br />

8-146. a: See graph below left, locator( −<br />

2 π , 0 ) , period = 2π, amplitude: 3<br />

b: See graph below right, locator (0, 0), period:<br />

2 π , amplitude: 2, inverted<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 69

Lesson 8.3.2 (Day 2)<br />

8-147. p(x) = x 3 + 5x 2 + 33x + 29<br />

8-148. a: p(2) = 0 b: (x – 2) c: (x 2 − 4x −1) d: 2, 2 ± 5<br />

8-149. a:<br />

17 8 + 15<br />

17<br />

i b: 2 + 5i<br />

8-150. a: Regular: (361, 367, 369 373, 380 grams); Diet (349, 354, 356.5, 361, 366 grams)<br />

b: See histograms at right.<br />

Regular<br />

c: Regular: The mean is 369.6 grams, which falls at the middle<br />

of the distribution on the histogram. The shape is singlepeaked<br />

and symmetric, so the mean should be a good<br />

measure of the center. There are no outliers, so the standard<br />

deviation of 4.34 grams could be used to describe spread.<br />

Diet: The mean is 357.5 grams; this mean also falls at the<br />

center of the data on the histogram. The data is doublepeaked<br />

but still fairly symmetric so the mean could be used<br />

to represent the center. There are no outliers so the standard<br />

deviation of 5.12 grams could be used to describe spread.<br />

d: The regular cola cans are noticeably heavier (or had more mass) than the diet cans.<br />

The lightest regular can is at the third quartile of the diet sample and the median of<br />

the regular cans is heavier than the most massive diet can. The spread of each<br />

distribution is similar and they are both reasonably symmetric but the diet cans have a<br />

double peaked distribution.<br />

e: Answers will vary.<br />

348 360 372 384<br />

Diet<br />

8-151. See graph at right. a: 4 b: (±4, 3) and (±3, −4)<br />

8-152. a: x = 4 ( 1 is extraneous) b: x = 1 4<br />

8-153. a: b:<br />

c: d:<br />

8-154. a: x = 2, (x – 2) b: x = 2, −3 ± 2i ; (x − 2) ( x − (−3+ 2i) )( x − (−3− 2i) )<br />

8-155. a: x = 2π 3 , 4π 3 b: x = π 6 , 7π 6 c: x = 0, π d: x = π 4 , 7π 4<br />

70 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 8.3.2 (Day 3)<br />

8-156. a: − 1 5 − 5 7 i b: 1 – 2i<br />

8-157. At 6 years, it will be worth $23,803.11. At 7 years it will be worth $25,707.36.<br />

8-158. a: x = 5 9<br />

b: x = 3 c: x = 48 d: x ≈ 1.46<br />

8-159. Students should show the substitution of the coordinates of the point into both equations<br />

to verify.<br />

8-160. x = 2 or x ≈ 1.1187<br />

8-161. a: x ≈ 781.36 b: x = 6 c: x = 1, 1 5<br />

d: x = 0, 1, 2<br />

8-162. When you find the complement of the angle, the x and y values reverse.<br />

8-163. a: −7 ⋅ −7 = i 7 ⋅i 7 = i 2 49 = −7<br />

b: She multiplied −7 ⋅ −7 to get 49 = 7 .<br />

c: −7 is undefined in relation to real numbers, and is only defined as the imaginary<br />

number 7i , so it must be written in its imaginary form before operations such as<br />

addition or multiplication can be performed.<br />

d: a and b must be non-negative real numbers.<br />

8-164. a: π 3<br />

5π<br />

12 c: 7π 6 d: 5π 4<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 71

Lesson 8.3.3<br />

8-169. (0, 0), (3, 0), and (−0.5, 0)<br />

8-170. See graph at right.<br />

8-171. a: (x + 10)(x − 10) b: x −<br />

3+ 37<br />

3− 37<br />

( x −<br />

2 )<br />

c: (x + 2i)(x − 2i) d: (x − (1+ i))(x − (1− i))<br />

8-172. a: real b: complex c: complex<br />

d: real e: real f: complex<br />

8-173. It is not; 16 + 8 ≠ 32 − 40<br />

8-174. a: x = 5 or 1 b: x = 4 or 0 c: x = 7 d: x = 1<br />

8-175. a: 24<br />

b: (x 3 − 3x 2 − 7x + 9) ÷ (x − 5) = (x 2 + 2x + 3) with a remainder of 24.<br />

8-176. a: y = x 2 +1 b: y = x 2 – 2x –1<br />

8-177. a: b:<br />

72 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 9.1.1<br />

9-7. a: Population: U.S. employees; the population is too large to conveniently measure so<br />

sampling should be used.<br />

b: Population: students in the class. A census can be taken.<br />

c: Population: All carrots. To measure the Vitamin A in a carrot, it must be destroyed, so<br />

even if it were possible to measure all carrots, it would not be wise. Sampling must be<br />

used.<br />

d: Population: The public (the media does not generally make this population very clear).<br />

It could be all voting adults, all adults, or all people in the state. In any case, the<br />

population is too large, so sampling must be used.<br />

e: Population: Elevator cables. To find this, elevator cables must hold greater and greater<br />

weight until they break. If all elevator cables were tested, there would be none left to<br />

use for elevators. Sampling must be used.<br />

f: Population: Your friends. A census can be taken.<br />

9-8. a: The five-number summary is (1, 19.5, 29, 40.5, 76 cups of coffee per hour).<br />

b: The typical number of cups sold in an hour is 29 as determined by the median.<br />

Looking at the shape of the distribution the median is a satisfactory representation of<br />

the distribution. The distribution has a skew. There is a gap between 60 and 70 cups.<br />

The IQR is 21 cups. Seventy-six cups of coffee in one hour is an apparent outlier.<br />

9-9. a: (x ±1), (x ± 7)<br />

9-10. a ≤ 25<br />

b: Neither are factors. Use substitution to determine whether x = –1 and x = 1 are zeros.<br />

Or you could use the Remainder Theorem and divide to see that neither are factors<br />

because there is a remainder.<br />

9-11. a: 30º or 150º b: 120º or 240º c: 45º or 225º<br />

d: 35.26º, 144.74º, 215.26º, or 324.76º<br />

9-12. f (g(x)) = g( f (x)) = x<br />

9-13. a: 10 times stronger b: 10 0.8 = 6.3 times stronger<br />

c: log(0.5) ≈ –0.3, so 6.2 – 0.3 ≈ 5.9 on the Richter scale<br />

9-14. a: (x + 2 − 3)(x + 2 + 3) = x 2 + 4x +1<br />

b: (x + 2 − i)(x + 2 + i) = x 2 + 4x + 5<br />

9-15. posts: $3, boards: $2, piers: $10<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 73

Lesson 9.1.2<br />

9-22. a: The question implies that the questioner holds this opinion, thus biasing results.<br />

b: The question assumes that the respondent believes that the climate is changing and<br />

will think that one of the given factors is important, and that it is important to slow<br />

global climate change, biasing results.<br />

c: The question implies that teacher salaries should be raised.<br />

9-23. Sample questions given:<br />

a: Are a majority of Americans in favor of replacing the Electoral College with a<br />

popular vote?<br />

b: Do consumers prefer the taste of the new “improved” cookie recipe?<br />

c: What was the class average on the semester final exam?<br />

d: What was the average for high school students taking the state math proficiency<br />

examination last year?<br />

Hush Puppy<br />

9-24. a: See plots at right. Hush Puppy: min = 19.7,<br />

Q1 = 44.5, med = 58.3, Q3 = 70.1, max = 79.5;<br />

Quiet Down: min = 14.2, Q1 = 37.4, med = 54.85,<br />

Q3 = 63.3, max = 102.1<br />

b: Hush Puppy: The distribution is left skewed so its<br />

center and spread are best described by the median<br />

of 58.3 dB and IQR of 25.6 dB there are no apparent<br />

outliers. Quiet Down: Has some potential outliers<br />

over 100 dB or is perhaps dual-peaked. The main<br />

body of data has a left skew. The center and spread<br />

are best described by the median of 54.85 dB and IQR<br />

of 25.9 dB.<br />

d: The Hush Puppy looks better now because those three<br />

high readings from the Quiet Down model are a lot<br />

more significant. Or perhaps the Quiet Down could<br />

be redesigned to eliminate those high readings.<br />

12 24 36 48 60 72 84 96 10<br />

Quiet Down<br />

9-25. y = 2(x + 2) 2 − 3 , (–2, –3). See graph at right.<br />

9-26. y = 6, z = 2<br />

9-27. a: x = 4 b: x = 200<br />

9-28. a: π 6 b: π 12<br />

c: –<br />

12 d: 7π 2<br />

9-29. y = − 1 4<br />

(x − 2)(x + 2)2<br />

9-30. a: 160π<br />

, about 167.6 cubic feet b: 6 feet<br />

c: It is not changing, the angle is ≈ 68.20°<br />

74 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 9.1.3<br />

9-36. a: This information could be found on the web for all American League players.<br />

It would be a census and the answer would be a parameter.<br />

b: An experiment would need to be conducted on a sample of eggs. The findings would<br />

be a statistic.<br />

c: Random high school students could be surveyed, possibly from different high schools<br />

in different parts of the country. Surveying every high school student would be almost<br />

impossible, so this survey would be a sample and the answer would be a statistic.<br />

9-37. a: closed b: open c: open d: closed<br />

9-38. Answers will vary.<br />

9-39.<br />

9<br />

; k = 7, 8 are factorable.<br />

9-40. blue block: 8 grams, red block: 16 grams<br />

9-41. a: The more rabbits you have, the more new ones you get, a linear model would grow by<br />

the same number each year. A sine function would be better if the population rises<br />

and falls, but more data would be needed to apply this model.<br />

9-42.<br />

x+5<br />

9-43.<br />

b: R = 80, 000(5.4772...) t<br />

c: ≈ 394 million<br />

d: 1859, it seems okay that they grew to 80,000 in 7 years, if they are growing<br />

exponentially.<br />

e: No, since it would predict a huge number of rabbits now. The population probably<br />

leveled off at some point or dropped drastically and rebuilt periodically.<br />

9-44. a: 4π 5<br />

15π<br />

c: 100º d: 255º e: 1710º f:<br />

11π<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 75

Lesson 9.2.1<br />

9-50. a: When asked to choose between an “m” and a “q,” most people prefer “m,” regardless<br />

of the Cola taste.<br />

b: The “to protect” interpretation is not part of the Bill of Rights; it will bias the results.<br />

c: The statistics chosen for the lead-in will bias the results.<br />

9-51. a: Only certain types of people typically respond.<br />

b-d: Answers will vary.<br />

e: Students should observe some clear preferences for some numbers, letters, and colors.<br />

This would provide evidence that people cannot behave or choose randomly.<br />

9-52. Mean: 7.6 g, mean distance-squared: 2.56+0.16+0.16+1.96+0.36<br />

5−1<br />

= 1.3 ,<br />

sample standard deviation≈ 1.14 g (and not ≈ 1.02).<br />

9-53.<br />

, 6, –3)<br />

9-54. x 2 + 25<br />

9-55. 2, ±5i<br />

9-56. ± 15<br />

9-57. a: 3 + 2i b: 1 + 4i c: 5 + i d: − 1 2 + 5 2 i<br />

9-58. a: x = 32 b: x = 1 6<br />

76 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 9.2.2<br />

9-62. a: Not likely; this samples the population of people with phone numbers listed online that<br />

are home midday. In each of these, we could also notice that we only get responses<br />

from those who agree to participate in our polling activities—already a very<br />

unrepresentative sample.<br />

b: Not likely; this samples the population of people who shop at this particular grocery<br />

store.<br />

c: Not likely; this samples the population of people who attend movies.<br />

d: Not likely: this samples the population of people who go downtown at the time you are<br />

there.<br />

e: This sample is likely to be more representative, as it is closer to random.<br />

9-63. Sample diagram:<br />

30 get<br />

classroom<br />

SAT prep<br />

90 student<br />

volunteers<br />

take SAT<br />

random assignment<br />

on-line<br />

30 get no<br />

additional<br />

instruction<br />

All Students retake<br />

the SAT. Compare<br />

average change in<br />

scores between the<br />

groups<br />

9-64. Children would need to be randomly assigned to treatment groups, one that gets spanked<br />

and another where there is no spanking. After a period of years the IQ of both groups can<br />

be tested and compared. Any variable that has the suggestion or potential to lower the IQ<br />

of a human does not belong in a clinical experiment. Who would decide who, when, and<br />

how the spankings would be administered? Would you spank kids randomly?<br />

9-65. Mean: 52 g, mean distance-squared: 64+64+4+144+4<br />

≈ 8.37g (and not ≈ 7.48g).<br />

9-66. one point of intersection: (2, 2)<br />

= 70 , sample standard deviation<br />

9-67. See graph at right; a sphere, V = 32π<br />

cubic units<br />

2 x<br />

9-68. x 3 + 8 = (x + 2)(x 2 − 2x + 4)<br />

9-69. a: b:<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 77

Lesson 9.3.1<br />

9-75. a: They will not show the people who named other stations or people saw the station<br />

logo and knew what station the interviewer was from.<br />

b: Surveying outside the gym does not give you a random sample.<br />

c: No, more people drive during the day. You should look at the probability of being in<br />

an accident.<br />

d: About half of all power plants are below average. It does not mean that it is unsafe.<br />

9-76. Answers will vary.<br />

9-77. a: 3 2 = 9 b: 3 0 = 1 c: 3 3 + 3 1 = 27 + 3 = 30 d: – 9 2<br />

9-78. a: n = 2; 1 7 b: n = 0, 1; 2 7 c: n = 3, 4, 5, 6; 4 7<br />

9-79. – 1 5<br />

9-80. a: x = 4 b: x = 9<br />

9-81. ≈ 278 months or 23 years<br />

9-82. a: y<br />

9-83. a: No<br />

b: No, no number of trials will assure there are no red ones.<br />

c: Not possible.<br />

78 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 9.3.2<br />

9-88. a: The typical number of tardy students (center) is the median, 3 students, because 50%<br />

of the students fall below 3. The shape is single-peaked and symmetric with no gaps<br />

or clusters. The IQR (spread) is 1 student, because Q1 is 2 and Q3 is 3. There are no<br />

apparent outliers.<br />

b: (0.43 + 0.13 + 0.07)(30) = 19 days<br />

c: ≈ 30%<br />

9-89. a: Answers will vary.<br />

b: Yes, assuming a sufficient sample size, a controlled randomized experiment can show<br />

cause and effect because of the random assignment of subjects to the groups.<br />

9-90. Experiments can be very expensive, time consuming, and in some cases involving<br />

humans or animals, unethical.<br />

9-91. 6 sq. units; see graph at right.<br />

9-92. a: f −1 3<br />

(x) = x +1 − 3<br />

b: See graph below right.<br />

c: Yes, each x is paired with no more than one y.<br />

9-93. a: double roots at –1, 2, 5 b: Same as the previous except<br />

reflected over the x-axis<br />

9-94. a: (– 4, 0), (–2, 0) and (0, –16) b: domain: all real numbers, range: y ≤ 2<br />

9-95. a: y = 1 4 (x +1)2 +<br />

8 3 , vertex = ( −1, 8<br />

3 ) , x = –1<br />

b: y = 1 4 (x +10)2 +16 , vertex = (–10, 16), x = –10<br />

9-96. a: x + 3 b: (x + 3) 2 + (y − 2) 2<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 79

Lesson 9.3.3<br />

9-103. a: 667.87 lunches; sample standard deviation is 56.17 lunches.<br />

b: (576, 624, 665, 700.5, 785)<br />

c: See histogram at right.<br />

d: Since the shape is fairly symmetric, we’ll use<br />

mean as the measure of center; the typical number<br />

of lunches served is 668. The shape is single<br />

peaked and fairly symmetric with no gaps or<br />

clusters, the standard deviation is about<br />

56 lunches, and there are no apparent outliers.<br />

e: 10.8%<br />

f: Use half of the 680 – 720 bin. 0.216 + 0.351 + (0.5)(0.108) ≈ 62.1%<br />

9-104. a: See graph at right.<br />

b: 2.7333 tardy students, 1.1427<br />

c: See graph middle right.<br />

d: See graph middle right. 11.0%<br />

e: See graph far right.<br />

normalcdf(4, 10^99, 2.7333, 1.1427) = 0.1338. 0.1338(180) ≈ 24 days<br />

9-105. a: See graph at right.<br />

b: 50 %<br />

c: See graph at right.<br />

normalcdf(11.5, 12.5, 12, 0.33) = 87%<br />

9-106. a: log 3 (5m) b: log 6 ( p m<br />

) c: not possible d: log(10) = 1<br />

0.108<br />

0.216<br />

0.351<br />

0.135<br />

0.081<br />

9-107. a:<br />

2x 2 −2x−7<br />

(x−3)(x+1)(x−2)<br />

b: −x2 +2x−4<br />

x(x−2) x+2<br />

x−5 d: x(x2 − 2x + 4)<br />

9-108. a: x = ± 26 b: x =<br />

9-109. See graphs at far right.<br />

−2± 10<br />

9-110. a: 1224 ≈ 34.99 b: (x +1) 2 + (y +1) 2<br />

9-111. a: f −1 (x) = 1 3 ( x−5<br />

2 )2 +1 = 1<br />

12 (x − 5)2 +1 for x ≥ 5<br />

80 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2<br />

Lesson 10.1.1<br />

10-7. a: $165 b: t(n) = 50 + 5(n −1) c: $930<br />

10-8. a: 4050 b: 300 + 550 + 800 + … + 4050; t(n) = 300 + 250(n −1)<br />

10-9. a: t(n) = 3+ 7(n −1) b: t(n) = 20 − 9(n −1)<br />

10-10. –2<br />

10-11. a: x-intercepts (2.71, 0) and (5.29, 0), y-intercept (0, 43)<br />

b: x-intercepts (–1, 0) and (2.5, 0), y-intercept (0, –5)<br />

10-12. a: normcdf(70, 79, 74, 5) = 0.629, About 63% would be considered average.<br />

b: normcdf(–10^99, 66, 74, 5) = 0.055, Between 5 and 6% of would be in excellent<br />

shape.<br />

c: normcdf(–10^99, 66, 70, 5) – 0.0548 from part (b) = 0.157; There would be a nearly<br />

16% increase in young women classified as being in excellent shape.<br />

10-13. a: 233 units b: (x − 5) 2 + (y − 2) 2 units<br />

10-14. $20.14<br />

10-15. 34,800 people<br />

10-16. Yes, because the sum of the diameters is 830 mm.<br />

10-17. 235<br />

10-18. (−6) + (−3) + 0 + 3+ 6 + 9 +12 +15 +18<br />

10-19. It is the 55 th term.<br />

10-20. 220<br />

10-21. a: 10 P 5 = 30, 240 b: 10 ⋅9 4 = 65, 610<br />

10-22. n = ±6 2<br />

10-23. a: 2 b: 3 4<br />

10-24. a: It looks like an endless wave repeating the original cycle over and over again.<br />

b: A polynomial of degree n has at most n roots, but f(x) = sin(x) has infinitely many<br />

roots. Also, every polynomial eventually heads away from the x-axis.<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 81

Lesson 10.1.2<br />

10-34. a: odds: t(n) = 1+ 2(n −1) , evens: t(n) = 2 + 2(n −1)<br />

b: odds: 5625, evens: 5700<br />

10-35. a: t(n) = 21− 4(n −1)<br />

b: 31; You can solve the equation 25 − 4n = −99 .<br />

c: –1209<br />

10-36. 15<br />

10-37. 6 P 4 = 360<br />

10-38. Degree 4; Graph shown at right.<br />

10-39. f (x) = 1 4<br />

(x − 3)(x − 2)(x +1)<br />

10-40. a: f (x) = (x + 3) 2 − 2 , vertex (–3, –2) b: f (x) = (x − 5) 2 − 25 , vertex (5, –25)<br />

10-41. For David: normcdf(122, 10^99,149,13.6) = 0.976<br />

For Regina: normcdf(130, 10^99,145,8.2) = 0.966<br />

For now David is relatively faster.<br />

10-42. a: π 4<br />

12 c: − π 12<br />

d: 5π 2<br />

82 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 10.1.3<br />

10-49. a: 16,200 b: 16,040 c: 564<br />

10-50. 11+ 22 + 33+ ...+ 99 = 495<br />

10-51. a: Sample response: The terms decrease by two, then add seven, then decrease by two,<br />

and then add seven continually.<br />

b: It is not arithmetic because the difference from one term to the next is not constant.<br />

c: Find the sum of each “unzipped” series and then add these sums together.<br />

The sum is 32,240.<br />

10-52. a: 12 C 10 = 66 b: 9 C 7 = 36<br />

10-53. Some may substitute for x, others may set x equal to 3+ i 2 and work back to the<br />

equation, others may write the two factors and multiply to get the original equation, and<br />

others may solve by completing the square.<br />

10-54. The graphs of y = 2 x and y = 5 − x intersect at only one point.<br />

10-55. h = $2.50, m = $1.75<br />

10-56. a: 17 b: 5<br />

10-57.<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 83

Lesson 10.1.4<br />

11<br />

10-62. a: ∑ (60 −13k) = −198 b: ∑<br />

k=1<br />

10-63. 495,550<br />

(3+ 7(k −1)) =<br />

n[3+(3+7(n−1))]<br />

10-64. It works for the integers from 1 through 39.<br />

10-65. a: 7 ⋅ 3 n b: 10(0.6) n−1<br />

10-66. 9!= 362,880<br />

10-67. a: normalcdf(–10^99, 59, 63.8, 2.7) = 0.0377; 3.77%<br />

b: (0.0377)(324)(half girls) = 6 girls<br />

= n(−1+7n)<br />

c: normalcdf(72,10^99, 63.8, 2.7) = 0.00119. (0.00119)(324)(half) = 0.19 girls.<br />

We would not expect to see any girls over 6ft tall.<br />

10-68. a: b:<br />

10-69. cos( 2π 3 ) = – 1 2 , cos( 4π 3 ) = – 1 2 , cos( 5π 3 ) = 1 2<br />

84 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 10.2.1 (Day 1)<br />

10-87. a: 3+ 30 + 300 + 3,000 + 30,000 + 300,000 = 333,333<br />

b: Write the series 3+ 30 + ...+ 300,000 = S(6) twice. Multiply one of them by 10.<br />

Subtract 10S(6) − S(6) = 2,999,997 = 9S(6) . Divide by 9 to get 333,333.<br />

c: ∑ 3⋅10 n−1 = 3⋅10n −3<br />

i=1<br />

10-88. a: A sequence would represent the list of the class sizes of the graduating classes as the<br />

number of years since the school opened increased. The corresponding series would<br />

represent the growing number of alumni.<br />

b: t(10) = 150 ; total = 960<br />

c: n(36 + 6n) = 36n + 6n 2<br />

10-89. a: 15 b: –615<br />

10-90. 210, arithmetic<br />

10-91. a: 23 P 3 = 10, 626 b: 23 C 3 = 1771 c: 1⋅22 ⋅22 = 484 d: 4 ⋅22 ⋅22 = 1848<br />

10-92. See graph at right.<br />

10-93. a: x−2<br />

c: Use the Distributive Property to factor and the multiplicative property of 1 to reduce.<br />

10-94. a and b: no amplitude, period = π , LP = (0, 0).<br />

10-95. a: x = 125<br />

2 b: x = − 4 5<br />

c: x = 0.04 d: y = 9 4<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 85

Lesson 10.2.1 (Day 2)<br />

10-96. Calculate the sums of two geometric series, the first with 25 terms, the second with 15.<br />

Retirement at age 55: $1,093,777; at age 65: $1,115,934<br />

10-97. $20,000 at 8% and $30,000 at 6.5%<br />

10-98. a: 8!= 40320 b: 1⋅ 7!= 5040 c: 1⋅ 7! + 7!⋅1 = 10080<br />

10-99. a: 272 = 4 17 units b: (x + 3) 2 + (y + 5) 2 units<br />

10-100. a: x = 5 2 b: y =10 c: x = –3, 2 d: y = − 15 4<br />

10-101. a: (2, 8) and (4, 4) b: (3+ i,6 − 2i) and (3− i,6 + 2i)<br />

c: In system (a), the solutions are the points of intersection. In system (b), the solutions<br />

show that they do not intersect.<br />

10-102. tan(160°) = –0.3640 , tan(200°) = 0.3640 , tan(340°) = –0.3640<br />

10-103. a: x = 4 b: x = 48 c: x = 3 d: x = 6<br />

10-104. 26 + i<br />

86 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 10.2.2<br />

10-117. 500 miles<br />

10-118. a: 7 C 2 = 21 b: 7 C 3 = 35 c: 7 C 4 = 35<br />

d: Choosing three points to form a triangle is the same as choosing four points to not be<br />

part of the triangle. Those four points form a quadrilateral, 7 C 3 =<br />

4!3! 7! =<br />

3!4! 7! = 7 C 4 .<br />

10-119. a: 10t + u − (10u + t) = 27 b: x = –13<br />

10-120. $1157<br />

10-121. a, d<br />

10-122. a: (x − 3)(x 2 − 2x + 5) b: 3, 1± 2i<br />

10-123.<br />

10-124. (−1+ i, 3), (−1− i, 3)<br />

10-125. When r ≥ 1, r n increases in size as n increases, so the expression 1− r n does not get<br />

close to 1, and being able to replace that expression with 1 is a key part of the<br />

derivation of the formula.<br />

10-126.<br />

121<br />

10-127. a: 45 b: 792 c: 7<br />

10-128. a: x = –3, 4 b: x = –1.5, 3 c: x =<br />

d: Never e: x = 0, –2, 4 3 f: x = 0<br />

10-129. a: −16x 5/2 y 4 z 2 b: 3 1/2 x 3/2 y 8/3<br />

−1 ± 57<br />

10-130. a: 0, 5 seconds b: 0 ≤ t ≤ 5 c: 5 seconds d: 1 < t < 4<br />

10-131. Yes; use the Quadratic Formula or direct substitution.<br />

10-132. a: x = –1, 4 b: x ≤ –1 or x ≥ 4 c: –1 ≤ x ≤ 4<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 87

Lesson 10.3.1 (Day 1)<br />

10-145. x 7 + 7x 6 y + 21x 5 y 2 + 35x 4 y 3 + 35x 3 y 4 + 21x 2 y 5 + 7xy 6 + y 7<br />

10-146. −640w 2 z 3<br />

10-147. 1365<br />

10-148. a: 16 b: Not possible. r > 1, and the terms keep increasing.<br />

10-149. 4 C 0 = 1, 4 C 1 = 4, 4 C 2 = 6, 4 C 3 = 4, 4 C 4 = 1<br />

a: The number of possibilities are the elements of the 4 th row of the triangle.<br />

b: 1, 6, 15, 20, 15, 6, 1; Use the 6 th row of the triangle.<br />

10-150. a: 9 C 3 = 84 b: 9 C 2 = 36 c: 10 C 3 = 9 C 3 + 9 C 2<br />

d: The tenth row entry of Pascal’s Triangle is the sum of the two ninth row entries<br />

above it and these numbers correspond to the total number of combinations when<br />

one more choice is added.<br />

10-151. See graph at right.<br />

10-152. a: See graph below right.<br />

b: Answers will vary. See graph below right.<br />

normalcdf (6.71, 13.29, 10, 2) = 0.9000<br />

10-153. (−2, 3, − 1 2 )<br />

10-154. a: y = x 2 − 4x + 5 = (x − 2) 2 +1<br />

b: (2, 1)<br />

88 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 10.3.1 (Day 2)<br />

10-155. 42x 3<br />

10-156. 728<br />

10-157. 81x 4 +108x 3 + 54x 2 +12x +1<br />

10-158. a: f (x) = (x + 2) 2 + 2 b: (x + 3) 2 + (y − 4) 2 = 25<br />

10-159. 32.9 mm<br />

10-160. y = −2x + 34<br />

10-161. a: See graph at right. b: f −1 (x) = [2(x +1)] 2 – 4<br />

c: x ≥ –1, y ≥ –4 d: 5<br />

10-162. a: x = 7 b: x = 1.5 c: x ≈ 1.75 d: x ≈ 1.87<br />

10-163. a: (0, –5), (4, 3), (8, 3) b: See graph at right.<br />

c: y = − 1 4 x2 + 3x − 5 d: 10 seconds<br />

height<br />

e: 0 ≤ x ≤ 10 f: 0 ≤ x < 2<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 89

Lesson 10.3.2<br />

10-169. Robin: $11,887.58; Tyrell: $11,808.38; difference: $79.20<br />

10-170. a: $10,304.55; it rounds off to the same amount.<br />

b: $10,832,870, 680 and $10,832,775,720, a difference of $94,960.<br />

c: Maybe billionaires, or other investors of large amounts.<br />

10-171. a: 1+ 3 n + 3<br />

n 2 + 1<br />

n 3<br />

b: 1+ 5 n + 10<br />

n 2 + 10<br />

n 3 + 5<br />

n 4 + 1<br />

n 5<br />

10-172. a: 14.7 lbs./sq. in. b: ≈ 12.55 lbs./sq. in. c: ≈ 14.83 lbs./sq. in.<br />

10-173. a: 2 = (1.015) 4t , 2 = e 0.06t<br />

b: Quarterly, 11.64 years; Continuously, 11.55 years<br />

c: The difference is about one month, so probably not.<br />

10-174. (−5, 0), ( 2 3 , 0), (− 1 4 , 0)<br />

10-175. 8x 3 − 36x 2 + 54x − 27<br />

10-176. a: log 2 (5x) b: log 2 (5x 2 ) c: x = 17<br />

d: x = −<br />

20 9 = −0.45 e: x = 15 f: x = 4<br />

10-177. a: 10t + u<br />

b: 10u + t<br />

c: t + u = 11 and 10t + u − (10u + t) = 27<br />

d: 74 and 47<br />

90 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 11.1.1<br />

11-5. a: preface b: biased wording c: desire to please d: fair question<br />

11-6. a: Using the normal model here is not a good idea because the data is not symmetric,<br />

single-peaked, and bell-shaped. A different model would represent the data better.<br />

b: 9/48 ≈ 19 th percentile; In 19% of the hours over the two day period the coffee shop<br />

was not profitable.<br />

c: 41/48 = 85 th percentile. In 85% of the hours over the two-day period, the coffee shop<br />

would not have been profitable. If this data represents a typical 48-hour period, now<br />

would not be the time to expand.<br />

11-7. If the nickel is tossed and the die rolled there are 12 equally likely outcomes. He can<br />

make a list of each of the possible outcomes, assign one player to each outcome<br />

(H1-Juan, H2-Rolf, … T6-Jordan), and then toss the coin and roll the die to select.<br />

11-8. a: No, by observation, a curved regression line may be<br />

better. See graph at right.<br />

b: Exponential growth.<br />

4 5<br />

c: m = 8.187 ⋅1.338 d , where m is the percentage of mold,<br />

and d is the number of days. Hannah predicted the<br />

1 2 3<br />

mold covered 20% of a sandwich on Wednesday.<br />

Day<br />

Hannah measured to the nearest percent.<br />

b: 0.60<br />

0.80 = 75% y<br />

11-9. a: f −1 (x) = ln x<br />

b: f(x): domain is all real numbers, range is y > 0, y-intercept is (0, 1),<br />

asymptote is y = 0. f –1 (x): domain is x > 0, range is all real numbers,<br />

x-intercept is (1, 0), asymptote is x = 0. See graphs at right.<br />

c: 2 and 3<br />

d: Above log base 2 for x > 1 and below it for 0 < x < 1, below<br />

log base 3 for x > 1 and above for 0 < x < 1.<br />

11-10. a: 9.00646832 for both b: 3.10628372 for both<br />

c: It will take about 9 years to double.<br />

d: After about three years and one month, the car<br />

will be worth less than half of the original price.<br />

11-11. 765<br />

Garage?<br />

yes no<br />

0.80 0.20<br />

11-12. a: 2i b: –2 + 2i<br />

yes<br />

0.60 0.15<br />

0.75<br />

11-13. a: 5%. See the table at right.<br />

no<br />

0.20 0.05<br />

0.25<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 91<br />

% Mold<br />

40<br />

20<br />

Large<br />

Backyard?<br />

Lesson 11.1.2<br />

11-18. Answers should be close to P(sum 6 or less) = 15<br />

≈ 0.42 , so 0.42(7) = 2.94 or about<br />

3 days per week.<br />

11-19. Theoretical probabilities: P(sum 6 or less) = 15<br />

36 ≈ 0.42 ,<br />

P(sum 7 or more) =<br />

36 21 ≈ 0.58 , so about3 days a week.<br />

11-20. a: F 2%, D 16 – 2 = 14%, C 84 – 16 = 68%, B 98 – 84 = 14%, A 100 – 98 = 2%<br />

b: F 0, D 76.5 – (2)17.4 = 41.7, C 75.5 – 17.4 = 58.1, A 76.5 – (2)17.4 = 111.3<br />

c: The normal model is not a good idea because the distribution of scores is strongly<br />

skewed left. Also, the minimum grade required for an A would be 111.3, which is<br />

probably not possible.<br />

11-21. Answers vary.<br />

11-22. a:<br />

, 11 5 ) b: ( −5, 1 2 )<br />

11-23. a: 12 b: 1 2<br />

11-24. Both equal 3 8 .<br />

11-25. The base of the natural logs is e; e is between 2 and 3, and ln e = 1; x = e<br />

11-26. a: 1.79175 b: 2.4849 c: 2.7726 d: –1.0986<br />

92 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 11.1.3<br />

11-28. Theoretically, the series is expected to last for 5.8125 games.<br />

11-29. Theoretically, a streak of 4 or more has probability of about 48%, a streak of five or more<br />

about 25%, a streak of six or more 12%, and a streak of seven or more about 6%.<br />

11-30. The survey is not random. They will get a lot more representation from adults. People<br />

may be influenced by the responses of others. An individual may have several favorites<br />

but only states one.<br />

11-31. a: x = 1 4 y2 −1, parabola b: x 2 + y 2 = 49 , circle<br />

11-32. a: 51 b: 64.77<br />

11-33. They are equivalent and simplify to x 2 .<br />

11-34. a: 1<br />

b: 580 c: (–9, 1) d: y − 2 =<br />

(x − 3)<br />

11-35. a: ≈ 266.67 b: 37.5% c: 27% d: 135<br />

11-36. a: See diagram at right.<br />

b: In the RR rectangle, 18<br />

38 ⋅ 18<br />

38 = 1444 324 ≈ 22.44% .<br />

c: Add the RR, BR, and GR rectangles,<br />

324<br />

1444 + 1444 324 + 1444 36 ≈ 47.37%.<br />

d: Considering only the column in which the<br />

second spin is red (RR, BR, GR), the probability<br />

the first spin is red (RR)<br />

is<br />

1444<br />

1444 + 1444 324 + 1444<br />

≈ 47.37%.<br />

R<br />

G<br />

e: They are the same.<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 93

Lesson 11.2.1<br />

11-41. Theoretically, there will be 7.39 streaks of three or more in 60 days.<br />

11-42. a: 7.83%<br />

b: 5% and 11%<br />

c: About 7.83% ± 3% def. flashlights<br />

11-43. Each used a convenience sample. Each sample came from a distinct population with<br />

people who have many things in common, including attitudes and beliefs about the<br />

subject matter of murals.<br />

11-44. a: –344 b: –6740<br />

11-45. a: x = 10p b: x = 3q – 2p<br />

11-46. y = 5, z = 3<br />

11-47. See table at right. 0.6 ⋅0.5 = 0.3 = 30%<br />

11-48. (–1, –3) and (3, 5)<br />

11-49. a: 10 log 2 ≈ 3<br />

b: 20 ⋅10 6<br />

c: Two sounds have equivalent pressures, or one sound has a pressure of 20 micropascals.<br />

d: 100<br />

Second Jar<br />

yellow<br />

0.30<br />

orange<br />

0.50<br />

white<br />

0.20<br />

black<br />

0.60<br />

First Jar<br />

purple<br />

0.40<br />

0.18 0.12<br />

0.30 0.20<br />

0.12 0.08<br />

94 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 11.2.2<br />

11-52. a: 0.56 and 0.74 b: ≈ 65% ± 9%<br />

11-53. 3% ± 0.85%. Answers vary, but should be 3% plus/minus a number smaller than 1.7%<br />

11-54. The energy usage will change by –1.3% to 1.7%. Indiana could save up to $11.7 million,<br />

but could end up spending $15.3 million.<br />

11-55. a: Answers will vary. Like a tournament, the students could be paired and the coin<br />

tossed for each pair. The “winners” are paired and the coin tossed again, repeating<br />

until there is just one student.<br />

b: 3 tosses. Tossing a coin 3 times has 8 equally likely outcomes: HHH, HHT, HTH, HTT,<br />

THH, THT, TTH, TTT. Assign each student an outcome and toss the coin 3 times.<br />

c: Yes. Use the method outlined in part b repeatedly until a baseball player is not<br />

selected.<br />

11-56. a: y = 2(x +<br />

4 7 )2 − 105<br />

, graph shown at right,<br />

vertex (−<br />

4 7 , − 105<br />

8 ) , axis of symmetry x = − 4<br />

b: y = 3(x − 1 6 )2 −<br />

12 97 , graph shown at far right,<br />

vertex( 1 6 , − 12 97 ) , axis of symmetry x = 1 6<br />

11-57. a: b:<br />

c: For part (a), the parts above the x-axis stay the same, the parts below the x-axis are<br />

reflected upward across the axis. For part (b), the part of the graph to the right of the<br />

y-axis remains the same, and the part to the left of the y-axis is replaced by a reflection<br />

of the part on the right of the axis.<br />

11-58. a: Some may predict the amount due will be far too much for a state to pay.<br />

b: ≈ 1.126 ⋅ 10 15 dollars<br />

c: A ≈ $2.791⋅10 16 , or about 2.68 ⋅10 16 dollars more.<br />

11-59. a: x = log(3)<br />

log(2)<br />

c: x = log(12)<br />

log(7)<br />

log(8)<br />

b: x =<br />

log(5)<br />

log(b)<br />

d: x =<br />

log(a)<br />

11-60. Both 31.5%. Neither 16.5%. See table at right.<br />

Dimples<br />

0.45<br />

Widow’s Peak<br />

0.70 0.30<br />

0.315<br />

0.55 0.165<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 95

Lesson 11.2.3<br />

11-64. Upper bound: 25145 lower bound: 24563; Students should report that 90% of the time we<br />

can expect that the copy machine will need maintenance after 24854 ± 291 copies. The<br />

interval of confidence is from 24563 to 25145. 25000 copies is within the interval of<br />

confidence, so the research company may support the copy machine company’s claim.<br />

They may also state that the copy machine company is pushing the limits with a claim of<br />

“at least 25000 copies” since the range within the margin of error is from 24563 to 25145.<br />

11-65. a: 0.12<br />

b: A difference of zero is not within the margin of error, so it is not a plausible result. A<br />

difference of zero means that there is no difference in the percentage of food removed<br />

with detergent compared with the percentage of food cleaned off with plain water.<br />

c: Yes. Because a difference of zero is not within the margin of error, a difference of<br />

zero is not a plausible result for the population of all food cleaned. We are convinced<br />

there is between 3.5% and 20.5% (12% ± 8.5%) more food removed with detergent<br />

than with plain water.<br />

11-66. a: 1/8 or 12.5%, yes<br />

b: Her study provides no reliable evidence of her conclusion. She used a convenience<br />

sample of only 4 people. Her question introduced bias with the preface about violence<br />

and crime. There may also have been a desire to please the interviewer. She used a<br />

closed question forcing romantic comedies as the only alternative to action movies.<br />

Even if there is no real preference among moviegoers, it is plausible that 4 people will<br />

have the same opinion between any two types of movies.<br />

11-67. a: The number of cards on the field is 768 ×1029 = 790, 272 cards. The probability is<br />

or 0.000 001265 .<br />

790272<br />

790,272 cards<br />

52 cards<br />

1 pack<br />

= 15,198 packs of cards.<br />

The maximum loss is if the first player chooses a card and wins:<br />

−$1, 000, 000 prize − ($0.99)(15,198) cost of packs + $5 from the player<br />

= −$1, 015, 041.02 . (If nobody plays, then the million dollars is not paid out, and the<br />

boosters do not have the maximum possible loss.)<br />

c: If all of the chances were purchased,<br />

−1, 000, 000 prize − ($0.99)(15,198) cost of packs + ($5)(790, 272) from players<br />

= $2, 936, 313.98<br />

d: On average half the cards would be sold before there was a winner,<br />

−1, 000, 000 prize − ($0.99)(15,198) cost of packs + ($5)(395,136) from players<br />

= $960, 633.98 .<br />

e: 176,000,000<br />

790,272<br />

≈ 223 football fields would have to be covered to give the same odds as<br />

winning the state lottery!<br />

96 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

11-68. (0, 0)<br />

11-69. a: 5 + i b: –1 + 9i c: 26 + 7i d: –0.56 + 0.92i<br />

11-70. a: 4 ≤ y ≤ 10 b: m > 1 or m < –2<br />

11-71. a: x = –3 or x = 2 b: x < –3 or x > 2<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 97

Lesson 11.2.4<br />

11-75. Yes, 20% is within the margin of error of 13% ± 10%.<br />

11-76. a: 0.10<br />

b: i: 25% of 40 + 15% of 40 = 16 putts went into the hole<br />

ii: 1 to 16 will represent a putt that went into the hole; 17 to 80 will represent a putt<br />

that missed.<br />

c: A difference of zero means that there is no difference between the proportion of putts<br />

that went in the hole with the new club and the proportion of putts that went in with<br />

the old club. A difference of zero is within the margin of error, so it is a plausible<br />

result.<br />

d: No. A difference of zero is within the margin of error, and a difference of zero is a<br />

plausible result for the population of all putts. We are not convinced there is a true<br />

difference in the number of putts that go in with the new club compared to the old<br />

club.<br />

11-77. Yes. As little as 11.75 ounces is still within specifications.<br />

11-78. The first process is wildly out of control; systems wildly out of control are often caused<br />

by inexperienced operators. The second process is fully in control. The third process is<br />

technically out of control at only one point, but the cyclical nature of the process is<br />

disconcerting. Any explanation that is cyclical over 20 hours is acceptable.<br />

11-79. a: y<br />

11-80. a: x = a+b<br />

c<br />

b: x = ab + ac c: x = a, b<br />

d: x = 0, c e: x = a+b<br />

f: x =<br />

b−a<br />

11-81. a: x = −26 b: x = 10 or x = 3<br />

11-82. a: x = 1 b: x = ±2<br />

parents<br />

niece<br />

boyfriend<br />

11-83. a: See diagram at right.<br />

b: 1 4 / 1 2 = 0.5<br />

c: 1 9 + 1 6 + 1 6 + 1 4 = 25<br />

36 ≈ 69%<br />

d: 1 6 / 25<br />

36 = 6 25 = 24%<br />

1 1<br />

9 18<br />

18<br />

98 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 11.3.1<br />

11-87. This is a “Gambler’s Ruin” problem. The player with more coins always has a better<br />

chance of winning in the long run. P(Jill) = 4 6 ≈ 67%, P(Jack) = 2 6 ≈ 33% .<br />

11-88. a: See possible diagrams at right and answers below.<br />

Cell A is the proportion of times the system correctly<br />

activated the alarm.<br />

Cell B is the proportion of times the alarm was<br />

correctly not activated.<br />

Cell C is the proportion of times A happened and the<br />

alarm was incorrectly not activated.<br />

Cell D is the proportion of times A did not happen and<br />

the alarm was activated.<br />

b: 0.03966/(0.03966 + 0.00096) = 97.6%<br />

c: Yes, it is independent because the accuracy of<br />

alarm is the same regardless of whether event A<br />

occurs or not.<br />

Detection System<br />

Event A<br />

Yes No<br />

Correct<br />

Incorrect<br />

A B<br />

C D<br />

correct<br />

0.00096<br />

incorrect<br />

0.00004<br />

11-89. y = 1 5 x + 27 5<br />

11-90. (± 7, 3), (0, −4)<br />

Not Event A<br />

11-91. a: 10 + 11i b: 13 c: 29 d: a 2 + b 2<br />

0.95904<br />

0.03996<br />

11-92. a: b:<br />

11-93. a: –35 b: 123<br />

11-94. a: x = ±2 3 b: x = 2 c: x = 2 9<br />

−1± 13<br />

or x ≈ 0.434 or –0.768<br />

11-95. a: any polynomial with 5 x-intercepts; b: a polynomial graph with 3 x-intercepts and<br />

another ‘bend’; c: no x-intercepts, could have two ‘humps’; d: 2 x-intercepts and up to<br />

two ‘humps.’<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 99

Lesson 12.1.1<br />

12-5. a: always b: never<br />

c: always d: True for x = π 4 + 2π n and x = 5π 4 + 2π n<br />

12-6. a: (x − 2)(x + 2) b: (y − 9)(y + 9)<br />

c: (1− x)(1+ x) d: (1− sin x)(1+ sin x)<br />

12-7. a: ≈ 80.86 b: ≈ 24.05 c: ≈ 15.50º<br />

trigonometric ratios, Law of Sines, Law of Cosines, Pythagorean theorem<br />

12-8. The graphs of y = sin(2x) and y = 2sin(x) intersect at integer multiples of π. Solving the<br />

equation algebraically yields x = 0 + πn.<br />

12-9. a: x ≥ 2, f (x) ≥ 2 b: f −1 (x) = (x−2)2<br />

+ 2 c: x ≥ 2, f −1 (x) ≥ 2<br />

12-10. a: Stretched (amplitude = 3), shifted left<br />

2 π , and shifted down 4<br />

12-11. The first process is fully in control. The second process is wildly<br />

out of control. The third process is out of control; beginning at the<br />

9 th hour, there are 12 consecutive points above the centerline.<br />

12-12. a: 90 b: 190 c: 35 d: 405,150<br />

12-13. a: 12 P 5 = 95, 040 b: 12 C 5 = 792<br />

12-14. Sample answers: h = π 2 , 5π 2 , − 3π 2<br />

12-15. a: negative b: negative c: positive d: negative<br />

12-16. a ≤ 25<br />

12-17. See graph at right.<br />

12-18.<br />

12-19. a: x = 9 b: x = –9<br />

12-20. a: 3π 5<br />

12-21. a: 5 C 2 i 4 C 1<br />

12 C 3<br />

d: 5 C 3 + 4 C 3 + 3 C 3<br />

16π<br />

c: 140º d: 285º e: 1530º f:<br />

13π<br />

=<br />

11 2 b: 4 C 3<br />

12 C = 1<br />

3 55 c: 5 C 1 i 4 C 1 i 3 C 1<br />

12 C = 3<br />

3 11<br />

44 3 e: 5 C 1 i 4 C 2<br />

3 22<br />

12-22. a: a 3 + 3a 2 b + 3ab 2 + b 3 b: 8m 3 + 60m 2 +150m +125<br />

f: 1−<br />

( ) = 29<br />

11 + 44<br />

100 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2<br />

Lesson 12.1.2<br />

12-29. a: x = π 6 , 5π 6 b: x = 5π 6 , 7π 6 c: x = π 4 , 3π 4 d: x = 0<br />

12-30. No, 52º and 308º have the same value for the cosine, while 128º<br />

has the exact opposite cosine value. See diagram at right.<br />

128º<br />

52º<br />

12-31. See graph at right.<br />

–x<br />

12-37. a: 24<br />

12-32. f −1 (x) = −x + 6<br />

12-33.<br />

12-34. a: yes b: x 4 + x 3 + x 2 + x +1; yes c: x n + x n−1 + x n−2 +…+ x +1<br />

Recipient<br />

12-35. a: See possible diagrams at right and answers below.<br />

Cell A is the proportion of people correctly<br />

identified as drug users.<br />

Cell B is the proportion correctly identified as<br />

not drug users.<br />

Cell C is the proportion the test failed to identify<br />

as drug users but who are.<br />

Cell D is the proportion identified as drug users<br />

who are not.<br />

This can also be modeled as a tree diagram.<br />

b: 0.02 are actually using; 0.01 are told they are<br />

User<br />

Not Using<br />

D<br />

0.02277<br />

using, but are actually not.<br />

Drug User<br />

c: 0.00977/(0.00977 + 0.02277) ≈ 30%<br />

0.00023<br />

d: From part (b), about 1 out of 100 people<br />

receiving assistance will lose their assistance<br />

correct 0.98703<br />

because they have been falsely accused of<br />

Not Drug User<br />

using drugs. That seems high considering that<br />

only 2 out of 100 are actually using drugs.<br />

From part (c), 30% of the people identified as<br />

using drugs will be falsely accused and unfairly<br />

lose their money.<br />

incorrect 0.00977<br />

e: Yes, they are independent because the accuracy of the test stays the same whether or<br />

not a person uses drugs. To test, check whether P(A)⋅ P(B) = P(A and B) , for<br />

example, P(drug user)⋅ P(test correct) = P(drug user and test correct) .<br />

12-36. a: 0.0253 b: 26 C5<br />

52 C 5<br />

c: 0.000495 d: 13 C5<br />

e: 0.0019808<br />

Drug Test<br />

360º – 52º<br />

=308º<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 101

Lesson 12.1.3 (Day 1)<br />

12-43. a: 30º, 50º or<br />

6 π , 5π 6 b: 120º, 140º or 2π 3 , 4π 3<br />

c: 45º, 225º or<br />

4 π , 5π 4<br />

d: ≈ 35.26º, 144.74º, 215.26º, 324.74º or 0.62, 2.53, 3.76, 5.67<br />

12-44. a: domain: –3 ≤ x ≤ 3, range: –3 ≤ y ≤ 3, not a function<br />

b: domain: –3 ≤ x ≤ 4, range: –2 ≤ y ≤ 4, not a function<br />

c: domain: x ≤ 3, range: y ≤ 4, yes a function<br />

d: domain: −∞ < x < ∞ , range: y ≥ –2, yes a function<br />

12-45. a: x = 2 b: no solution<br />

12-46. a: b:<br />

–2 –2<br />

12-47. a: (4, 8) b: (0, –2, 3)<br />

Suspect<br />

Person<br />

Not Suspect<br />

12-48. a: See possible diagrams at right and answers below.<br />

Cell A is the proportion correctly identified as<br />

suspects.<br />

Cell B is the proportion correctly identified as not<br />

being suspects.<br />

Cell C is the proportion the software failed to<br />

identify but who actually are suspects.<br />

Cell D is the proportion the software identified as<br />

suspects who are not.<br />

b: 0.000999995/(0.000004995 + 0.000999995)<br />

≈ 99.5%<br />

12-49. 12 C 5 + 12 C 4 + 12 C 3 + 12 C 2 + 12 C 1 + 12 C 0 = 1586<br />

12-50. 2x 4 − 2x + −1<br />

Facial ID Software<br />

Not a Suspect<br />

0.000004995<br />

0.000000005<br />

0.99899501<br />

0.000999995<br />

12-51. a: See graph at right.<br />

b: The number of defects seems to be staying at or within<br />

control limits, but there is a cycle apparent every eight<br />

hours. Perhaps as the inspectors work through their<br />

shift, they get tired and catch fewer errors.<br />

102 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 12.1.3 (Day 2)<br />

12-52. The restrictions are needed so that the inverses will be functions. The domain of the sine<br />

function is restricted to −<br />

2 π ≤ x ≤ 2 π , the domain of the cosine function is restricted to<br />

0 ≤ x ≤ π , and the domain of the tangent function is restricted to −<br />

2 π < x < 2 π .<br />

12-53. a: x = 7π 6<br />

+ 2π n,<br />

6 + 2π n b: x = 6 π + 2π n,<br />

6 + 2π n<br />

c: x = 3π 4 + π n d: x = π n<br />

12-54. a: shifted up 1 unit b: shifted left<br />

c: reflected over the x-axis d: vertically stretched by a factor of 4<br />

12-55. a: y<br />

c: g(x) = − f (x)<br />

12-56. a: 5 6<br />

3x+8<br />

2x 2<br />

c: x2 +2x+3<br />

(x+1)(x−1)<br />

12-57. f (x) = 2(x −1) 2 −1; domain: all real numbers; range: f (x) ≥ −1;<br />

vertex: (1, –1); line of symmetry: x = 1; See graph at right.<br />

d: sin2 θ+cosθ<br />

sinθ cosθ<br />

12-58. a: x ≈ 1.356 b: x ≈ 2.112 c: x ≈ 1.792<br />

12-59. a: a 4 + 4a 3 b + 6a 2 b 2 + 4ab 3 + b 4<br />

b: 81m 4 − 216m 3 + 216m 2 − 96m +16<br />

12-60. a: 8 C 3 + 8 C 4 = 56 + 70 = 126<br />

b: If mushrooms are a known topping, then choose the rest of the toppings from only<br />

7 remaining toppings so 7 C3+7C2<br />

126<br />

126 56 = 4 9<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 103

Lesson 12.1.4<br />

12-67. a: a c b: c b c: c b d: b a<br />

12-68. a and b: ± π 6 , ± 5π 6 , ± 7π 6 , ± 11π<br />

12-69. The solution is equivalent to the solutions of cos(x) = 1 2<br />

300°; or 0, π,<br />

3 π , 5π 3<br />

and sin(x) = 0 . 0°, 180°, 60°,<br />

12-70. 9.10<br />

12-71. 1.083, 8.3%<br />

12-72. a: a 3 + b 3 b: x 3 − 8 c: y 2 +125 d: x 3 − y 3<br />

e: They consist only of two terms; they are sums or differences of cubes.<br />

12-73. a: (x + y)(x 2 − xy + y 2 ) b: (x − 3)(x 2 + 3x + 9)<br />

c: (2x − y)(4x 2 + 2xy + y 2 ) d: (x +1)(x 2 − x +1)<br />

12-74. y = 10<br />

216 (x + 6)3 −10<br />

12-75. a: 3C 1 i 10 C 3<br />

13C4<br />

= 360<br />

715 ≈ 0.503 b: 11<br />

13C4 = 1 65 = 0.015<br />

12-76. a: c a b: a b c: b a d: c a<br />

12-77. The solution is equivalent to the solutions of sin(x) = − 1 2<br />

and sin(x) = 0 . 90° + 180°n,<br />

210° + 360°n, 330° + 360°n; or<br />

2 π + π n, 7π 6<br />

12-78. 2x 2 + 4x −1<br />

12-79. a: x 2 (x + 2y)(x 2 − 2xy + 4y 2 )<br />

b: (2y 2 − 5x)(4y 2 +10xy 2 + 25x 2 )<br />

c: (x + y)(x 2 − xy + y 2 )(x − y)(x 2 + xy + y 2 )<br />

12-80. Possible equation: y = 1 8 (x − 3)3 + 3 Inverse: y = 3 8(x − 3) + 3<br />

12-81. y = 4(0.4) x + 5<br />

12-82. a: 126a 5 b 4 b: 1120x 4 y 4<br />

12-83. x 2 − 6x + 34 = 0<br />

12-84. P(3 or 4 or 5) ≈ 0.99<br />

104 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 12.2.1<br />

12-90. a: 1 b: cos(4w) c: tan(θ)<br />

12-91. ≈ 75.52°, 75.52°, and 28.96°<br />

12-92. a: x = 30º + 360ºn or x = 150º + 360ºn b: no solution<br />

12-93. 3x 2 − x + 2<br />

12-94. x 3 − 2x 2 − 3x + 9<br />

12-95.<br />

10!<br />

12-96. (5 – 2)! because 3! > 2!<br />

12-97. a: 18 b: –12 c: –1 + 7i d: –14.5 e: x = 0, –7<br />

12-98. a: p = 44, a = 20 b: y = 20 cos<br />

( 22<br />

(x −15) ) + 3<br />

12-99. Possibilities include: sin 2 x = 1− cos 2 x , sin x = ± 1− cos 2 x ,<br />

sin 2 x = (1− cos x)(1+ cos x)<br />

12-100. − 4 5<br />

12-101. a: sinθ<br />

cosθ b: 1<br />

sinθ<br />

cosθ<br />

sinθ d: 1<br />

12-102. a: y − 9 = 315<br />

(x − 2) or y =<br />

315<br />

12-103. They intersect at<br />

, 0) and (3, 10).<br />

12-104. a:<br />

2(x−1) b: 4x<br />

3x 2 +10x+3<br />

12-105. a: 41.41° b: 28.30°<br />

x − 306 b: y = 0.25(6)x<br />

12-106. roots: −0.4 ± 0.8i 6 ; vertex: (–0.4, 19.2); f (x) = 5(x + 0.4) 2 +19.2<br />

12-107. a: (0.9) 5 ≈ 0.59<br />

b: 10(0.9) 2 (0.1) 3 + 5(0.9)(0.1) 4 + (0.1) 5 ≈ 0.00856<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 105

Lesson 12.2.2 (Day 1)<br />

12-109. 90.21 feet or 4.71 feet<br />

12-110. a: 2x 4 − x 2 + 3x + 5 = (x −1)(2x 3 + 2x 2 + x + 4) + 9<br />

b: x 5 − 2x 3 +1 = (x − 3)(x 4 + 3x 3 + 7x 2 + 21x + 63) +190<br />

12-111. a: x = 3π 2 b: x = π 3 , 5π 3 c: x = π 4 , 5π 4 d: x = 7π 6 , 11π<br />

12-112. a: x ≈ 69.34 b: x ≈ 5.35<br />

12-113. a: 10 P 5 = 30, 240 b: 10 i 9 4 = 65, 610<br />

12-114. ( ±<br />

5 3 , 4 5 )<br />

12-115. (x + 4) 2 + (y − 6) 2 = 64 ; circle, center: (–4, 6), r = 8<br />

12-116. a: See graph at right below.<br />

b: The process has a lot of variability for the first 14 hours.<br />

There are two out-of-control points (one upper and one<br />

lower). Apparently an adjustment was made at hour 14<br />

because the process is much less variable, but now there are<br />

nine consecutive points above the centerline of 0.075.<br />

Apparently another adjustment was made at hour 22, but<br />

this apparently swung the process to the very low end.<br />

12-117. a: 2x+1<br />

3x−2<br />

b: x2 +2x+4<br />

x(4x+5)<br />

106 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

Lesson 12.2.2 (Day 2)<br />

12-118. a: (sinθ + cosθ) 2 =<br />

sin 2 θ + 2 sinθ cosθ + cos 2 θ =<br />

1+ 2 sinθ cosθ<br />

( ) =<br />

c: (tanθ cosθ) sin 2 θ + 1<br />

sec 2 θ<br />

( ) (sin 2 θ + cos 2 θ) =<br />

cosθ cosθ<br />

(sinθ)(1) = sinθ<br />

b: tanθ + cotθ =<br />

cosθ + cosθ<br />

sinθ =<br />

sin 2 θ+cos 2 θ<br />

= cscθ secθ<br />

12-119. See unit circle at right. θ = π 6 , 5π 6 , 7π 6 , 11π<br />

12-120. m∠B = 86.17º or 1.5 radians<br />

12-121. The equation of the parabola is y = 1 8 (x − 3)2 + 3 .<br />

It is a function; every input has only one output.<br />

12-122. a: x ≈ 1.839 b: x ≈ –1.839 c: x ≈ 1.839<br />

12-123. a: The two lines intersect at (8, 17).<br />

b: No solution; the lines are parallel.<br />

12-124. a: There is one way to choose all five.<br />

5!<br />

5!0!<br />

= 1 . In order to have the formula give a<br />

reasonable result for all situations, it is necessary to define 0! as equal to 1.<br />

b: There is one way to choose nothing.<br />

0!5! = 1<br />

12-125. AC = 10 inches<br />

12-126. Possible answer: f (x) = x 3 − 5x 2 + 8x − 6<br />

Selected Answers © 2013 CPM Educational Program. All rights reserved. 107

Lesson 12.2.3<br />

12-130. sin π 12 = sin π 3 − π 4<br />

12-131. a: sin π 3 + π 4<br />

( ) = 6− 2<br />

( ) = 6+ 2<br />

( ) = cos ( 7π 6 − 4<br />

π ) = − 6+ 2<br />

b: cos 3π 4 + π 6<br />

; cos π 12 = cos π 3 − π 4<br />

12-132. sin(x + x) = sin x cos x + cos x sin x = 2 sin x cos x<br />

( ) = 2+ 6<br />

cos(x + x) = cos x cos x − sin x sin x = cos 2 x − sin 2 x<br />

12-133. a: See graph at right.<br />

b: Possible answer: f (x) = − sin x<br />

c: cos x + π 2<br />

12-134. sin x + cos x<br />

( ) = cos x cos π 2 − sin x sin π 2 = − sin x<br />

12-135. Divide by x – 3, then solve the resulting quadratic; x = 1 ± i.<br />

12-136. a: 2 b: a – 2<br />

12-137. 3 C 1 ( 1 4 ) 2 3<br />

( 4 ) = 9<br />

64 ≈ 0.141 x<br />

108 © 2013 CPM Educational Program. All rights reserved. <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

  • Recommendations

Selected Answers for <strong>Core</strong> <strong>Connections</strong> <strong>Algebra</strong> 2

  • Page 2 and 3: Lesson 1.1.1 1-4. a: 1 2 b: 3 1-5.
  • Page 4 and 5: Lesson 1.1.3 1-34. a: The numbers b
  • Page 6 and 7: Lesson 1.2.1 (Day 2) 1-65. a: 2 b:
  • Page 8 and 9: Lesson 1.2.2 (Day 2) 1-91. a: x = y
  • Page 10 and 11: Lesson 1.2.4 1-112. a: A portion of
  • Page 12 and 13: Lesson 2.1.2 2-16. Answers will var
  • Page 14 and 15: Lesson 2.1.4 2-50. a: f (x) = (x +
  • Page 16 and 17: Lesson 2.2.1 (Day 1) 2-81. Possible
  • Page 18 and 19: Lesson 2.2.2 (Day 1) 2-107. a: y =
  • Page 20 and 21: Lesson 2.2.3 2-125. a and : Neither
  • Page 22 and 23: Lesson 2.2.5 2-162. x < 2, y = -(x
  • Page 24 and 25: Lesson 3.1.3 3-45. a: n = -2 b: x =
  • Page 26 and 27: Lesson 3.2.3 3-90. 2x 3(2x-1) = 2x
  • Page 28 and 29: Lesson 4.1.1 4-7. See graph at righ
  • Page 30 and 31: Lesson 4.1.3 4-40. a: (-2, -11); Th
  • Page 32 and 33: Lesson 4.2.2 4-83. x = -2, y = 3, z
  • Page 34 and 35: Lesson 5.1.2 5-26. See graph at rig
  • Page 36 and 37: Lesson 5.2.1 5-60. Domain: x > 0; R
  • Page 38 and 39: Lesson 5.2.3 5-84. Possible answer:
  • Page 40 and 41: Lesson 6.1.1 6-8. a: Their y- and z
  • Page 42 and 43: Lesson 6.1.3 6-35. See graph at rig
  • Page 44 and 45: Lesson 6.2.1 6-95. y = 3 x 6-96. In
  • Page 46 and 47: Lesson 6.2.3 6-127. a: y = 40(1.5)
  • Page 48 and 49: Lesson 7.1.1 7-3. a: The shape woul
  • Page 50 and 51: Lesson 7.1.2 (Day 2) 7-24. −∞ <

Lesson 7.1.4 (Day 1) 7-53. 15 ( 4 ,

Lesson 7.1.5 7-77. a: Same; π 3 an

Lesson 7.1.7 7-104. 420° a: π 3

Lesson 7.2.2 7-129. a: y = sin x

Lesson 7.2.4 7-158. a: Yes b: y = c

Lesson 8.1.1 (Day 2) 8-17. The func

Lesson 8.1.3 8-54. Stretch factor i

Lesson 8.2.2 8-87. Possible Functio

Lesson 8.3.1 8-120. a: -7 c: (x + 7

Lesson 8.3.2 (Day 2) 8-147. p(x) =

Lesson 8.3.3 8-169. (0, 0), (3, 0),

Lesson 9.1.2 9-22. a: The question

Lesson 9.2.1 9-50. a: When asked to

Lesson 9.3.1 9-75. a: They will not

Lesson 9.3.3 9-103. a: 667.87 lunch

Lesson 10.1.2 10-34. a: odds: t(n)

Lesson 10.1.4 11 10-62. a: ∑ (60

Lesson 10.2.1 (Day 2) 10-96. Calcul

Lesson 10.3.1 (Day 1) 10-145. x 7 +

Lesson 10.3.2 10-169. Robin: $11,88

Lesson 11.1.2 11-18. Answers should

Lesson 11.2.1 11-41. Theoretically,

Lesson 11.2.3 11-64. Upper bound: 2

Lesson 11.2.4 11-75. Yes, 20% is wi

Lesson 12.1.1 12-5. a: always b: ne

Lesson 12.1.3 (Day 1) 12-43. a: 30

Lesson 12.1.4 12-67. a: a c b: c b

Lesson 12.2.2 (Day 1) 12-109. 90.21

Lesson 12.2.3 12-130. sin π 12 = s

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Core Connections Algebra 2, 2013

Investigations and functions, transformations of parent graphs, equivalent forms, solving and intersections, inverses and logarithms, 3-d graphing and logarithms, trigonometric functions, polynomials, randomization and normal distributions, simulating sampling variability, analytic trigonometry, appendix a: sequences, appendix b: exponential functions, appendix c: comparing single-variable data.

  • Core Connections Algebra 1, 2013
  • Core Connections Geometry, 2013
  • Core Connections Integrated I, 2013
  • Core Connections Integrated I, 2014
  • Core Connections Integrated II, 2015
  • Core Connections Integrated III, 2015
  • Core Connections: Course 1
  • Core Connections: Course 2
  • Core Connections: Course 3
  • Section 1.1
  • Section 1.2
  • Chapter Closure
  • Section 2.1
  • Section 2.2
  • Section 3.1
  • Section 3.2
  • Section 4.1
  • Section 4.2
  • Section 5.1
  • Section 5.2
  • Section 6.1
  • Section 6.2
  • Section 7.1
  • Section 7.2
  • Section 8.1
  • Section 8.2
  • Section 8.3
  • Section 9.1
  • Section 9.2
  • Section 9.3
  • Section 10.1
  • Section 10.2
  • Section 10.3
  • Section 11.1
  • Section 11.2
  • Section 11.3
  • Section 12.1
  • Section 12.2
  • Section A.1
  • Section A.2
  • Section A.3
  • Appendix Closure
  • Section B.1
  • Section B.2
  • Section C.1

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Cpm algebra 2

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Home > CCA2 > Chapter 2 > Lesson 2.1.3

Lesson 2.1.1, lesson 2.1.2, lesson 2.1.3, lesson 2.1.4, lesson 2.1.5, lesson 2.2.1, lesson 2.2.2, lesson 2.2.3, lesson 2.2.4, lesson 2.2.5.

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Algebra Connections Preview

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Welcome to CPM e-books

Please open Chapter 11 from the menu on the left for a preview.

This chapter is typical of those in all of the CPM e-books. The actual e-book will also have bolded terms linked to the glossary and index, and additional links to related resources will be added this summer and in the future. The resources for the e-books will continue to evolve.

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  1. Algebra 2 Cpm Answers Pdf

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  2. Cpm Homework Answers Algebra 1

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  3. Cpm Algebra 2 Chapter 8 Answers

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  4. Algebra 2 Cpm Answers Pdf

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  5. [PDF] Core Connections Algebra 2, 2013 PDF

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  6. CPM Algebra 2

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  1. CPM Algebra Chapter 5 Problem 55

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COMMENTS

  1. Core Connections Algebra 2

    2-142. Answers will vary.<br /> $3.00<br /> 2-143. The second graph shifts the first 5 units left and<br /> 7 units up and stretches it by a factor of 4.<br /> 2-144. a: x 2 -1 b: 2x 3 + 4x 2 + 2x<br /> c: x 3 − 2x 2 − x + 2 d: y: (0, 2), x: (1, 0), (-1, 0), (2, 0)<br /> 2-145. a: (a, b) = ( 2, ± 1 2 ) b: (a, b) = ( 1 2 , ± 2 )<br />

  2. CPM Educational Program

    Core Connections: Course 1 Core Connections: Course 2 Core Connections: Course 3 Core Connections Integrated III, 2015 CPM homework help. Answers and solutions to CPM Educational textbooks. World class homework help, a private tutor in your pocket. Download for free and get better grades.

  3. Core Connections Algebra 2

    Find step-by-step solutions and answers to Core Connections Algebra 2 - 9781603281157, as well as thousands of textbooks so you can move forward with confidence. ... you'll learn how to solve your toughest homework problems. Our resource for Core Connections Algebra 2 includes answers to chapter exercises, as well as detailed information to ...

  4. CPM Homework Help : CCA2

    CPM Education Program proudly works to offer more and better math education to more students.

  5. Algebra 2 Common Core

    Get Ready! Section 1-1: Patterns and Expressions Section 1-2: Properties of Real Numbers Section 1-3: Algebraic Expressions Page 25: Mid-Chapter Quiz Section 1-4: Solving Equations Section 1-5: Solving Inequalities Section 1-6: Absolute Value Equations and Inequalities Page 51: Chapter Review Page 53: Chapter Test Page 54:

  6. Core Connections Algebra

    Section 1-1-2: Investigating the Growth of Patterns Section 1-1-3: Investigating the Graphs of Quadratic Functions Section 1-2-1: Describing a Graph Section 1-2-2: Cube Root and Absolute Value Functions Section 1-2-3: Function Machines Section 1-2-4: Functions Section 1-2-5: Domain and Range Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5

  7. CPM Homework Help : CC2 Lesson 3.1.1

    CPM Homework Help : CC2 Lesson 3.1.1 Lesson 3.1.1 3-7 3-8 3-9 3-10 3-11 Lesson 3.1.2 3-19 3-20 3-21 3-22 3-23 Lesson 3.2.1 3-34 3-35 3-36 3-37 3-38 Lesson 3.2.2 3-46 3-47 3-48 3-49 3-50 Lesson 3.2.3 3-59 3-60 3-61 3-62 3-63 Lesson 3.2.4 3-73 3-74 3-75 3-76 3-77 Lesson 3.2.5 3-82 3-83

  8. Chapter 3

    Chapter 3 2. Chapter 4 6. Chapter 5 0. Chapter 6 0. Generate Manual PDF Other Resources. Student: CPM eBooks (Student Version) ... CPM Student Tutorials / Algebra 2 Connections. Chapter 3 2 Articles CCA 7.1.2: 7-21 Student eTool (Desmos) ...

  9. CC Algebra 2 eTools

    CC Algebra 2 eTools. Generate Manual PDF Other Resources. Student: CPM eBooks (Student Version) ... Algebra Tiles (CPM) Data Representations (CPM) 3D Plotter (CPM) ... CCA2 1.1.2: 1-10 Student eTool (Desmos) Chapter 2 9 Articles CCA2 2.1.2: 2-12 Student eTool (Desmos) CCA2 2.1.3: 2-30 Transforming Parabolas (Desmos) CCA2 2.1.4: 2-43 Student ...

  10. CPM Homework Help : Homework Help Categories

    CPM Education Program proudly works to offer more and better math education to more students.

  11. Core Connections Algebra 2, 2013

    1 Chapter 1 Investigations and Functions 2 Chapter 2 Transformations of Parent Graphs 3 Chapter 3 Equivalent Forms 4 Chapter 4 Solving and Intersections 5 Chapter 5 Inverses and Logarithms 6 Chapter 6 3-D Graphing and Logarithms 7 Chapter 7 Trigonometric Functions 8 Chapter 8 Polynomials 9 Chapter 9 Randomization and Normal Distributions 10

  12. CPM Learning Platform for Mathematics

    Homework Help. Online step-by-step support for homework problems. CPM helps students and parents help themselves when practicing their math abilities at home. ... Many algebra teachers feel reenergized and are having more fun teaching math with the CPM approach. Algebra classes focus on both basic skills and problem solving strategies that are ...

  13. CCG-CCA-CCA2 Table of Contents

    Algebra, Geometry, & Algebra 2 Table of Contents Core Connections Algebra Chapter 1: Functions Section 1.1 1.1.1 Solving Puzzles in Teams 1.1.2 Investigating the Growth of Patterns 1.1.3 Investigating the Graphs of Quadratic Functions Section 1.2 1.2.1 Describing a Graph 1.2.2 Cube Root and Absolute Value Functions 1.2.3 Function Machines 1.2.4 Functions 1.2.5 Domain and

  14. Core Connections Course 2

    Find step-by-step solutions and answers to Core Connections Course 2 - 9781603280846, as well as thousands of textbooks so you can move forward with confidence. ... you'll learn how to solve your toughest homework problems. Our resource for Core Connections Course 2 includes answers to chapter exercises, as well as detailed information to ...

  15. Cpm Algebra 2 Teaching Resources

    It is a resource for printable homework and answers. CC2 Algebra 2 Course Includes most review/preview questions from the textbook PDF blank copy and answer key for the ... File is a Word document that you can revise if you need to. I used it with CPM Integrated Math 3 chapter 5 section 5. 2. 2 to give my students a little more practice in ...

  16. High School

    CPM Educational Program is a 501 (c) (3) educational nonprofit corporation. This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to ...

  17. CPM Homework Help : CC2 Lesson 2.2.3

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  18. Homework Help

    Homework Help Sample. CPM Educational Program ... and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources. Page 2 of the ... They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks.

  19. Algebra 2

    Find step-by-step solutions and answers to Algebra 2 - 9780130625687, as well as thousands of textbooks so you can move forward with confidence. ... Chapter 1:Tools of Algebra. Section 1.1: Properties of Real Numbers. Section 1.2: Algebraic Expressions. Section 1.3: Solving Equations. Page 24: Checkpoint Quiz 1. ... Extra Practice Chapter 2 ...

  20. CPM Homework Help : CCA2 Lesson 2.1.3

    CPM Education Program proudly works to offer more and better math education to more students.

  21. CPM Algebra Connections Preview

    Please open Chapter 11 from the menu on the left for a preview. This chapter is typical of those in all of the CPM e-books. The actual e-book will also have bolded terms linked to the glossary and index, and additional links to related resources will be added this summer and in the future. The resources for the e-books will continue to evolve.

  22. Core Connections Course 3

    Find step-by-step solutions and answers to Core Connections Course 3 - 9781603280914, as well as thousands of textbooks so you can move forward with confidence. ... you'll learn how to solve your toughest homework problems. Our resource for Core Connections Course 3 includes answers to chapter exercises, as well as detailed information to ...

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    Exercise 112. Exercise 113. Exercise 114. At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Core Connections Integrated 3 1st Edition, you'll learn how to solve your toughest homework problems.