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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 />

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 />

Lesson 1.1.2 (Day 2)<br />

1-19. y = 30 – x<br />

Graph and table shown at right.<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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

Lesson 2.1.2<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 />

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 />

2-27. 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 />

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 />

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 />

Lesson 2.1.5<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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

\$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 />

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

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

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 />

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 />

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 />

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 />

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 />

3-93. 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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

5-77. 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 />

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 />

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 />

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 />

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 />

Lesson 6.1.3<br />

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

6-36. Yes.<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 />

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 />

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 />

6-99. 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 />

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 />

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 />

6-130. 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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

7-161. a: 180º b: 540º c: π 6 radians<br />

d: 45º e: 5π 4<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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

9-39.<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 />

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 />

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 />

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 />

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 />

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 />

9-77. 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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

% 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 />

11-22. 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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

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 />

because the process is much less variable, but now there are<br />

nine consecutive points above the centerline of 0.075.<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 />

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 />

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 />

• 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 11.2.1 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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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.

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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 />

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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

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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

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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

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