a102 answers to odd-numbered exercises and...

A102 Answers to Odd-Numbered Exercises and Tests

21. (a)

(b) Reflection in the axis (no effect), vertical stretch, anda vertical shift seven units downward

(c)

22. (a) (b)

(c) (d)

23. 24. No inverse

25.

Chapter 2Section 2.1 (page 172)

Vocabulary Check (page 172)1. equation 2. solve

3. identities, conditional equations 4.

5. extraneous 6. Mathematical modeling

7. formulas

1. (a) Yes (b) No (c) No (d) No

3. (a) Yes (b) No (c) No (d) No

5. (a) No (b) No (c) No (d) Yes

7. Identity 9. Identity 11. Conditional equation

13. 15. 17. 12 19. 1 21.

23. 25. 27. 29. 10 31. 4

33. 5 35. 37. 39. No solution

41. 43. 45.

47. 49. 51.

53. 55. 57. 61.2 inches

59. (a) (b)

(c) 7.5 meters long 5 meters wide

61. (a)

(b) 97

63. 3 hours 65. miles per hour

67. (a) (b) 91.4 feet

69. $1950 71. $4000

73. $40,000 in DVD players; $10,000 in VCRs

75. 50 pounds of each kind 77. feet

79. (a) (b)

81. 83. feet

85. False. It is quadratic;

87.

89. Equations with the same solution set

91.

93. 95.

1412108642−4 −2

16

14

12

10

8

6

4

2

x

y

5

43

21

−3

−4−5

7 865431−1−2x

y

58

4x � 16 � 0, 2x � 8 � 0

9x � 27 � 0

3x � x2 � 10.⇒x�3 � x� � 10

x � 6

25

20

15

Time

Tem

pera

ture

(C

)°

10:0

0 A

.M.

11:0

0 A

.M.

12:0

0 P.

M.

1:00

P.M

.

2:00

P.M

.

3:00

P.M

.

4:00

P.M

.

5:00

P.M

.

6:00

P.M

.

24 � 12 � 8 inchesh

wl

h � 27

h

3 ft12

4 ft

80 ft

Not drawn to scale

�46.3

Test average �test 1 � test 2 � test 3 � test 4

4

�

l � 1.5w; P � 5w

w

l

R �PVnT

r �S

2�h

h �V

�r 2w �P � 2l

2b �

3V4�a2

r �S � aS � L

P � A�1 �rn�

�nth �

2Ab

53

116

1748�

65�10

�92081�

9623

ax � b � 0

f �1�x� � �83 x�2�3

, x ≥ 0

f �1�x� � 3�x � 8

�2 � x2, ��2, �22 � x, ��, 2

x2

�2 � x, ��, 2�x2 � �2 � x, ��, 2

21

1 2 3 4 5

−7

−2−3−4−5

−8

x

y

y-

f �x� � �x�

333370_02_ans_odd.qxp 1/3/07 2:28 PM Page A102

x 1.5 1.6 1.7 1.8 1.9 2

3.2x � 5.8 �1 �0.68 �0.36 �0.04 0.28 0.60

x �1 0 1 2 3 4

3.2x � 5.8 �9 �5.8 �2.6 0.6 3.8 7

97.

99. 101. 103.

Section 2.2 (page 183)

Vocabulary Check (page 183)1. -intercept, -intercept 2. zero

3. point of intersection

1. 3.

5. 7. No intercepts 9.

11. 13.

15–19. Answers will vary.

21.

23. 25. 6;

27.

29. 31.

33. 35. 2.172, 7.828

37. 39. 41.

43. 45. 47.

49. 51. 11 53. 21

55. (a)

Answers will vary.

(b)

Answers will vary. Sample answer:Use smaller intervals of to increase accuracy.

57. 59. 61. 63.

65. 67.

69.

71. (a) 6.46

(b) The second method decreases the accuracy.

73. (a)

(b)

(c) 164.5 miles

75. (a)

(b)

(c) 22.2 gallons

77. (a)

(b) (c) 16.7 units

79. (a) (b) $6800

(c) $7600 (d) $7500

81. (a)

In 1986, both states had the same population.

(b) In 1986, both states had the same population.

(c) Change in population per year; Arizona’s populationis growing faster.

(d) South Carolina: 4,443,000; Arizona: 6,379,000

Answers will vary.

83. True 85. False. The lines could be identical.

�6.7, 3388.7�;

�6.7, 3388.7�;

0 242000

6000

T � 10,000 �12x

00

20

240

A�x� � 12x

0 ≤ x ≤ 55

00

55

55

A � 0.33�55 � x� � x

0 ≤ x ≤ 280

00

280

10

t�x� �x

63�

280 � x

54

1.730.27 � 6.41.

�0, 0�, ��2, 8�, �2, 8��1.45, 1.90�, ��3.45, �7.90��4, 1�

��1, 3��8, �2��2, 2��1, 1�

x1.8 < x < 1.9;

1 < x < 2;

�1, 2.333

�1, 7±3.162�1.333

�0.717, 2.1070.5, �3, 3�1.379

�310; f �x� � 10x � 3 � 0

15; f �x� � 3x � 45 � 097; f �x� � 9 � 7x � 0

�194; f �x� � 0.20x � 38.8 � 0

f �x� � 7x � 42 � 08913; f �x� � 13x � 89 � 0

1223; f �x� � 2.3x � 1.2 � 0

�10, 0�, �0, 30��3, 0�, �0, �6�

−35

−10

40

40

−6

−8

12

4

�1, 0�, �0, 12��2, 0�, �0, 0�

��2, 0�, �1, 0�, �0, �2��5, 0�, �0, �5�

yx

�357�2580�28

1−1−2−3−5−6−7−8−9

3

2

1

−2

−4

−5

−6

−7

x

y

Answers to Odd-Numbered Exercises and Tests A103

CH

AP

TE

R 2



87. 3 89. 1 91. 93.

95. 97.


Vocabulary Check (page 193)1. (a) ii (b) iii (c) i 2.

3. complex, 4. real, imaginary

5. Mandelbrot Set

1. 3. 5.

7. 9. 11. 13.

15. 17. 19.

21. 23. 25.

27. 29. 31. 33. 24

35. 37. 25 39. 41

41. 43. 11

45. 47. 49.

51. 53. 55.

57. 59. 61.

63. (a) 8 (b) 8 (c) 8; Answers will vary.

65. 67. 69. 2

71. 73.

75.

77.

Yes, bounded

79.

81. False. Any real number is equal to its conjugate.

83. False. Example: which is not animaginary number.

85. True 87. 89.


Vocabulary Check (page 205)1. quadratic equation

2. factoring, extracting square roots, completing thesquare, Quadratic Formula

3. discriminant

4. position, initial velocity, initialheight

1. 3.

5. 7. 9. 11.

13. 15. 17. 16, 8

19. 21. 2 23.

25. 27. 29.

31.

33. (a) (b) and (c)

35. (a) (b) and (c)

37. (a) (b) and (c)

39. No real solutions 41. One real solution

43. No real solutions 45. 47.

49. 51. 53.

55. 57. 59. �121 ± 3

2i6, �12

1 ± �2�2 ±12

i�32

±�23

2i

34

±�23

4i1 ± �3

�2.5, 0�

−1

−1

5

3

��0.5, 0�, �1.5, 0�−9

−6

9

6

��1, 0�, ��5, 0�−12

−6

6

6

�54

±�89

4

1 ± �5 i1 ±�63

�3 ± �7

�8, 41 ± �6 i

3; 0.33 ± 0.82i

±7�a � b, �a � b

2, �63, �124, �20, �1

2

3x2 � 60x � 10 � 02x2 � 5x � 3 � 0

�16t2 � v0 t � s0,

3x2 �232 x � 216x2 � 25

�1 � i� � �1 � i� � 2,

3.12 � 0.97i

�0.1643 � 0.4778i, �0.2013 � 0.3430i;

0.5i, �0.25 � 0.5i, �0.1875 � 0.25i, �0.0273 � 0.4063i,

Realaxis4321−1−2−3

4

3

2

1

−2

−3

−4

Imaginaryaxis

Realaxis4321−1−2−3−4

4

3

2

1

−2

−3

−4

Imaginaryaxis

321

−2−3−4−5−6−7

7654321−1−2−3

Realaxis

Imaginaryaxis

5i4 � 3i

i�375�3 i�1 � 6i

62949 �

297949i�1

2 �52 i�

401681 �

91681i

35 �

45 i8

41 �1041i�6i

3 � ��2;��20 i; 20

�6 � �5 i;4 � 3i;80i

�20 � 32i5 � i�10

�2�3�4.2 � 7.5i196 �

376 i

�14 � 20i7 � 3�2 i�3 � 3i

0.3i�75�1 � 5i�6

5 � 4ia � 6, b � 5a � �9, b � 4

a � bi

��1, �1

4x2 � 813x2 � 13x � 30

3�8 � �11�53

4�35


t 0 2 4 6 8 10 12

s 1815 1751 1559 1239 791 215 �489

61. 63. 65.

67.

69.

71.

73.

75.

77. (a)

(b)

(c) Width: 34 feet; length: 48 feet

79.

81. (a)

(b)

(c) 10.65 seconds

83. (a) seconds (b) miles

85. (a) 1998 and 2000 (b) Answers will vary.

(c)

(d) 2006 (e) Answers will vary.

87. (a)

(b) (c) 2.5

89. Eastbound plane:

Northbound plane:

91. False. Both solutions are complex.

93. False. Imaginary solutions are always complex conjugatesof each other.

95. (a) and (b) (c) Answers will vary.

97. Proof 99. Answers will vary. 101. e

103.

105. 107. Function

109. Not a function 111. Function

113. Answers will vary.


Vocabulary Check (page 216)1. 2. extraneous 3. quadratic

1. 3. 5. 7.

9. 11. 13.

15. (a)

(b) and (c)

(d) They are the same.

17. (a)

(b) and (c)


19. 21. 26 23. 25.

27. 6, 7 29. 0 31. 0 33. 35. 9

37. 39. 41.

43. 45. 2, 3 47. 1

49. (a)

(b) and (c) (d) They are the same.

51. (a)

(b) and (c) (d) They are the same.x � 0, 4

−3

−0.5

5

0.5

x � 5, 6

−1

−5

11

3

�117, 133

�59, 691, �1258

112

14

�256.5�161009

��3, 0�, ��1, 0�, �1, 0�, �3, 0�

−5

−20

5

20

��1, 0�, �0, 0�, �3, 0�

−9

−7

9

5

2, �35�

15, �1

3±12, ±4

±1, ±�33, ±1�3, 00, ±2

n

�x � 5��x ��2��x ��2�x2�x � 3��x2 � 3x � 9�

x � �5, �103

�600 miles per hour

�550 miles per hour

16.8�C

1050

25

300

7 1420

80

� 3.73� 22.36

�10, 12�;

s � �16t 2 � 1815

14 centimeters � 14 centimeters

1632 � w2 � 14w

w

w + 14

x2 � 4x � 5 � 0; �x2 � 4x � 5 � 0

x2 � 2x � 11 � 0; 5x2 � 10x � 55 � 0

x2 � 75 � 0; x2

5� 15 � 0

21x2 � 31x � 42 � 0; 3x2 �317 x � 6 � 0

x2 � x � 30 � 0; 2x2 � 2x � 60 � 0

5 ± �174

32

�7 ± �734


CH

AP

TE

R 2


Year 1990 1991 1992 1993 1994

Number of lungtransplants 206 455 558 637 703

Year 1995 1996 1997 1998 1999

Number oflung transplants 762 815 864 909 952

Year 2000 2001 2002 2003 2004

Number oflung transplants 992 1031 1068 1103 1137


53. 55. 57.

59. 61. 63.

65.

67. (a) (b) and (c)


69. (a) (b) and (c)


71. 34 students 73. 191.5 miles per hour 75.

77. (a)

(b) 1991; 2000 (c) and (d)

(e) 2017, 2042; Answers will vary.

79. 26,250 81. 249,900

83. (a)

(b) (c) 24.725 pounds per square inch

85. False. For example, has two extraneoussolutions.

87.

89.

91. 93.

95. or 97.

99. 101. 103. 11


Vocabulary Check (page 228)1. negative 2. double 3.

4. 5. zeros, undefined values

1. f 2. a 3. d 4. b 5. e 6. c

7. (a) Yes (b) No (c) Yes (d) No

9. (a) No (b) Yes (c) Yes (d) No

11. 13.

15. 17.

19.

21. 23.

25. 27.

(a) (a)

(b) (b)

29. 31.

33. 35.

−1 0 1 2

x

14

34−35 −28 −21 −14 −7 0 7

x

14 < x < 3

4x < �28, x > 0

420 6 8 10 12 14

1 13x−3 −2 −1 0 1 2 3

x

1 < x < 13x < �2, x > 2

x ≤ 4x ≤ 32

�2 ≤ x ≤ 4x ≥ 2

−6

−2

6

6

−4

−5

8

3

x < 2x ≤ 2

−9

−6

9

6

−9

−6

9

6

−6 −4 −2

−

0 2 4 6

22

8

9 15

x

�92 < x < 15

2

−2 −1 0 1 2 3 4 5

x

2 3 4 5

x

�2 < x ≤ 5x ≥ 4

−2

2

−1

−

0 1

x

1

−4 −3 −2 −1

x

x < �12x > �4

x ≤ �a, x ≥ a

�a ≤ x ≤ a

�3z2 � 2z � 4z�z � 2�

256x

a � 4, b � 24a � 0, b � 18a � b � 9,

x � 6, x � �4x 4 � 3x2 � 4 � 0

x 4 �32 x3 � 6x2 �

72x � 3 � 0

x3 � 4x2 � 2x � 8 � 0

�x� � x2 � x � 3

211.6�F

5150

40

300

t � 1.4; t � 10.2

�4%

x � 1, �3

−10

−4

8

8

x � �1

−4

−24

4

24

�1 � �172

, 3

�3, �33, �21 ± �31

3

4, �5�3 ± �21

62, �

32


37. (a)

(b)

39. 41. 43.

45.

47. Positive on:

Negative on:

49. Positive on:

Negative on:

51. Positive on:

53. 55.

57. 59. No solution

61.

63. (a) (b) (c)

65. (a)

(b)

67. 69.

71. (a)

(b)

73. 75. 77.

79. (a) 1994 (b)

81. (a) 10 seconds (b)

83. (a) (b)

(c)

(d) No; Answers will vary.


87. 20.70; Answers will vary.

89. vibrations per second 91.

93. (a)

(b)

(c) Option B is the better option for monthly usage of upto 240 minutes. For more than 240 minutes, option Ais the better option.

(d) Sample answer: I would choose option A because Inormally use my cell phone more than 240 minutesper month.

95. False. 97. 99. iv, ii, iii, i

101. 103.

105. 107.



Vocabulary Check (page 237)1. positive 2. negative 3. fitting a line to data

4. �1, 1

y�1 � 3�x � 7y�1 �x

12

1

−2

−3

−4

−5

−6

−7

−8

−9

1−1−2−3−4−5−6−7−8−9x

y

642−4−6

8

4

2

−2

−4

x

y

a, b10 ≥ �x

0 4800

100

AB

A � 12 � 0.15x, B � 0.20x

1.2 < t < 2.433313

t ≥ 2.11;

1.28 < t < 10.09

�1991, 2000�

0 130

25

�4, 6��1990, 1994�; �1994, 2004�

��, �2, 2, ��, ��5, ��

2 < x ≤ 4

0 ≤ x < 2

−6

−4

12

8

−2 −1 0 1 2 3 4 5

x

−1−2 0 21

x

��, �1�, �4, ��, �1�, �0, 1�

0 ≤ x ≤ 2

x ≤ �1, x ≥ 3

−5

−2

7

6

x > 1x ≥ 1x � 1

−1 0 1 2 3

x

4 5−2−3−4

32

��3, �1�, �32, ��

−2 −1 0 1 2 3 4

x

�2, 0, 2, ��

x

−6 −5 −4 −3 −2 −1 0 1 2−8 −4−6

−

0 2 4−2

x7 3

��, �5, 1, ��7, 3��, ��

�2 � �102

, 2 � �10

2 ��,

2 � �102 �� 2 � �10

2, ��

��1, 5��, �1� � �5, ��

�x � 3� ≥ 5

�x � 7� ≤ 10�x� > 3�x� ≤ 3

x ≤ �1, x ≥ 7

1 ≤ x ≤ 5

−3

−1

9

7


CH

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R 2


1. (a) (b) Answers will vary.

3. Negative correlation 5. No correlation

7. (a)

(b) 0.95095

(c)

(d) The models appear valid.

9. (a)

(b) 0.90978

(c)

(d) The models appear valid.

11. (a) (b)

(c)

(d) 3.63 centimeters

13. (a) (b)

(c)

The model fits the data.

(d) 2005: $1,516,500; 2010: $2,197,000; Answers will vary.

(e) 136.1; The slope represents the average annual increasein salaries (in thousands of dollars).

15. (a)

(b) 0.99544

(c)

(d) Yes; answers will vary.

(e) 2005: $38.98; 2010: $46.74

(f) Answers will vary.

−1 150

60

C � 1.552t � 15.70;

−1 150

60

−1 50

1600

S � 136.1t � 836

−1 50

1600

d � 0.066F

d � 0.07F � 0.3

Force

Elo

ngat

ion

d

F20 40 60 80 100

1

2

3

4

5

6

7

−4

−1

8

7

y � 0.95x � 0.92;

y

x

(0, 2)

(1, 1)

(2, 2)

(5, 6)

(3, 4)

−1−2 1 2 3 4 5 6

1

2

3

4

5

6

y = x −32

12

−4

−1

5

5

y � 0.46x � 1.62;

y

x−1−2−4 1 2 3 4

−1

−2

−3

1

2

3

4

5

(−3, 0)(−1, 1)

(0, 2)(2, 3)

(4, 3)

y = x +23

53

Years of experience

Mon

thly

sal

es(i

n th

ousa

nds

of d

olla

rs)

y

x1 2 3 4

10

20

30

40

50

60



Year 1997 1998 1999 2000 2001

Actual T-values(in thousands) 1130 1182 1243 1307 1381

T-values frommodel (in thousands)

1183 1220 1256 1293 1330

Year 2002 2003 2004 2005 2006

Actual T-values(in thousands) 1475 1553 1308 1400 1505

T-values frommodel (in thousands)

1366 1403 1440 1477 1513


17. (a)

(b)

(c)

The model is not the best fit for the data.

(d) 542,000 people; answers will vary.

19. (a)

(b)

(c) The slope represents an increase of about 37 Targetstores annually.

(d) 2013

(e)

Answers will vary.

21. True. To have positive correlation, the values tend toincrease as increases.

23. Answers will vary. 25. (a) 10 (b)

27. (a) 5 (b) 1 29. 31.

33.

Review Exercises (page 242)1. (a) No (b) No (c) No (d) Yes 3.

5. 7. 9. 11.

13. September: $325,000; October: $364,000

15. (a) (b) meters

17. 19. 21.

23. 25. 27.

29. 31. 33.

35. 37. 39.

41. 43. 45.

47. 49. 51. 53.

55. 57.

59.

61. 63. 65. 67.

69. 71. 73. 75.

77. 79. 81.

83. 85.3 ± �33 i

2�2 ± �6i

�1 ± �612

12

, �56 ± �6

�4 ± 3�2�52, 3�1, 32�1, 4

�1, 50, 223, 5�3, 12

Realaxis4321−1−2−3−4

4

3

2

1

−2

−3

−4

Imaginaryaxis

321

−2−3

−7

−4−5−6

54321−1−2−3−4−5

Realaxis

Imaginaryaxis

4321

−2−3−4−5−6

54321−1−2−3−4−5

Realaxis

Imaginaryaxis

�3 � 2i1726 �

726 i1 � 6i�80

�4 � 46i3 � 9i�26 � 7i

40 � 65i3 � 7i2 � 7i

6 � 5i�4.5, �3.125�, ��3, 2.5��1, �2�x � 0.338, 1.307x � �1.301x � 2.2

�1, 0�, �8, 0�, �0, 8��3, 0�, �0, 3��3.5�C

h �643

8 m2 m

h

75 cm

x �73x � 6x �

12x �

113

x � 9

7 ± �174

�14, 32�

35

2w2 � 5w � 7

xy-

5 180

2000

T � 36.7t � 926; 0.79495

0 350

700

P � 0.6t � 512

0 350

700

CH

AP

TE

R 2


Year 2000 2001 2002 2003 2004

Population(in millions) 18.31 18.51 18.59 18.65 18.71

87. (a)

(b) 2001 (c) or 2001

(d) 2004 and 2008 (e) Answers will vary.

89. 91. 93.

95. 97. 5 99.

101. No solution 103.

105. 107. 109.

111. 2, 6 113. 115. 1, 3

117. Four farmers 119. 3%

121. (a)

(b)

(c) 2000 (d)

(e) 2012; Answers will vary. (f) Answers will vary.

123. 125.

127. 129.

131. 133.

135. 137.

139. 141.

143. 145.

147. 149.

151. (a)

(b) Yes. Answers will vary.

153. (a)

(b) Answers will vary. Sample answer:

(c) This model fits the data better.

(d) 24.7 meters per second

155. False. A graph with two distinct intercepts is not afunction.

157. False. A regression line can have a positive or negativeslope.

159. Answers will vary. 161.

163. (a) 1 (b) (c) (d)

Chapter Test (page 246)1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11.

12. 13. 0 14. 15. 1, 9±1, 0±0.5

±1.414

321

−2−3−4−5−6−7

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215x � 3

�i�1i

��6��6 � 6i2 � �6

y-

s � 9.70t � 0.4;

S � 10t � 0.4

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eed

(in

met

ers

per

seco

nd)

t1 2 3 4

5

10

15

20

25

30

35

40

s

Exam score

Gra

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ave

rage

y

x65 70 75 80 85 90 95

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4

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16. 17. 18. 19.

20. 2 21. 22.

23. 24.

25. 26.

27. 0.99622; 2005

Cumulative Test for Chapters P–2 (page 247)

1. 2. 3.

4. 5. 6.

7. 8.

9.

10. Midpoint:

11.

12. 13.

14.

15. (a)

(b) Answers will vary. Sample answer:

16. (a)

(b) Answers will vary.Sample answer:

17. (a)

(b) Answers will vary.

Sample answer:

18. (a) (b)

19. (a) (b) Undefined (c)

20. (a) (b) 4 (c) 20 21.

22. 23.

24. 25. Odd

26. No. It doesn’t pass the Vertical Line Test.

27. Decreasing on

Increasing on

28. (a) Vertical shrink (b) Vertical shift two units up

(c) Horizontal shift two units left, reflection in axis

29. 30. 31.

32. 33.

34. 35. 0, 1, 2

36. 37. 38. 4.444

39. 40.

41. 42.

43. inches

44. (a)

(b)

(c) feet 196.8 feet�� 76.2

0 < x < 273

00

273

25,000

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x

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12

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CH

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TE

R 2


a102 answers to odd-numbered exercises and...

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