Alg 2 Practice Answers

Practice Workbook Answer Key To jump to a location in this book 1. Click a bookmark on the left. To print a part of the book 1. Click the Print button. 2. When the Print window opens, type in a range of pages to print. The page numbers are displayed in the bar at the bottom of the document. In the example below, “1 of 151” means that the current page is page 1 in a file of 151 pages.

Answers Practice — Chapter 1

2

Lesson 1.1 1. yes 2. yes 3. no 6. yes 7. yes 8. no 11. no 12. yes

4. yes 9. yes

5. no 10. no

5. y ⴝ

1 6

xⴙ

11. m ⴝ ⴚ

3

6. y ⴝ

3

6

15. y ⴝ

4 2

O

2

4

6

8

x

5 6

bⴝ

xⴙ

Lesson 1.3 1. y ⴝ x ⴙ 3. y ⴝ ⴚ

y

5

7. y ⴝ x

6

4

12. y ⴝ ⴚ

15.

8

x

1 2

xⴙ xⴚ

14. y ⴝ ⴚ4

8

5

4

2

4

6

8

16. (6, 19) 17. (4, 20) 18. not linear 19. (ⴚ4, 23) 20. (8, ⴚ29) 21. (5, ⴚ14)

xⴙ

1

11 10

x ⴙ 9. y ⴝ x ⴚ 11. y ⴝ ⴚ x ⴚ 13 y ⴝ ⴚ x ⴙ 15. y ⴝ x ⴚ 17. y ⴝ ⴚ x ⴙ 19. y ⴝ ⴚ x ⴚ 3

1

4

.

3

7

3

5

4

5

1

1

2

21. y ⴝ

1 2

xⴚ

3

24. y ⴝ ⴚ

xⴚ

25. y ⴝ

26. y ⴝ ⴚ

xⴚ

1

2

28. y ⴝ x ⴙ 2 30. y ⴝ

4 3

xⴙ

32. y ⴝ ⴚ

1

4

2

4

xⴚ

27. y ⴝ ⴚ

1

4

29. y ⴝ ⴚ

4

3

1

3

3

10

xⴙ

xⴙ

31. y ⴝ ⴚ

8

xⴚ

1 2

5

1

23. y ⴝ ⴚ2x ⴙ 8

1

x

3

2

22. y ⴝ ⴚ3x ⴙ 3 3

2

4 5

xⴙ

3

20. y ⴝ 3x ⴚ 4

6

bⴝⴚ

3

2

18. y ⴝ 4x ⴚ 16

8

6. y ⴝ 2

16. y ⴝ 2x ⴙ 15

y

Algebra 2

4. y ⴝ ⴚ

8 5

2 6

,

2. y ⴝ ⴚx ⴙ 2

2

10. y ⴝ 4x ⴚ 13

4

3

xⴙ

3

1

4

2

14. m ⴝ ⴚ3, b ⴝ ⴚ7

8. y ⴝ ⴚ 1

7. ⴚ

4

8

16. y ⴝ ⴚ

4

2

xⴙ

5

3

2

5. y ⴝ ⴚ9x ⴚ 13

8

4

2

12. m ⴝ ⴚ

3

3

xⴙ

1

1

xⴚ

4 5

10. 3

13. m ⴝ ⴚ2, b ⴝ ⴚ4

8

Copyright © by Holt, Rinehart and Winston. All rights reserved.

,

4. y ⴝ

3

9. 1

57 100

4

14.

2. y ⴝ 3x ⴙ 1

5

4

8.

y

13.

Lesson 1.2 1. y ⴝ x ⴚ 3. y ⴝ ⴚ x ⴙ

7 2

2

x

15 4

1

Answers Lesson 1.4 1. k ⴝ ⴚ y ⴝ ⴚ x 5;

3. k ⴝ ⴚ

4 3

5. k ⴝ

2 7

;

;

2. k ⴝ

5

7 3

;

yⴝ x 7

3

3. y 艐 ⴚ3.26x ⴚ 4.5; negative y

y ⴝ ⴚ x 4. k ⴝ y ⴝ x 4

1

3

4

10

1

;

4

5

O

6

–10

y ⴝ x 6. k ⴝ y ⴝ x 2

5

7

6

7. k ⴝ 2; y ⴝ 2x

8. k ⴝ ⴚ3; y ⴝ ⴚ3x

9. x ⴝ 3

10. x ⴝ 4

12. x ⴝ 10

13. z ⴝ

15. x ⴝ ⴚ1

;

11. y ⴝ

16. z ⴝ

18. no; there is no constant, k, such that y ⴝ kx 19. yes; y ⴝ 2x

(1, –2)

(7, –26)

(9, –34) –40

4. y ⴝ 0.01x ⴙ 0.24

Lesson 1.6 1. x ⴝ 2. x ⴝ 5. x ⴝ 6. x ⴝ 2

y

9

(0, 4)

O

10

20

(2, 10)

10

O

2

4

6

8

10

x

19. x ⴝ ⴚ4

5

20. x ⴝ ⴚ6

21. x ⴝ ⴚ

V

24. r ⴝ π

6

7

C

2

Lesson 1.7 1. x ⱖ ⴚ 4. x ⱕ ⴚ

22. x ⴝ

1 2

VP

25. P ⴝ V 2

1

T ⴚT 27. a ⴝ z ⴚ z

1

0

2. x ⬎ 2

3. x ⱕ 2

4

x

–10 –5 –20

–30

–4

–3

–2

–1

0

1

–2

–1

0

1

2

3

(6, –20.15)

(8, –27.45)

5.

xⱕ –3

2

2

0

A 28. h ⴝ a ⴙ b

3

(0, 1.9)

6

22

26. qp ⴝ D ⴛ Q

2. y 艐 ⴚ4.44x ⴙ 8.85; negative y

1

3

5

18. x ⴝ ⴚ

q

x

2

16. x ⴝ ⴚ

1

3

23. W ⴝ LD

(2, 10)

2

1

x Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

18

4. x ⴝ 6

xⴝ 13. x ⴝ ⴚ

10.

1

15. x ⴝ ⴚ

17. x ⴝ 18

(6, 22)

6. 0.360

7. x ⴝ ⴚ2

12. x ⴝ ⴚ21

14. x ⴝ 7

(8, 28)

27

9. x ⴝ

11. x ⴝ 16

4; positive

3. x ⴝ 9

5

8

8. x ⴝ ⴚ3

3

5. r 艐 0.96

7

8

Lesson 1.5 1. y ⴝ x ⴙ

x

10

2

17. yes; y ⴝ 3x

3

8

–30

4

1

6

(2, –18)

5

2

4

–20

9

14. y ⴝ ⴚ

5

2

Answers 6. no solution

11

8. x ⬍ 5

7. x ⱖ ⴚ2 –4

–3

–2

–1

0

1

2

x

–4

–2

0

2

4

6

x

150

160

Lesson 1.8 1. ⴝ 2

and x

–8

–6

170

180

190

200

x

0

–4

–2

0

2

4

4

6

8

10

–2

0

2

4

0

2

4

–2

0

2

2

4

6

8

0

1

2

3

x

2

x

Copyright © by Holt, Rinehart and Winston. All rights reserved.

3. x ⴝ ⴚ6 and x ⴝ 1 –8

4. x ⴝ 59 –8

–6 and x

–6

–4

x

ⴝ ⴚ3 –4

–2

x

5. x ⴝ ⴚ10 and x ⴝ 2 –10

–8

–6

–4

x

6. x ⬍ 1 and x ⬎ ⴚ95 –4

7. x ⬍ 67 –3

Algebra 2

–2

and x

–2

0

x

1

⬎6 –1

–8

–6

–4

2

3

x

3 –2

0

2

4

6

x

–6

–4

–2

0

2

4

6

x

Practice — Chapter 2

ⴝ ⴚ8

2. x ⴝ 10 and x ⴝ ⴚ2 –2

1

10. x ⱕ ⴚ 2.5 or x ⱖ 5

9. 162 ⬍ t ⬍ 192

x

0

1

⬎5

9. x ⬍ ⴚ 7 or x ⬎

8. x ⬍ 5 –6

and x

x

Lesson 2.1 1. rational, real 2. irrational, real 3. irrational, real 4. rational, real 5. integer, rational, real 6. rational, real 7. Inverse Property of Addition 8. Identity Property of Multiplication 9. Associative Property of Addition 10. Inverse Property of Multiplication 11. Commutative Property of Multiplication 12. Distributive Property 13. Identity Property of Addition 14. ⴚ33 15. 4 16. 43 17. 43 18. 49 19. 28 20. 26 21. 7.2 22. 56 23. 90

3

Answers Lesson 2.2 1.

6.

11.

16.

21.

24.

28.

1

9 25

2.

1

ⴚ15

7.

25 9 z17

32 x14 81x12y 20

8.

12.

25.

1

xy 3z 4

29.

1 ⴚ217 2 16 1 1 w 4y 2z2 d k8 1 y 5z 1 x 35 16a12b4c 24 125a6b 9 w18 16m12p4 k3

13.

17.

x4 w 2z 8

36 32

3.

4.

9.

10.

14.

18.

22.

15.

19.

20.

23.

a4 b6

1

5.

26.

xy 6

30.

27.

81x 26y 2

6.

7.

3.

4.

5.

8.

9.

10.

Lesson 2.4 1. ( f ⴙ g)(x) ⴝ 8x 2 ⴙ 5x ⴚ 13; ( f ⴚ g)(x) ⴝ 6x 2 ⴙ 5x ⴙ 13 2. ( f ⴙ g)(x) ⴝ 13x 2 ⴚ 5x ⴙ 41; ( f ⴚ g)(x) ⴝ ⴚ13x 2 ⴚ 5x ⴙ 41 20 3. ( f ⴙ g)(x) ⴝ x 2 ⴚ 3 x ⴙ 2; ( f ⴚ g)(x) ⴝ x 2 ⴙ 223 x ⴙ 16

4

(( )( )() ) 7 3 1 17 (( )( )() ) ,256; (( )( ))( ) , 8 f g

x ⴝ xⴙ 6. f ⴢ g x ⴝ x 3 ⴙ f g

x 2 ⴙ 25

f g

x 2 ⴙ 16

x 2 ⴙ 75x ⴙ 425;

2

x ⴝ 3x ⴙ 17 x ⴝ ⴚ53 7. f ⴢ g x ⴝ x 4 ⴚ

9. ( f ⴚ g)(x) ⴝ ⴚ3x ⴚ 12

10. ( g ⴚ f )(x) ⴝ 3x ⴙ 12

11. ( f ⴢ g)(x) ⴝ ⴚ2x2 ⴚ 22x ⴚ 20

() (( ) )( ) f

2x ⴙ 2

12. g (x) ⴝ ⴚx ⴙ 10 , x ⴝ ⴚ10 g x ⴙ 10 13. f (x) ⴝ ⴚ2x ⴙ 2 , x ⴝ ⴚ1 14. f ⴰ g x ⴝ x ; (g ⴰ f )(x) ⴝ x

15. ( f ⴰ g)(x) ⴝ 4x2 ⴚ 4; (g ⴰ f )(x) ⴝ 16x2 ⴚ 1

16. ( f ⴰ g)(x) ⴝ ⴚx 2 ⴙ 1; (g ⴰ f )(x) ⴝ ⴚx 2 ⴙ 1 17. ⴚ44 18. ⴚ52 19. ⴚ10 20. ⴚ5 21. ⴚ5 22. 22 23. ⴚ55 24. ⴚ28 25. 44

Lesson 2.5 1. {(ⴚ16, ⴚ1), (ⴚ6, 0), (14, 2)}; yes; yes 2. {(2, 7), (3, 6), (4, 7), (5, 6)}; no; yes 3. {(16, ⴚ2), (1, ⴚ1), (1, 1), (16, 2)}; yes; no 4. {(7, ⴚ5), (7, ⴚ3), (7, ⴚ1), (7, 1)}; yes; no 5. {(4, ⴚ5), (9, ⴚ3), (12, 1), (13, 7)}; yes; yes 6. f ⴚ1(x) ⴝ 3x ⴚ 1 3x ⴚ 1 7. hⴚ1(x) ⴝ 2 Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

yes yes no yes yes no yes no domain: 再ⴚ1, 0, 21 , 23 冎 ; range: {ⴚ3, 1, 3, 7} domain: x ⱖ ⴚ5; range: y ⱖ ⴚ2 11. domain: {ⴚ4.5, 3, 6.5, 12}; range: {6, ⴚ1.5, ⴚ5, ⴚ10.5} 12. domain: {ⴚ2, 0, 1, 5}; range: {12, 8, 9, 33} 13. f (ⴚ2) ⴝ ⴚ44; f (8) ⴝ 156 14. f (ⴚ3) ⴝ 45; f (5) ⴝ 125 15. f (7) ⴝ ⴚ9; f (ⴚ5) ⴝ 27 16. f (11) ⴝ 361; f (ⴚ4) ⴝ 46 17. f (0.5) ⴝ 1.25; f (0) ⴝ 0 2.

5. ( f ⴢ g)(x) ⴝ 175x ⴙ 25;

x ⴝ x 2 ⴚ 16 x ⴝ ⴚ4 and x ⴝ 4 8. f ⴙ g x ⴝ ⴚx ⴙ

Lesson 2.3 1.

4. ( f ⴙ g)(x) ⴝ 3x 2 ⴙ 6; ( f ⴚ g)(x) ⴝ ⴚ21x 2 ⴙ 6

Answers 8. gⴚ

1

9.

(x)

ⴚ1(x) f

10. gⴚ

1

11. hⴚ

(x)

1

(x)

12.

ⴝ

x

Lesson 2.6

ⴙ4

y

1.

11

ⴝ 2x ⴙ 2.5

4

x

ⴝ ⴚ2 8

2

ⴝ 4x ⴙ 32 y

–4

–2

O

2

4

2

4

2

4

x

–2 16

–4

12 8

–4

–2

y

2.

4

O

2

4

4

x

2 –4

not a function

–2

x

–2

y

13.

O –4

8

Copyright © by Holt, Rinehart and Winston. All rights reserved.

4 –2

–1

O

1

2

x

y

3. 4

–4

2

–8 –4

y

14.

x

–4

8

O –4 –8

4. f (x) ⴝ ⴚ2 if x ⱕ ⴚ4, f (x) ⴝ x if ⴚ4 ⬍ x ⬍ 2, f (x) ⴝ 1 if x ⱖ 2 1

2

4

function

O –2

function

–2

–2

1

2

x

5. f (x) ⴝ x ⴙ 3 if x ⱕ ⴚ3, ⴚ3 ⬍ x ⬍ 0,

f (x )

ⴝ 0 if

ⴝ x if x ⱖ 0

6. f (x) ⴝ x ⴚ 2 if x ⬍ 0, f (x)

f (x)

f (x)

ⴝ 0 if x ⴝ 0,

ⴝ x ⴙ 2 if x ⬎ 0

7. ⴚ10 8. 32 9. 13.13 10. 0 11. 7 12. ⴚ7.5 13. 1.5 14. 1 15. ⴚ19 16. ⴚ7 Algebra 2

5

Answers 6. independent; (1, 6) 7. (6, ⴚ1)

10. (ⴚ4, 8)

Lesson 3.1 1. independent; (0, 4) 2. dependent; infinitely many solutions 3. independent; (ⴚ1, ⴚ1) 4. inconsistent; no solution 5. independent; (1, 3)

6

11. (ⴚ8, 5)

( ) 12. ( 3, 12 )

9. 12 , 4

Lesson 3.2 1. (2, ⴚ1) 2. no solution 3. (6, 2) 4. (3, 0) 5. (4, ⴚ3) 6. no solution 7. (ⴚ9, ⴚ4) 8. infinitely many solutions 9. (8, 8) 10. (ⴚ4, 1) 11. (2, ⴚ1) 12. (ⴚ3, 3) 13. (1, ⴚ2) 14. (5, ⴚ8) 15. 12 , 12 16. (1, 7) 17. 12 , 3 18. infinitely many solutions 19. 13 , 23 20. (3, 10) 21. no solution

( )

( )

( ) 22. ( 14 , 1 )

( )

23. 23 , 2

24. (11, ⴚ3)

Lesson 3.3 y

1. 4 2

ⱍⱍ

Practice — Chapter 3

8. (12, 1)

Copyright © by Holt, Rinehart and Winston. All rights reserved.

Lesson 2.7 1. a horizontal translation 7.5 units to the left 2. a vertical translation 7.5 units up 3. a horizontal compression by a factor of 52 4. a vertical stretch by a factor of 2 and a reflection across the x-axis 5. a vertical stretch by a factor of 14 and a vertical translation 6 units up 6. a vertical stretch by a factor of 12 and a horizontal translation 7 units to the right 7. a translation 21 units to the left 8. a vertical stretch by a factor of 17 9. a horizontal stretch by a factor of 2 10. a vertical translation 13.7 units up 11. a vertical stretch by a factor of 3 and a reflection across the x-axis 12. a vertical stretch by a factor of 41 and a horizontal translation 8 units to the right 13. g(x) ⴝ ⴚx 3 14. g(x) ⴝ (x ⴙ 7)5 x 15. g(x) ⴝ (26x)4 16. g(x) ⴝ 12 17. g(x) ⴝ ⴚ32 x ⴙ 9 18. g(x) ⴝ x3 ⴚ 33

–4

–2

O

2

4

2

4

x

–2 –4

y

2. 4 2 –4

–2

x

–2 –4

Algebra 2

Answers y

3.

7a. 8x ⴙ 12y ⱕ

2 –4

–2

O

2

4

32

x

24

–2

16

–4

8

O

y

4.

y

b.

4

400

10

20

c. 50 hours; 33

4

1 3

2 –4

–2

O

2

4

x

Copyright © by Holt, Rinehart and Winston. All rights reserved.

4 2 –4

–2

–2

O

4

–2

2

–4

O

2

4

x

2

4

2

4

x

y

2.

–2

–4

4 2

y

6.

hours

y

1.

y

–4

x

40

Lesson 3.4

–4

5.

30

–4

–2

x

4 –4

2 –4

–2

O

2

4

x

–2

–4

Algebra 2

7

Answers Lesson 3.5

y

3.

2 –4

–2

O

2

4

8

x

6

–2

4.

再

再

4 2

yⱕ4 y ⱖ 2x ⴚ 4 y ⱖ ⴚ2x ⴚ 4

O

xⱕ4

6

8

2

4

6

8

2

4

6

8

x

6 4

yⱖ1

2

O

y ⱕ ⴚx ⴙ 5

y

3.

x ⴙ y ⱕ 30 6x ⴙ 7y ⱖ 126

x

8

y

6 4

30

2

15

O

O

15

30

x

x

4. maximum: 41; minimum: 4

5. maximum: 17; minimum: ⴚ12 6. maximum: 12; minimum: ⴚ7 7. maximum ⴝ 50 minimum ⴝ 0

maximum ⴝ 68 minimum ⴝ 0 9. maximum ⴝ 200 10. maximum ⴝ 62 minimum ⴝ 20 minimum ⴝ ⴚ25

8

8.

Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

再

4

8

1 6. y ⬍ 2 ⴙ 2 7.

2

y

2.

5. y ⱖ ⴚ x 1 y ⬍ 2x ⴙ 3

再

y

1.

4

Answers Lesson 3.6

10a.

y

1.

b.

4 2 –4

O

–2

2

4

y

200 100

–6

O

y

2000

4000

x

11a. 25 seconds b. 3750 feet

4 2

O

2

4

6

8

x

–2 –4

y

3. 6

Copyright © by Holt, Rinehart and Winston. All rights reserved.

y t

ⴝ 150t ⴝ 12t

300

–4

4 2 –6

–4

O

–2

–2 –4

4. y ⴝ 21 x ⴚ 14 5. y ⴝ 6x ⴙ 2

6. y ⴝ ⴚ21 x ⴙ 8

7. y ⴝ ⴚ21 x ⴙ 16 8. y ⴝ 31 x ⴚ 2 2

9. y ⴝ x9 ⴙ 1

Algebra 2

x t

400

x

–2

2.

再 (( ))

2

x

Practice — Chapter 4 Lesson 4.1 1. 2 ⴛ 2 2. 2 ⴛ 2 3. 3 ⴛ 3 4. 3 ⴛ 3 ⴚ2 ⴚ4 ⴚ2 5. ⴚ3 ⴚ3 ⴚ6 ⴚ7 0 5 6. not possible; the matrices do not have the same dimensions. 0 ⴚ6 7. 冤 ⴚ3 12 冥 7 4 8. 冤 4 ⴚ3 冥 ⴚ7 ⴚ4 9. 冤 ⴚ4 3冥 7 5 0 10. 6 7 14 20 ⴚ2 ⴚ8 ⴚ6 6 8 11. 0 ⴚ2 ⴚ4 ⴚ12 4 ⴚ4

冤

冥

冤 冤

冥

冥

9

Answers 7 6 12. 3 2 4 1 2 ⴚ7 14 ⴚ2 13. 冤 3 14 冥 14. 3 ⴛ 3 15. 101 medals 16. 90 gold medals 17. the number of bronze medals, 27, won by Germany 18. Gold Silver Bronze United States 44 32 25 Germany 20 18 27 Russia 26 21 16 China 16 22 12

冤

ⴚ1

冥

冤

冤 冤

冤 冥

10

冥

冤1134

11.

y

6

Y'

4 X'

X

Y

2

–6 –4

2 –4

x

Z

–6

Z'

3

12. an enlargement by a factor of 2

Lesson 4.3 1. yes 2. yes 5. yes 6. yes

3. no

冤 ⴚ34

4. yes ⴚ5

7冥 4 ⴚ7 8. D ⴝ 1; inverse: 冤 ⴚ5 9冥 1 ⴚ1 9. D ⴝ 5; inverse: 冤 ⴚ1.4 1.6 冥 2 ⴚ3 10. D ⴝ 2; inverse: 冤 ⴚ3.5 5.5 冥 11. D ⴝ 0; no inverse 1 ⴚ0.75 12. D ⴝ 4; inverse: 冤 3.25 冥 ⴚ4 ⴚ1 1 13. 冤 3 ⴚ2 冥 ⴚ3.5 3 14. 冤 2.5 ⴚ2 冥 15. no inverse 7. D ⴝ 1; inverse:

冥

6

Copyright © by Holt, Rinehart and Winston. All rights reserved.

Lesson 4.2 ⴚ1 45 1. 冤 ⴚ9 44 冥 2. [ⴚ20 4] 3. does not exist 4 ⴚ6 4. 冤 7 4冥 10 ⴚ10 5 5. 2 ⴚ2 1 6 ⴚ6 3 32 13 6. 12.5 4 18 3 2 3 7. ⴚ5 0 8. does not exist

冥

32 ⴚ8 冥 10. X ⴕ(ⴚ3, 0), Y ⴕ(6, 6), Z ⴕ(3, ⴚ6) 9.

Algebra 2

Answers 16.

冤ⴚ

1

3

2

ⴚ5

冥

11.

17. no inverse

18.

冤

4

5

2

3

冥

12.

Lesson 4.4

1.

2.

3.

Copyright © by Holt, Rinehart and Winston. All rights reserved.

4.

5.

6.

7.

8.

9.

10.

冤 冤 冤

ⴚ1

ⴚ1 ⴚ1

3

2

2

1

5

ⴚ2

1

ⴚ1

4

ⴚ1

4

ⴚ8

3

再 再 冤 冤 冤

冤 冤

9

ⴚ5

3

1

4

ⴚ3

1

ⴚ1 ⴚ2

x ⴚ19 21 y ⴝ ⴚ7 z

13.

x 13 y ⴝ ⴚ1 6 z

14.

冥冤 冥 冤 冥 冥冤 冥 冤 冥 冥冤 冥 冤 冥

1

3

1.

x ⴙ 3y ⴚ z ⴝ 1 3x ⴙ 4y ⴙ z ⴝ 6 ⴚx ⴚ y ⴙ 2z ⴝ 7

2.

x ⴙ 2y ⴚ z ⴝ ⴚ6 2x ⴙ 3y ⴙ z ⴝ 1 4x ⴙ 4y ⴙ 3z ⴝ 20 3

4

7

3.

冥冤 冥 冤 冥 ⴚ 冥冤 xy 冥 ⴝ 冤 冥 ⴚ ⴚ x ⴝ ⴚ ⴚ 冥冤 ⴚ y冥 冤 冥 7

ⴚ9

x ⴝ y

5

; (5,

14

3

9

; (

4

3

7

25

8

27

4 8

1

1

ⴚ4 ⴚ7

0

5

9

3

ⴚ3

5

5

6

ⴚ2

7

5

0

Algebra 2

1,

冥冤 冥 冤 冥 冥冤 冥 冤 冥 x y ⴝ z x y ⴝ z

4.

3, 7)

; (

5

5)

65

5

5.

4)

1 2

; (0.5,

ⴚ3, 2)

6.

3

13 10 18

; (4,

3 3

冥冤 冥 冤 冥冤 冥 冤 冥冤 冥 冤 冥冤 冥 冤 x y ⴝ z

ⴚ2 ⴚ3 1

1

ⴚ2 ⴚ4

1

ⴚ2

1

3

1

ⴚ2

5

ⴚ10

5

12

7

1

3

4

2

5

3

ⴚ3

8

1

5

2

ⴚ1 ⴚ9

12

1

5

x y ⴝ z

3

12 15

15 8

21

x ⴚ5 y ⴝ 3 z 12 x 0 y ⴝ ⴚ3 z 8

冥 冥 冥 冥

; (3, 9,

ⴚ6)

; no solution

ⴚ3, 5, ⴚ4)

; (

ⴚ1, 10, 2)

; (

Lesson 4.5

x 6 y ⴝ 2 ⴚ 1 z

2

8

冤 冤 冤 冤

1

ⴚ2, ⴚ1)

7.

冤 冤 冤 冤 冤 冤 冤

M M M

4

5

1

7

9

2

1

1

1

2

1

5

6

7

8

ⴚ3 M 1 M ⴚ3 M

1

1

1

2

3

3

6

7

3

1

0

0

0

1

0

0

0

1

1

0

0

0

1

0

0

0

1

1

0

0

0

1

0

0

0

1

1

0

0

0

1

0

0

0

1

2 7 2

冥 4 6 2

M ⴚ1 4 M M 8 M 1 M ⴚ2 M ⴚ1 M ⴚ2 1 M M ⴚ1 M M M

1 3 2

冥 冥 冥 冥

冥

M 2 M ⴚ1 M 4

冥 11

Answers 0 0 M 3 1 0 M ⴚ2 8. 0 1 M 1 0 0 M 0 1 0 M 5 9. 0 1 M ⴚ4 10. (ⴚ3, 8) 11. (7, ⴚ1) 12. (ⴚ5, 4) 13. (1, ⴚ4, 6) 14. (ⴚ3, 2, 5) 15. (2, ⴚ4, 6) 16. (3, 4, ⴚ1) 17. (4, ⴚ1, 2) 18. (1, 4, 2)

冤 冤

1 0 0 1 0 0

冥 冥

Practice — Chapter 5

12

6 4 2 –4

–2

2

x

4

(0, ⴚ3) y

17.

4 2 –4

–2

O

x

4

–2

(ⴚ0.5, 6.25) y

18.

Copyright © by Holt, Rinehart and Winston. All rights reserved.

Lesson 5.1 1. f (x) ⴝ x 2 ⴚ 8x ⴙ 15; a ⴝ 1, b ⴝ ⴚ8, c ⴝ 15 2. g(x) ⴝ x 2 ⴚ 16x ⴙ 63; a ⴝ 1, b ⴝ ⴚ16, c ⴝ 63 3. k(x) ⴝ ⴚ3x 2 ⴙ 30x ⴙ 33; a ⴝ ⴚ3, b ⴝ 30, c ⴝ 33 4. h(x) ⴝ 6x 2 ⴙ 13x ⴚ 5; a ⴝ 6, b ⴝ 13, c ⴝ ⴚ5 5. d(x) ⴝ x 2 ⴚ 6x ⴙ 5; a ⴝ 1, b ⴝ ⴚ6, c ⴝ 5 6. yes 7. no 8. no 9. no 10. yes 11. yes 12. up; minimum value 13. up; minimum value 14. up; minimum value 15. down; maximum value

y

16.

6

2 –6

–2

O

2

4

x

–2 –4

(ⴚ1.75, 5.0625) Lesson 5.2 1. ⴚ10 or 10 2. ⴚ兹3 艐 ⴚ1.73 or 兹3 艐 1.73 3. ⴚ12 or 6 4. ⴚ2兹5 艐 ⴚ4.47 or 2兹5 艐 4.47 Algebra 2

Answers 5. ⴚ4 or 4 6. ⴚ

兹3

2

3

5. x ⴙ 9x ⴙ 20.25; (x ⴙ 4.5) 2

艐 ⴚ1.15 or

兹3

2

3

艐 1.15

7. ⴚ兹6.5 艐 ⴚ2.55 or 兹6.5 艐 2.55 8. 2 ⴚ 兹5 艐 ⴚ0.24 or 2 ⴙ 兹5 艐 4.24 9. ⴚ3兹2 艐 ⴚ4.24 or 3兹2 艐 4.24 10. ⴚ1 ⴚ 兹23 艐 ⴚ5.80 or ⴚ1 ⴙ 兹23 艐 3.80

2

6. x ⴚ 19x ⴙ 90.25; (x ⴚ 9.5) 2

2

7. ⴚ1.8 or 3.8 8. 2.3 or 5.7 9. ⴚ0.1 or 14.1 10. ⴚ20.1 or 0.1 11. 0.2 or 4.8 12. ⴚ0.6 or 6.6 13. ⴚ2.1 or 3.1 14. ⴚ6.7 or ⴚ0.3 15. ⴚ8.2 or 0.2 16. f (x) ⴝ ⴚ x 1

11. c ⬇ 9.4 12. j ⬇ 5.8 13. r ⬇ 5.0 14. c ⬇ 16.6 15. b ⬇ 6.9 16. a ⬇ 2.4 17. c ⬇ 11.5

2

2

; (0, 0);

xⴝ0

17. f (x) ⴝ ⴚ3x ⴙ 7; (0, 7); x ⴝ 0 2

18. f (x) ⴝ (x ⴚ 6) ⴚ 39; (6, ⴚ39); x ⴝ 6 2

19. f (x) ⴝ (x ⴚ 1) ⴚ 11; (1, ⴚ11); x ⴝ 1 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

Lesson 5.3

2

1. 12(x ⴚ 5) 2. ⴚ4x(6 ⴚ x) 3. (2 ⴚ 7x)(1 ⴚ 3x) 4. (4x ⴚ 3)(x ⴚ 12) 5. 3x(x ⴙ 7) 6. ⴚ3x(x ⴚ 35) 7. (x ⴙ 4)(x ⴙ 13) 8. (x ⴚ 5)(x ⴙ 4) 9. (x ⴚ 9)(x ⴙ 2) 10. (x ⴙ 4)(x ⴙ 7) 11. (x ⴚ 10)(x ⴙ 9) 12. (x ⴙ 13)(x ⴚ 2) 13. (2x ⴙ 1) 14. (3x ⴚ 1)(x ⴙ 2) 15. (2x ⴙ 1)(x ⴚ 2) 16. ⴚ16 or 16 17. ⴚ5 or 5 18. ⴚ7 or ⴚ2 2

19. x ⴝ 1 22. ⴚ

2

3

or

20. 1.5 2 3

20. f (x) ⴝ (x ⴚ 5) ⴚ 35; (5, ⴚ35); x ⴝ 5

21. ⴚ

23. 1 or

1

3

1 5

or

1 2

24. ⴚ

2 7

or 1

25. ⴚ3, 4 26. ⴚ2.5, 1 27. ⴚ15, 3 28. 6, 7 29. ⴚ2, 0.5 30. ⴚ1.5

21. f (x) ⴝ 3(x ⴙ 2.5) ⴚ 20.75; (ⴚ2.5, ⴚ20.75); x ⴝ ⴚ2.5 2

Lesson 5.5 1. 0.3 or 9.7 2. 0.3 or 3.7 3. ⴚ3.3 or 3.3 4. ⴚ5.7 or 2.7 5. ⴚ5.6 or 1.6 6. ⴚ6.9 or 1.9 7. ⴚ2.9 or 2.4 8. 1.4 or 5.6 9. ⴚ1.1 or 4.1 10. ⴚ0.9 or 2.2 11. ⴚ2.2 or 3.7 12. ⴚ0.6 or 0.4 13. x ⴝ ⴚ1; (ⴚ1, ⴚ5) 14. x ⴝ 1.5; (1.5, 11.75) 15. x ⴝ 1; (1, ⴚ1) 16. x ⴝ ⴚ

2

Lesson 5.4

3

1. x ⴙ 24x ⴙ 144; (x ⴙ 12) 2

2

2. x ⴚ 40x ⴙ 400; (x ⴚ 20) 2

;

2

1

( ⴚ3 , ⴚ10 3 )

17. x ⴝ 1; (1, ⴚ3) 18. x ⴝ ⴚ

2

5

;

2

4

( ⴚ5 , ⴚ15 )

2

3. x ⴚ 20x ⴙ 100; (x ⴚ 10) 2

2

4. x ⴙ 5x ⴙ 6.25; (x ⴙ 2.5) 2

Algebra 2

2

13

Answers Lesson 5.6

8. f (x) ⴝ 2x ⴙ 4x ⴚ 5 2

1. 1; two; x ⴝ 1.5 or x ⴝ 1 2. ⴚ27; none; x ⴝ ⴚ ⴚ 3

3i

2

x

3

3i

ⴝⴚ ⴙ

i

兹17 3

1

3i

8

1

ⴝ ⴙ

3i

8

1

i

4

1

ⴝ ⴙ

i

兹87 12

i

6

i

2

2

x

ⴙ3

Lesson 5.8 or

1. x ⱕ ⴚ4 or x ⱖ 4

or

–4

–2

0

2

4

6

–2

0

2

4

6

–2

0

2

4

2. ⴚ4 ⱕ x ⱕ 2

兹6

2

1

12. f (x) ⴝ 5x ⴙ x ⴚ 7 13. f (x) ⴝ ⴚ16x ⴙ 20x ⴙ 3 14. 9.25 feet 15. about 0.6 second 16. 3 feet 17. about 1.4 seconds

–6 2

1

2

12 1

ⴝ ⴚ

ⴚxⴙ4

10. f (x) ⴝ x ⴚ 9x ⴙ 2

兹87

4

6. ⴚ96; none; x ⴝ ⴙ 兹 x

or

8

5. ⴚ87; none; x ⴝ ⴚ x

兹7

兹7

8

2

2

3

4. ⴚ63; none; x ⴝ ⴚ x

x

2

or

兹17

3

2

2

3

i

3

11. f (x) ⴝ x ⴙ 1

ⴝ ⴙ

or

2

3. ⴚ68; none; x ⴝ ⴚ x

2

兹3

2

1

兹3

9. f (x) ⴝ

–6

2

–4

3. ⴚ5 ⱕ x ⱕ ⴚ2

19. ⴚ4 ⴚ 28i

5. x ⬍ ⴚ0.30 or x ⬎ 3.30

20.

12

ⴚ

13

5i 13

22. 4 ⴚ 2i 23. ⴚ21 ⴙ 20i 25. ⴚ4 ⴚ 5i 26. ⴚi

21. 30

–8

24. 18 ⴙ 6i

–2

–1

0

1

2

3

4

5

–2

–1

0

1

2

2

4

6. ⴚ3.79 ⬍ x ⬍ 0.79 –5

2

–4

4. no solution

Lesson 5.7 1. f (x) ⴝ ⴚ4x ⴙ 3x ⴙ 2

–6

–4

–3

y

7.

2. f (x) ⴝ 3x ⴚ 2x ⴙ 5 2

6

3. f (x) ⴝ 0.5x ⴙ x ⴚ 3 2

4

4. f (x) ⴝ 5x ⴙ 2x ⴚ 3 2

5. f (x) ⴝ 6x ⴚ 3x ⴚ 1

2

2

6. f (x) ⴝ ⴚ2x ⴙ 7x ⴚ 3 2

–4

–2

O

x

–2

7. f (x) ⴝ ⴚ3x ⴙ 3x ⴚ 2 2

14

Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

7. ⴚ2 ⴙ 11i 8. 7 ⴚ 10i 9. 13 ⴙ 9i 10. ⴚ1 ⴙ 3i 11. ⴚ15 ⴙ 5i 12. 5i 13. ⴚ4 ⴙ i 14. 4 ⴚ 5i 15. ⴚ8 ⴙ 7i 16. ⴚ15i 17. 27 ⴙ 4i 18. ⴚ12 ⴚ 19i

Answers y

8.

y

12. 6 4 2

2

O

–6

2

x

–4

–2

2

4

x

–2

–2

y

9.

Practice — Chapter 6

2 –2

2

4

6

x

1. 1.01 2. 0.9 3. 0.93 4. 1.12 5. 1.1 6. 0.97 7. 0.948 8. 1.075 9. 1.004 10. 0.941 11. 1.414 12. 15.874 13. 0.016 14. 28 15. 35.318 16. 226.274 17. 1.875 18. 8.25 19. 630.346 20. 271.529

–4 –6

y

10.

Copyright © by Holt, Rinehart and Winston. All rights reserved.

–2

Lesson 6.1

2

4

6

x

21a. 1,275,868 b. 1,307,375 22a. 6400 b. 25,600

–6

Lesson 6.2

–8

1. quadratic 2. linear 3. linear 4. exponential 5. quadratic 6. exponential 7. linear 8. exponential 9. exponential

y

11. 4 2 –2

O

2

4

6

x

10. exponential growth

–2

11. exponential decay

–4

12. exponential decay

–6

13. exponential growth 14. exponential growth 15. exponential decay

Algebra 2

15

Answers 16. exponential decay

5. log

64

17. exponential growth

6. log

3

18. exponential growth

0.5

19. $2117.56 22. $1226.08 25. $5325.11

8

9

20. $1075.52 21. $977.06 23. $343.10 24. $1294.22 26. $2358.76

361

2. log

8000

20

15

3375

3

9. log

8

12. log

3

ⴝ3

27 343

ⴝ

64

y

ⴝ2

5

4

144

ⴝ2

135

x

3

14. logb x ⴝ logb 4

zy

ⴝ3

4

ⴝ ⴚ3

1331

8. 5 ⴝ 15,625

2

6

1

4

ⴚ4

)

2

14,641

ⴝ 625

13. x ⬇ 1.54 14. x ⬇ 1.96 15. x ⬇ ⴚ0.70 16. x ⬇ 0.26 17. x ⬇ ⴚ1.10 18. x ⬇ 3.02 19. v ⴝ 3 20. v ⴝ 2 21. v ⴝ 2 22. v ⴝ 256

23. v ⴝ

25. v ⴝ 10

26. v ⴝ 3

24. v ⴝ

1 625

27. v ⴝ 4

1 343

1. log

4

2. log

72

3. log

5

4. log

15

5

7

3

16

100

10

ⴚ log

ⴙ log

7

ⴙ log

5

25

3

3

ⴝ log

10

ⴝ log

5

ⴙ log

7

4

72

ⴙ2

4

21. 10

22. 2

23. 2

27. 3

Lesson 6.5 1. x ⬇ 4. x ⬇ 7. x ⬇ 10. x ⬇ 13. x ⬇ 16. x ⴝ 19. x ⴝ ⴚ 22. x ⴝ 25. x ⴝ ⴚ 28. x ⴝ

1.72 1.19 1.05 1.16 4.09 1.76

0.46

7.32

ⴚ2

2

18.

1.16

ⴙ log

zy

17. 73

0.57

Lesson 6.4

4

2.5

24.

28. 4

19. 4.7 4 3

20. ⴚ1

25. ⴚ3, 3

29. 2

2. x ⬇ 0.95 3. x ⬇ 6.64 5. x ⬇ 2.81 6. x ⬇ ⴚ0.48 8. x ⬇ ⴚ0.11 9. x ⬇ 1.46 11. x ⬇ 1.43 12. x ⬇ 0.90 14. x ⬇ 1.33 15. x ⬇ 0.42 17. x ⴝ 2.18 18. x ⴝ 3.70 20. x ⴝ 3.19 21. x ⴝ 0.40 23. x ⴝ 3.09 24. x ⴝ 1.30 26. x ⴝ ⴚ0.55 27. x ⴝ 1.43 29. x ⴝ 3.42 30. x ⴝ ⴚ0.65

4

q Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

10. 3600 ⴝ 60

3

2

16. 12

26. ⴚ1, 6

1

9. 21 ⴝ 9261 11. 11ⴚ ⴝ

x

15. logb z ⴝ logb

7. 12 ⴝ 144

10

7

m

3

1

11

9

x

13. logb x

1

7

6. log

log

ⴝ

7

2

3

3

5

5

9

4

30

12

ⴝ ⴚ3

64

5. log

12. (

8. log

11. log

ⴝ2

4

1

3

log

8

2

3. log 4. log

7. log

9

1. log

19

9

aⴚ

aⴚ 9

ⴝ 2 ⴚ log

4

8

ⴙ log

ⴙ log

10. log

Lesson 6.3

ⴚ log

Answers Lesson 6.6 1. 2980.958 2. 12.182 3. 181.272 4. 109.196 5. 3.555 6. 2.534 7. not defined 8. 1.242 9. 4.718 10. ln 55 ⬇ 11. 3.78 ⬇ 44 12. ln 0.05 ⬇ ⴚ3 13. 2.30 ⬇ 10 14. ln 54.6 ⬇ 4 15. 4.83 ⬇ 125 16. ln 148 ⬇ 5 17. 0 ⴝ 1 18. ln 0.45 ⬇ ⴚ0.8 19. ⬇ 1.23 20. ⬇ 1.10 21. ⬇ 2.17 22. ⬇ ⴚ8.67 23. ⬇ 10.48 24. ⬇ ⴚ0.75 25. ⬇ ⴚ1.17 26. ⬇ ⴚ1.34 27. ⬇ 0.78 28. $1215.31 x

e

e

e

e

x

x

x

x

x

x

x

x

x

Lesson 6.7 1. ⴝ 4 2. 4. ⴝ 1000 x

Copyright © by Holt, Rinehart and Winston. All rights reserved.

x

Practice — Chapter 7 Lesson 7.1 1. yes; quintic trinomial 2. yes; quadratic trinomial 3. no 4. yes; cubic polynomial 5. no 6. no 7. ⴚ36 8. ⴚ2 9. 61 10. 410 11. 80 12. ⴚ152 13. 8 4 ⴙ 11 3 ⴙ 5 2 14. 22 5 ⴚ 13 4 ⴚ 3 2 ⴚ ⴙ 8 15. ⴚ 4 ⴚ 5 3 ⴙ 10 2 ⴚ 1.2 ⴙ 2 16. 5.1 3 ⴙ 12.2 2 ⴚ 7 ⴙ 26 x

x

x

x

x

x

2

1

3. x ⴝ 2

4 2 –4

–2

1

2

4

x

–4

8. x ⴝ 5

14. x ⴝ 43

O –2

7. x ⴝ 3 ln 15 艐 0.90

13. x ⴝ 3

x

y

5. x ⴝ 2

11. x ⴝ 4

x

6

ⴝ 3 艐 0.67

9. x ⴝ log 28 ⬇ 1.45

x

x

17. x

x

x

x

ln 6 艐 0.82 6. x ⴝ ln 9

10. x ⴝ 4

x

upside-down W-shape 12. x ⴝ 6

y

18.

3

15. x ⴝ 2 艐 10.0 16. x ⴝ 3 ln 0.64 ⬇ ⴚ1.34 17. 5.0 ⴛ 1021 ergs e

2 – 4 –2

18. 7.2

2

4

x

-shape

W

Algebra 2

17

Answers y

19.

10.

11.

4

12.

2 13.

–4

–2

O

2

4

x

falls on the left, rises on the right falls on the left and on the right rises on the left and on the right 4 3 2 f (x) ⴝ ⴚ4.17x ⴚ 30.83x ⴙ 473.42x ⴚ 1019.27x ⴙ 6039.64

–2 –4

Lesson 7.3

-shape

1.

Lesson 7.2

3.

S

1.

2.

3.

4.

5.

7.

8.

9.

4.

5.

6.

7. 11.

13.

14.

15.

16.

18.

20.

21.

9.

10.

12.

x

x

4x 2 ⴙ 4x ⴙ 1 ⴙ 2 4ⴙ 1 5x 2 ⴚ 4x ⴙ 3 x ⴚ 3 2 x ⴙ 3x ⴙ 4 x ⴙ 3 6 ⴚ3 3 x ⴙ 2x ⴙ 2 ⴚ3 11 25 10 83 x

17.

19.

x

x

22.

23.

24.

Lesson 7.4 1.

3.

5.

7.

9.

11.

18

8.

Copyright © by Holt, Rinehart and Winston. All rights reserved.

6.

local minimum at (ⴚ1.5, 1.75) local maximum at (0.2, 6) local maximum at (0, 1); local minimum at (0.7, 0.7) local maximum at (ⴚ0.2, 2.2); local minima at (ⴚ1.7, 2.7) and (1.3, ⴚ2.3) local maximum at (0, 2); local minimum at (0.5, 1.8); increasing for ⴚ6 ⱕ x ⱕ 0 and 0.5 ⬍ x ⱕ 6; decreasing for 0 ⬍ x ⱕ 0.5 local maximum at (ⴚ0.7, 0.4); local minima at (ⴚ2.3, ⴚ1.5) and (0.5, ⴚ0.4); increasing for ⴚ2.3 ⱕ x ⱕ ⴚ0.7 and 0.5 ⱕ x ⱕ 4; decreasing for ⴚ4 ⱕ x ⱕ ⴚ2.3 and ⴚ0.7 ⱕ x ⱕ 0.5 local maximum at (ⴚ0.8, ⴚ1.7); local minimum at (0, ⴚ2); increasing for ⴚ5 ⱕ x ⱕ ⴚ0.8 and 0 ⱕ x ⱕ 4; decreasing for ⴚ0.8 ⱕ x ⱕ 0 local maxima at (0, 1) and (1.6, 2.1); local minimum at (0.3, 1.0); increasing for ⴚ4 ⱕ x ⱕ 0 and 0.3 ⱕ x ⱕ 1.6; decreasing for 0 ⱕ x ⱕ 0.3 and 1.6 ⱕ x ⱕ 4 rises on the left, falls on the right

2.

8x 5 ⴚ 5x 4 ⴙ 3x 2 2x 2 ⴚ 17x ⴚ 30 5x 3 ⴚ 17x 2 ⴚ 5x ⴚ 28 3 2 x ⴚ 7x ⴚ 10x ⴙ 16 2x 3 ⴚ x 2 ⴚ 8x ⴚ 5 27x 3 ⴚ 27x 2 ⴙ 9x ⴚ 1 no yes no yes yes no 2x ⴚ 5 2x ⴚ 1 ⴚ 3 5ⴙ 5

ⴚ9, 0, and 9

0, 1, and 10 1 ⴚ5, 0, and 3 ⴚ2 , 0, and 1 ⴚ3, 0, and 4 0, 13 , and 1 ⴚ2, 2, and 3 ⴚ3, ⴚ2, and 1 3, ⴚ4, and 31 ⴚ1, 6, and 7 ⴚ1 and 6 (multiplicity 2) 2.

4.

6.

8.

10.

Algebra 2

Answers 12. ⴚ4 and 4 (multiplicity 2)

14. ⴚ2.24, 0, and 2.24

14. ⴚ兹3, 兹3, ⴚ兹7, and 兹7

16. ⴚ1.85 and 1.16

13. ⴚ2, 2, ⴚ兹6, and 兹6 15. ⴚ兹6, 兹6, ⴚ3, and 3

16. ⴚ兹2, 兹2, ⴚ兹5, and 兹5 17. ⴚ4, 4, ⴚ1, 1

18. ⴚ兹2, 兹2, ⴚ兹10, and 兹10 19. 1.3, 0.3, and ⴚ1.5

20. ⴚ1.2, ⴚ0.4, and 0.3

21. ⴚ0.9, 0 (multiplicity 2), and 0.9 22. ⴚ0.2, 0.4, and 1.1 23. ⴚ0.4, 0.3, and 0.9

Copyright © by Holt, Rinehart and Winston. All rights reserved.

24. ⴚ2.9, ⴚ2.4, ⴚ0.2, and 1.4

Lesson 7.5 1 1. 5 and 1 1 2. ⴚ2, 3 , and 2 1

1

3. ⴚ1, 3 , and 2

1

4. ⴚ4 , 1, and 2

1 5. ⴚ1 (multiplicity 2), 2 , and 4 2 1 2 6. ⴚ3 , ⴚ2 , 3 , and 1 7. ⴚ5, i兹2, and ⴚi兹2 8. ⴚ3, 2i, and ⴚ2i

9. 3, 2i兹3, and ⴚ 2i兹3

10. 5, 3i, and ⴚ3i

11. 2, ⴚ2 ⴙ 2i, and ⴚ2 ⴚ 2i 12. 1, 4, i, and ⴚi

13. ⴚ1.46 and 1.66

Algebra 2

15. ⴚ1.41, 0, and 1.41 17. P(x) ⴝ 5x 3 ⴚ 15x 2 ⴚ 50x ⴙ 120 18. P(x) ⴝ ⴚ2x 3 ⴚ 6x 2 ⴚ 32x ⴚ 96

Practice — Chapter 8 Lesson 8.1 84 1. y ⴝ x ; 16.8, 8.4, 5.25, 4.2 0.8 ; 8, 0.16, 0.1, 0.04

2. y ⴝ x

150 ; 25, 10, 7.5, 2.5

3. y ⴝ x

4.8

4. y ⴝ x ; 9.6, 0.8, 0.48, 0.3 5. y ⴝ 8xz; 4 6. y ⴝ 24xz; 144

7. y ⴝ 0.6xz; 10.8 8. y ⴝ 32xz; 96

20xy

9. z ⴝ w

8xy

10. z ⴝ w

5xy

; 75

;9

11. z ⴝ 2w ; 10

12xy

12. z ⴝ w ; 17.5 13. 0.5; A ⴝ 0.5ap; 13.8 in.2

Lesson 8.2 1. yes; all real numbers except ⴚ兹3 and 兹3 2. no; |x| ⴚ 2 is not a polynomial. 3. yes; all real numbers except ⴚ1 and 1 4. vertical: x ⴝ 9; horizontal: y ⴝ 2

19

Answers 5. vertical: x ⴝ 1.5; horizontal: y ⴝ 0 6. vertical: x ⴝ ⴚ兹7 and x ⴝ 兹7; horizontal: y ⴝ 0

7. all real numbers except 0 and 6; vertical: x ⴝ 0, x ⴝ 6; horizontal: y ⴝ 0 8. all real numbers except 1 and ⴚ5; vertical: x ⴝ ⴚ5; horizontal: y ⴝ 0; hole at x ⴝ 1

9. all real numbers except ⴚ3 and ⴚ4; vertical: x ⴝ ⴚ3, horizontal: y ⴝ 3; hole at x ⴝ ⴚ4 y 10.

Lesson 8.3 1. 32

4 5. ⴙ ⴚ2

4

–4

y

4

9. ⴙ 2

y

O

8

x

x

–8

Lesson 8.4 ⴚ 22 1. 7 12

x

x

x

x

ⴚ3

x

8. ⴙ 8 x

x

x

ⴚ1

x

x

=

= 0

x

–4

–2

2

O

y

19.

x

2

4

x

x

13.

x

2ⴙ3

3

x

x

2(

1

17. ⴙ 3 x

x

x

= 1

x

x

or x

or x

x

x

or

x

20

x

16. ⴙ 7

or x

x

x

x

Lesson 8.5 1. 3.5 2. 11 3. 7.5 4. 15 5. 21 , ⴚ3 6. ⴚ2, ⴚ4 7. ⴚ2.5 8. 2 9. 7, 1 10. 0, ⴚ43 11. 6 12. 1 13. ⬍ 2 ⬎ 4 14. ⬍ 6 ⬎ 12 15. ⴚ1 ⬍ ⬍ 0 ⬎ 1 16. ⬍ 2 ⬎3 17. 1 ⬍ ⬍ 3 18. ⬍ ⴚ3 ⴚ2 ⬍ ⬍ 2 1 19. ⬍ⴚ1 ⴚ3 ⬍ ⬍ 1 15 20. ⴚ3 ⬍ ⬍ 4 ⬎ 2 x

= 1

–2

–4

ⴙ 28

10. 2 ⴚ 3

x

2

4

hole

7. ⴚ2

1

y

12.

x

x

or

or x x

x

or x

Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

y

O

hole

15. 0

ⴚ2 4. 35 2 ⴚ 12

x

ⴚ 2) x ⴙ 6 20. (x ⴙⴚ3)( ⴚ4 x ⴚ 3) 2 ⴚ 2(3x ⴙ 2x ⴙ 5) x ⴚ 3 21. x 22. (3x ⴙ 2)(x ⴚ 5) 3 ⴙ 4y ⴙ 2x 23. (x ⴙ 3)(y ⴚ 2)

2

x

1

ⴚ3

x

18. ⴚ 5

2

x

12. 2 ⴚ 1

14. 2 ( ⴙ 1) x

1

x

3. 65

6. 2 16 ⴚ 16

9. ⴚ ⴚ 5

ⴚ1

x

y

x

ⴚ7 2. 3 3 ⴙ 1

2 5. 2 2ⴙⴙ2 ⴚⴙ613

x

11.

5 17. 3 ⴙ ⴙ 21

y

11. 4 ⴚ 2

= 4

x

x

x

x

x

x

x

x

–4

x

x

3 3( ⴚ ) 4

2 3 14. 3 ⴚ ⴚ 12

x

16. ⴚ 3

x

x

18.

1 13. ⴚ ⴙ1

x

15. 2 ⴚⴚ21

8. 1

11. x2 ⴚ x ⴚ 12

12. 2 ⴚ 51 ⴚ 50 x

4. 21 2 x

7. 3x ⴚ 9

10. x

x

x

= 3

x

6. 3x 6

x

8

x

x

x x

2 3. 33 ⴙ ⴚ2

7 2. ⴚ ⴙ7 x

x

Answers 21. x ⬍ ⴚ1 or x ⬎ 1 22. ⴚ2.2 ⱕ x ⬍ 3 or x ⬎ 3 23. ⴚ4 ⬍ x ⬍ 0.5 or x ⬍ ⴚ4.5 24. x ⬍ 0.7 or 4 ⬍ x ⬍ 4.3 25. 0 ⬍ x ⬍ 2 26. x ⬍ ⴚ6.5 or 0 ⬍ x ⬍ 2.5 or x ⬎ 4 27. ⴚ1.4 ⬍ x ⬍ 0 or 1.4 ⬍ x ⬍ 2

9. y ⴝ 1 ⴚ 兹x ⴙ 6, y ⴝ 1 ⴙ 兹x ⴙ 6 y

y = 1 +

√x + 6 2

x O y = 1 –

√x + 6

y = x

Lesson 8.6 1. x ⱖ 2.5

2. x ⱖ 4

3. x ⱕ ⴚ6 or x ⱖ 6

4. x ⱕ ⴚ2.5 or x ⱖ 2.5

5. x ⱖ 5

10. 4

2

– 2x – 5

11. 7.5

14. 4

2

12. ⴚ6

15. ⴚ2

13. ⴚ24

兹π 3

16. d ⴝ

6. x ⱕ ⴚ3 or x ⱖ ⴚ1 7. y ⴝ 3 ⴚ 兹x ⴙ 1, y ⴝ 3 ⴙ 兹x ⴙ 1 2

y = x

– 6x + 8

2. 3

5. 4x

y = 3 +

√x + 1

Copyright © by Holt, Rinehart and Winston. All rights reserved.

x 2

4

6

y = 3 –

√x + 1

8. y ⴝ ⴚ兹2 ⴚ x, y ⴝ 兹2 ⴚ x

3

1

6. ⴚ2xy(2y)

2

9. 10x

11. 2yz兹3xyz

12. 2x

13. 25 ⴙ 2兹2

14. 3 ⴙ 13兹3

4

2

y

2

y

5

2

3

yz

兹2xy

2

4

2

15. 5 ⴚ 兹2

17. ⴚ58 ⴚ 13兹5

18. 432

20. 4兹2

22. 16 ⴙ 8兹3

z

10. 2y 兹x

兹y

16. ⴚ24 ⴚ 15兹2 19. 兹2

2

2

8. 4xy 兹x 3

3

7. 2x

3

3

O

4. 7xy 兹x

2

(5x) 2

6

3. 12|x|y 兹2

1

2

8

; 12.4 feet

Lesson 8.7 1. 2

y

6V

21. 7兹2 ⴚ 7

23. 5兹3 ⴚ 5兹2

24. 兹 ⴙ 兹

y

9

7

9

2

5

4

y =

Lesson 8.8

√2 – x x 6

4

2

√2 – x

O –2

y = –

2

y = 2 – x

–4

1. 95

2. 10

3. ⴚ4, 4

4. no solution 6. 2, 6 9. 5

7. no solution 10. 3 ⱕ x ⱕ 12

12. 0 ⱕ x ⬍ 8

1 3

14. x ⬎ 1

Algebra 2

5. ⴚ兹2 , 兹2 8. 2, 3 11. x ⬎ 14

13. x ⬍ ⴚ0.5 or x ⬎ 2.5

15. 8 ⬍ x ⬍ 13

16. no solution

21

Answers 17. x ⬍ ⴚ6.5

18. ⱕ x ⱕ 13 3 4

20. ⴚ1.8 ⱕ x ⱕ 1.5 22. x ⱖ 5.8

19. x ⬎ 5.6

21. ⴚ4 ⱕ x ⱕ 1.3

3. y ⴝ ⴚ3兹x ⴚ 1, y ⴝ 3兹x ⴚ 1 y 2

2

4

23. x ⬎ 0.4

24. 0.4 ⱕ x ⱕ 0.8 or x ⱖ 6.2 25. ⴚ9 ⱕ x ⱕ ⴚ0.8 or x ⱖ 3.9 26. x ⬎ 3.4

–4

27. x ⱖ 10.5

hyperbola

4. 13; (2.5, 6)

Lesson 9.1 1

7. 兹85 艐 9.22; (3, 4)

y

8. 12兹2 艐 16.97; (ⴚ2, ⴚ2)

8

9. 兹13 艐 3.61; (0, 0.5)

6

10. (9, 14); 10π; 25π

4

11. (4.5, 20); 41π;

2

O

2

4

x

12. (0, 8.5); 17π;

π

1681 4

π

289 4

13. (3.5, 1); π兹145; parabola

2. y ⴝ ⴚ兹400 ⴚ x , y ⴝ 兹400 ⴚ x y 2

π

145

14. (15, 5.5); π兹101;

4

π

101

15. (2.5, 2.5); π兹562;

4

π

562 4

Lesson 9.2

10 –10 O –10

2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

–2

5. 10; (8, ⴚ2)

6. 2兹101 艐 20.10; (2, 3)

2

3

–4

x

4

2

–4

Practice — Chapter 9 1. y ⴝ x

O

–2

10

x

1. y ⴝ

1 12

x ⴚ 3)

2

(

2. x ⴙ 1 ⴝ y 1

2

4

3. y ⴙ 1 ⴝ (x ⴚ 3)

2

circle

22

Algebra 2

Answers y

4.

5.

6.

4

x ⴙ 2) (x ⴙ 3) (

2

ⴙ (y ⴚ 1)2 ⴝ 6.25

2

ⴙ (y ⴙ 3)2 ⴝ 576 y

7.

2

V(0, 0)

F(1, 0)

O

x 6

4

2

–2

8

x = –1

r = 16

(0, 0)

directrix

–8

O

x

8

–8

y

5.

8

F(1, 5)

6

V(1, 4)

4

y=3 –4

8

directrix

2

r=4

x

O

–2

y

8.

2

6 (0, 5) 4

4

2

y

6.

–4

–2

O

2

4

x

Copyright © by Holt, Rinehart and Winston. All rights reserved.

6

F(3, 2)

2

2

V(1, 2)

O

x = –1

y

9.

4

2

x

O

6

4

–2

directrix

7.

9.

11.

1

2

1

2

y ⴝ 24 x

x ⴝ 12 y

8.

x ⴚ 10 ⴝ 8 y

10.

1

1

1

12.

2.

3.

4.

x ⴙ 5) ⴙ (y ⴚ 2) (x ⴚ 6) ⴙ (y ⴚ 3) x ⴙ (y ⴙ 4) ⴝ 25 x ⴙ y ⴝ 169

Algebra 2

2

ⴝ 16

2

2

ⴝ

2

2 2

2

2

25

r=3

2

1

y ⴝ 20 (x ⴚ 9)2

10.

Lesson 9.3

(

x

–6

y ⴚ 2 ⴝ 4 (x ⴚ 5)

x ⴚ 6 ⴝ ⴚ 8 (y ⴙ 7)2

6

(3, 3)

–4 2

11.

1.

2

x ⴚ 5) ⴙ (y ⴚ 8) ⴝ 1; C(5, 8); r ⴝ 1 (x ⴙ 11) ⴙ (y ⴚ 1) ⴝ 2; C(ⴚ11, 1); r ⴝ 兹2 2

(

2

2

2

Lesson 9.4

4

x ⴙy ⴝ1 64 36 (x ⴙ 3) (y ⴙ 2) 2

2

1.

2

2.

4

2

ⴙ

16

ⴝ1

23

Answers 3.

x ⴚ 3)

y ⴚ 2)

2

(

Lesson 9.5

2

(

ⴙ

25

y

4.

ⴝ1

9

1. x ⴚ 2

9

2

16

–8

4

8

2

ⴝ1

25

(0,

4

–4

ⴚ

16

√77)

(2, 0)

x

2

y

4 (–2, 0)

y

2.

ⴝ1

3.

(0, 9) (0,

y

x

y

5

= –

3

x

√34)

(0, 3)

C

2

(0, 0)

y

=

5 3

x

(0, 0) (–5, 0) – 4

–2

√77)

(0, –

2

(5, 0)

4

x

–2

(0, –9) (0, –3)

y

5.

√34)

(0, –

(0, 1)

4 (1, –3)

(–7, 0) –8

(0, 3)

O

–4

y

4.

(0, 7)

4

(1, 4) (7, 0) 8

C

x (– 4, 1)

(0, –5)

–6

(1, 1)

(–3, 1)

–4

(5, 1)

O

–2

–8

2

4

(1, –2)

y

y

6.

=

3 4

x

+

y

1

(6, 1)

3

= –

4

x

6

–

x

1 4

4

(4, 2)

(4, 1)

O

2

4

6

8

x

–2 (7, –3)

(1, –3)

–6

(4, –7)

(4, –8)

8. 9. 10.

x x

y

2

ⴙ

625

ⴙ

y

109

x

2

225

2

y

2

ⴙ

2

2

36

ⴝ1

ⴝ1

464

x ⴙ 3)

(

ⴙ

ⴝ1 y

2

9

ⴝ 1; center: (ⴚ3, 0)

ⴚ3 ⴚ 3兹3, 0) and (ⴚ3 ⴙ 3兹3, 0); vertices: (ⴚ9, 0) and (3, 0); co-vertices: (ⴚ3, ⴚ3), and (ⴚ3, 3)

foci: (

24

10

y

2

15

y ⴚ 1)

7.

(

8.

(

6. x ⴚ 2

ⴝ1

2

ⴚ

25

9

x ⴚ 1)

y ⴙ 2)

2

(

16

ⴝ1

2

(

144

x ⴚ 14)

ⴝ1

2

ⴚ (y ⴙ 3) ⴝ 1; center: (14, ⴚ3); vertices: (12, ⴚ3) and (16, ⴚ3); co-vertices: (14, ⴚ4) and (14, ⴚ2); foci: (14 ⴚ 兹5, ⴚ3) and (14 ⴙ 兹5, ⴚ3) 2

4

2

9

400

2

(4, –3)

–4

7.

5. x ⴚ

Lesson 9.6 1. (1, 6) and (4, 21)

2. none

3. (ⴚ2.83, ⴚ2.83) and (2.83, 2.83) 4. (ⴚ3, 0) and (3, 0)

Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

1

Answers 5. (ⴚ2.24, ⴚ1.73), (ⴚ2.24, 1.73),

(2.24, –1.73), and (2.24, 1.73) 6. (ⴚ4.24, ⴚ2.45), (ⴚ4.24, 2.45), (4.24, ⴚ2.45), and (4.24, 2.45) 7. none 8. (ⴚ2.08, ⴚ1.44), (ⴚ2.08, 1.44), (2.08, ⴚ1.44), and (2.08, 1.44) 9. none 1 10. parabola; y ⴚ 3 ⴝ 4 (x ⴚ 7)2 y

8 6 4 2

O

2

4

6

8

x

Copyright © by Holt, Rinehart and Winston. All rights reserved.

–2

(x ⴚ 5)2 (y ⴚ 4)2 11. hyperbola; 9 ⴚ 4 ⴝ 1 y

6 4 2

O

2

4

6

8

x

Practice — Chapter 10 Lesson 10.1 7 1. 10 ⴝ 70% 1

4. 2 ⴝ 50%

Algebra 2

4

2. 5 ⴝ 80%

11

5. 13 艐 85%

5

3. 11 艐 45%

1

6. 3 艐 33%

21

1

7. 26 艐 81%

65

10. 150 艐 43%

107

12. 150 艐 71%

8. 6 艐 17%

43

42

9. 150 ⴝ 28%

11. 150 艐 29%

85

13. 150 艐 57%

14. 1,000,000 15. 676,000 16. 456,976,000 17. 67,600,000 18. 6,760,000

Lesson 10.2 1. 5040 2. 2520 3. 840 4. 840 5. 479,001,600 6. about 4.36 ⴛ 1010 7. about 2.18 ⴛ 1011 8. about 6.03 ⴛ 1013 9. 20,160 10. 2520 11. 10,080 12. 5040 13. 4,989,600 14. 907,200 15. 43,758 16. 720 17. 5040 18. 3,628,800 Lesson 10.3 1. 56 2. 120 3. 35 4. 6435 5. 84 6. 60 7. 40 8. 5 9. 40 10. about 33% 11. about 39% 12. about 16% 13. combination 14. combination 15. permutation 16. permutation Lesson 10.4 4 1. inclusive; 13 艐 31% 6 2. mutually exclusive; 13 艐 46% 19 3. inclusive; 26 艐 73% 39

4. inclusive; 52 ⴝ 75%

25

Answers 27

1

5. mutually exclusive; 52 艐 52%

16. 3 艐 33%

9

41

6. inclusive; 52 艐 79%

5

5

7. 8 ⴝ 62.5%

19

11. 36 艐 53%

5

13. 9 艐 56%

5 艐 28% 15. 18

3

10. 4 ⴝ 75%

13

12. 36 艐 36%

Lesson 10.7 1–6. Simulation results will vary.

22

14. 36 艐 61%

Practice — Chapter 11

Lesson 10.5 1. 0.02 ⴝ 2% 2. 0.08 ⴝ 8% 3. 0.04 ⴝ 4% 4. 0.05 ⴝ 5% 5. 0.008 ⴝ 0.8% 6. 0.01 ⴝ 1% 1 49 7. 144 艐 34% 8. 24 艐 4% 3

25

9. 16 ⴝ 18.75%

1

13. 9 艐 11%

1

15. 36 艐 3%

1

17. 24 艐 4%

1

19. 12 艐 8%

Lesson 10.6 1 1. 6 艐 17% 1

4. 3 艐 33%

1

7. 8 ⴝ 12.5%

1

10. 4 ⴝ 25%

1

13. 5 ⴝ 20%

26

10. 36 艐 69%

1

12. 18 艐 6%

1

14. 4 ⴝ 25%

4

16. 9 艐 44%

1

18. 8 ⴝ 12.5%

1

20. 3 艐 33%

1

2. 2 ⴝ 50%

1

5. 2 ⴝ 50%

1

8. 2 ⴝ 50%

3

11. 5 ⴝ 60%

4

14. 5 ⴝ 80%

2

3. 3 艐 67%

1

6. 8 ⴝ 12.5%

9. 1 ⴝ 100%

2

12. 5 ⴝ 40%

1

15. 2 ⴝ 50%

Lesson 11.1 1. 2.5, 5, 7.5, 10, 12.5, 15 1 1 1 2. 0, 2 , 1, 12 , 2, 22 3. 13, 16, 21, 28, 37, 48 4. 20, 70, 220, 670, 2020, 6070 5. 1, 101, 201, 301, 401, 501 6. ⴚ5, ⴚ15, ⴚ45, ⴚ135, ⴚ405, ⴚ1215 7. a1 ⴝ 1; an ⴝ 11an ⴚ 1; 14,641; 161,051; 1,771,561 8. a1 ⴝ 81; an ⴝ an ⴚ 1 ⴚ 3; 69, 66, 63 9. a1 ⴝ 2; an ⴝ ⴚ3an ⴚ 1; 162, ⴚ486, 1458 1 10. a1 ⴝ 4 ; an ⴝ ⴚ4an ⴚ 1; 64, ⴚ256, 1024 11. a1 ⴝ 2; an ⴝ 3an ⴚ 1 ⴙ 5; 362, 1091, 3278 12. a1 ⴝ ⴚ2; an ⴝ 5an ⴚ 1 ⴚ 4; ⴚ1874; ⴚ9374; ⴚ46,874 13. 4.5 ⴙ 9 ⴙ 13.5 ⴙ 18 ⴙ 22.5 ⴙ 27 ⴙ 31.5; 126 14. 11 ⴙ 22 ⴙ 35 ⴙ 50 ⴙ 67; 185 15. 210 16. ⴚ24 17. 10 18. 1432.5 19. 397 20. 1911.4 Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

7

11. 72 艐 10%

1

19. 2 ⴝ 50%

20. 0.064 ⴝ 6.4% 21. 0.4 ⴝ 40% 22. 0.5625 ⴝ 56.25%

8. 8 ⴝ 62.5%

3

9. 8 ⴝ 37.5%

18. 10 ⴝ 90%

17. 0.625 ⴝ 62.5%

Answers

Copyright © by Holt, Rinehart and Winston. All rights reserved.

Lesson 11.2 1. yes; d ⴝ 3 2. no 3. yes; d ⴝ 2.5 4. no 5. yes; d ⴝ 53 6. yes; d ⴝ ⴚ2.3 7. tn ⴝ 25 ⴚ 9n 8. tn ⴝ 8n ⴚ 23 9. tn ⴝ 3n ⴙ 10 10. tn ⴝ 12n ⴚ 37 11. tn ⴝ 11n ⴚ 2 12. tn ⴝ 9.9 ⴚ 1.3n 13. 50, 150, 250, 350 14. 7.5, 10, 12.5, 15 15. ⴚ20, ⴚ12, ⴚ4, 4 16. 25, 65, 105, 145 17. 8.5, 9, 9.5, 10 18. ⴚ15, ⴚ27, ⴚ39, ⴚ51 19. ⴚ5, 2, and 9 20. 52, 64, 76, and 88 21. 62 and 74 22. 10.5, 14, and 17.5 23. 34, 28, and 22 24. ⴚ2, 4, 10, and 16 Lesson 11.3 1 1. 350 2. 16 2 3. ⴚ165 4. 2905 5. 711 6. 1482 7. 25,425 8. 360 9. 1300 10. 9555 11. 9555 12. 330 13. 990 14. 165 15. 239.25 16. ⴚ1914 17. 528兹5 艐 1180.64 18. 84 19. ⴚ132 20. 590 21. 228 22. 795 23. ⴚ351 Lesson 11.4 1. no 2. yes; r ⴝ 0.4 3. yes; r ⴝ ⴚ53 2 4. yes; r ⴝ 1.5 5. yes; r ⴝ 3 6. no 7. 18, ⴚ36, 72, ⴚ144 8. ⴚ4, ⴚ10, ⴚ25, ⴚ62.5, ⴚ156.25 9. 10, 5, 2.5, 1.25 10. 0.625 or ⴚ0.625 11. 32兹2 or ⴚ32兹2 1 12. 164014 or ⴚ16404

(2)

nⴚ1

13. tn ⴝ 250 5 14. tn ⴝ ⴚ30(ⴚ0.2)n ⴚ 1

Algebra 2

15. tn ⴝ 40(0.8)n ⴚ 1

(5)

16. tn ⴝ 2 2

nⴚ1

1

18. tn ⴝ ⴚ4 (ⴚ6)n 19. 35 and 175

(1)

17. tn ⴝ 80 4

n

20. ⴚ14 and ⴚ7

21. 48, 192, and 768 or ⴚ48, 192, and ⴚ768 22. 15, 18, and 21.6 or ⴚ15, 18, and ⴚ21.6 23. 60, 300, and 1500 or ⴚ63, 300, and ⴚ1500 24. 12, 36, 108, and 324

Lesson 11.5 1. 6,973,568,800 2. 86.4 3. ⴚ147 5467 4. 3125 ⬇ 1.7 5. ⴚ1064.7 6. 6144 7. 1,572,864 8. 12,285 9. 3,145,725 10. 378 11. 1,708,554.00 12. 1.67 13. 14,348,906 14. Show the statement is true for n ⴝ 1: 12(1 ⴙ 1)2 3 1 ⴝ 1 and 4 ⴝ 1. Assume that the statement is true for a natural number k. Then k 2(k ⴙ 1)2 13 ⴙ 23 ⴙ 33 ⴙ … ⴙ k3 ⴝ 4 and 13 ⴙ 23 ⴙ 33 ⴙ … ⴙ k3 ⴙ (k ⴙ 1)3 ⴝ k2(k ⴙ 1)2 ⴙ (k ⴙ 1)3 ⴝ 4 k2(k ⴙ 1)2 ⴙ 4(k ⴙ 1)3

4

ⴝ

(k ⴙ 1)2[k2 ⴙ 4(k ⴙ 1)] 4

(k ⴙ 1)2(k2 ⴙ 4k ⴙ 4) 4

(k ⴙ 1)2(k ⴙ 2)2 4

ⴝ

ⴝ

(k ⴙ 1)2[(k ⴙ 1) ⴙ 1]2 ⴝ . 4

Thus, the statement is true for k ⴙ 1.

27

Answers Lesson 11.6 1. does not exist 2. 1.2 3. 2.625 4. 25 5. 4 6. does not exist 7. 12.375 8. 3 9. 1.81 10. 11.5 11. does not exist 12. 50 13. 2292 14. 19

25 18. 111

15. 37 99

10 19. 27

49 16. 99

17. 251 333

1 21. 兺 93 ⴢ ( 100 ( ) ) 1 1 1 1 22. 兺 15 ⴢ ( 100 23. 兺 358 ⴢ ( 1000 ) ) 1 1 1 1 24. 兺 11 ⴢ ( 1000 ) 25. 兺 445 ⴢ ( 1000 ) 1 1 20.

1 兺 7 ⴢ 100 ⬁

kⴝ ⬁

kⴝ ⬁

kⴝ

k

k

⬁

kⴝ

k

⬁

k

kⴝ

⬁

k

k

kⴝ

28

243 a5 ⴚ 405 a4d ⴙ 135 a3d 2 ⴚ 45 a2d 3 ⴙ 8. 1024 256 32 8 15 ad4 ⴚ d 5 4

9. 64m6 ⴚ 576m5q ⴙ 2160m4q2 ⴚ 4320m3q3 ⴙ 4860m2q4 ⴚ 2916mq5 ⴙ

729q6 10. about 0.20 12. about 0.74 14. about 0.61

11. about 0.26 13. about 0.11

Practice — Chapter 12 Lesson 12.1 1. 66; 62; 62 2. 24.571; 28; 28 3. 3.617; 3.6; 3.6 4. 622.833; 725; 725 5. 2593.333; 1714; 1600 6. 24.05; 24.25; 25; all are reasonable measures because they are so close, but the mean and median are better than the mode because 6 of the 8 numbers are less than the mode.

Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

Lesson 11.7 1. sixth entry, row 7; 21 2. fourth entry, row 6; 20 3. seventh entry, row 8; 28 4. sixth entry, row 10; 252 5. eleventh entry, row 13; 286 6. sixth entry, row 12; 792 7. 120 8. 1716 9. 6435 10. 153 11. 0.3125 12. about 0.66 13. about 0.01 14. about 0.64 15. 0.5 16. 0.4375 17. about 0.23 18. about 0.89 19. about 0.34 20. about 0.09 21. about 0.66 22. about 0.34

Lesson 11.8 1. s 5 ⴙ 5s4t ⴙ 10s3t 2 ⴙ 10s 2t 3 ⴙ 5st 4 ⴙ t 5 2. b6 ⴙ 6b5w ⴙ 15b4w 2 ⴙ 20b3w 3 ⴙ 15b2w 4 ⴙ 6bw 5 ⴙ w 6 3. 16 terms 4. 3 5. 3003r 5s10 6. 3125x 5 ⴙ 3125x 4 y ⴙ 1250x 3y 2 ⴙ 250x 2y 3 ⴙ 25xy 4 ⴙ y 5 1 7. 16 w 4 ⴙ w 3z ⴙ 6w 2z 2 ⴙ 16wz 3 ⴙ 16z 4

Answers 7. Age (years) Tally Frequency

14 15 16 17 18

3. Number Frequency

3 3 4 6 2

1.0 1.1 1.2 1.3 1.4

8. No. of books Class mean Freq. Product

1–5 6–10 11–15 16–20 21–25 25–30

3 8 13 18 23 28

estimated mean: 10.75

8 4 3 1 2 2

24 32 39 18 46 56

Frequency

mean: 16.05

10 11 12 13 14

1 2 3 4

7 3, 3 1, 6, 9 0, 3, 8, 8

3.75; 2.3 and 4.8; mound-shaped

Algebra 2

16% 24% 14% 22% 24%

0.3 0.2 0.1 0

45; 64; flat

2. Stem Leaf 3|1 ⴝ 3.1

8 12 7 11 12

Probability

Copyright © by Holt, Rinehart and Winston. All rights reserved.

1. Stem Leaf 3|8 ⴝ 38

3, 7, 8 0, 2, 5 4, 6, 8 4, 4

1.0 1.1 1.2 1.3 1.4 Number

4. Number Frequency Rel. Freq.

Lesson 12.2 3 4 5 6

6 5 4 3 2 1 0

5 2 3 6 4

5.

10 11 12 13 14 Number Motor Vehicle Registration by Type, 1994

0.9% Motorcycles

33.2% 15.9% Passenger cars Buses 50% Trucks

29

Answers Lesson 12.3 1.

Q1 ⴝ 2, Q2 ⴝ 7, Q3 ⴝ 8; range ⴝ 8; IQR

ⴝ6

2. Q1 ⴝ 10, Q2 ⴝ 14.5, Q3 ⴝ 17; range ⴝ 14; IQR ⴝ 7

3. Q1 ⴝ 12.1, Q2 ⴝ 23.9, Q3 ⴝ 38.5; range ⴝ 33.8; IQR ⴝ 26.4 4. minimum ⴝ 3, maximum ⴝ 17; Q1 ⴝ 5, Q2 ⴝ 10, Q3 ⴝ 15; range ⴝ 14; IQR ⴝ 10

2

4

6

8

10

12

14

16

18

5. minimum ⴝ 10, maximum ⴝ 39; Q1 ⴝ 16, Q2 ⴝ 23, Q3 ⴝ 35; range ⴝ 29; IQR ⴝ 19

8

12

16

20

24

28

32

36

40

7. The quartiles and the extremes all

decreased, so it appears that the birth rates decreased in general. 8. about 75% Lesson 12.4 1. 32; 9.6 2. 19; 5.3 3. 55; 16.3 4. 80; 22 5. 7.1; 2 6. 62; about 18.9 7. 16; 4 8. 721.6; about 26.9 9. 74,064; about 272.1 10. 5; about 2.2 11. 83.7856; about 9.2 12. 0.08; about 0.3 13. 20 14. 4.3 15. 26.24 16. about 5.1

30

Lesson 12.6 1. 0.5 2. 0.8849 3. 0.9641 4. 0.1554 5. 0.4772 6. 0.0793 7. 0.1359 8. 0.1586 9. 0.5403 10. 16% 11. 2% 12. 82% 13. 16% 14. about 420 customers 15. about 820 customers Practice — Chapter 13 Lesson 13.1 1. 40 41 ; 0.9756 9 ; 0.2195 4. 41 41

9 ; 0.2195 2. 41 40 ; 0.9756 5. 41 41

3. 40 9 ; 4.4444

9

6. 40 ; 0.225

40

7. 9 ; 4.5556 8. 9 ; 4.5556 9. 9 ; 4.4444 10. 8.3; 57ⴗ; 33ⴗ 11. 11.6; 61ⴗ; 29ⴗ 12. 21.6; 34ⴗ; 56ⴗ 13. 59ⴗ; 4.9; 4.2 14. 36ⴗ; 4.9; 3.5 15. 56ⴗ; 5.2; 4.3

Lesson 13.2 1. –313ⴗ; 47ⴗ 2. 237ⴗ; 57ⴗ 3. ⴚ142ⴗ; 38ⴗ 4. 152ⴗ; 28ⴗ 5. 138ⴗ; 42ⴗ 6. ⴚ53ⴗ; 53ⴗ 7. 42ⴗ; 42ⴗ 8. 175ⴗ; 5ⴗ 9. 285ⴗ; 75ⴗ 10. 75ⴗ 11. 33ⴗ 12. 5ⴗ Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

6. the data for 1992

Lesson 12.5 1. 9.375% 2. 9.375% 3. 34.375% 4. 10.9375% 5. 0.8% 6. 81.92% 7. 6.4% 8. 94.208% 9. 0.672% 10. about 20.1% 11. 7.68% 12. 68.256% 13. 31.104% 14. 17.92% 15. about 2.3% 16. about 0.27% 17. about 99.7% 18. about 1.1%

Answers 13. 36ⴗ 17. 80ⴗ

14. 40ⴗ 18. 60ⴗ

兹13

19.

2

20.

2

21.

9

13

兹5

兹13

3

;

13

兹5

;

ⴚ

兹97

4

5

97

兹97

;

97

22. ⴚ

4

3

16. 2ⴗ

兹13 兹13

;

;

2

兹5

ⴚ2;

;

2 1 2

兹97 兹97 ;

9

4

兹39

24.

5

3

ⴚ兹5; ⴚ

;

5

; 2.25;

3

14. 103.13ⴗ

;

25.

8

兹2

5

2

3. ( ⴚ

15 2

,

,

兹2

5

2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

17.

兹3

兹3

15

21.

兹2

ⴚ

2

14. ⴚ

10. (0.574, ⴚ0.819)

4.

5

4

6. ⴚ 8.

1

2

兹3

23.

2

3

5

radians

5.

7

π radians

radians

Algebra 2

;

兹3 2

;

兹3

ⴚ

兹3

3

20. ⴚ兹3

3

24. ⴚ1

π

2.

11. 140ⴗ

3

32. 2

y = cos ␪

°

°

␪

°

180

270

y = cos 2␪

2. 4.5; π radians 3. does not exist; π radians 5. shift of 45ⴗ right; translation of 1.5 units up

y

25. ⴚ2 3

radians

36

兹3

4. 1.2; 2π radians

2

2

1

π

12

ⴚ1

;

19. ⴚ

17

5

2

兹3

π

6

;

2

16. ⴚ

18. ⴚ

–1

12. (ⴚ0.259, ⴚ0.966)

1

π

3

29.

8. (ⴚ0.629, 0.777)

Lesson 13.4 1.

31. 0

90

6. (2兹3, 2)

兹2 兹2

22.

2

28. ⴚ1

4. (20兹3, ⴚ20)

)

2

2

27. ⴚ兹3

1

ⴚ ; ⴚ兹3

2

25. 0

2. (6, 6兹3)

)

11. (0.755, ⴚ0.656)

;

24. 200 feet

1. 1; 0.5; 0; ⴚ0.5; ⴚ1; ⴚ0.5; 0; 0.5; 1

9. (ⴚ0.438, ⴚ0.899)

2

23. 146 feet

Lesson 13.5

7. (0.743, 0.669)

兹3

22. 80 feet

3

7

5. (ⴚ5兹2, 5兹2)

15.

21. 50 feet

兹2

3

13. 0; 1; 0

20. 10.5 feet

30. ⴚ

Lesson 13.3 1. (

19. 41.9 feet

2

4

16. 28.65ⴗ

18. 5.2 feet

1

9

15. 171.89ⴗ

17. 47.1 feet

26. ⴚ

4

兹7

27.

5 13

2

兹89

23.

3

26.

;

5

;

15. 72ⴗ

radians

3

12

7.

π 5

2

radian 1

π radians

0

π

7

18

9. 450ⴗ

12. 195ⴗ

3.

90

°

°

180

°

270

␪ °

360

radians –1

10. 165ⴗ

13. 472.69ⴗ

31

Answers 6. shift of π units left;

10. m⬔B ⴝ 44ⴗ, a ⴝ 5.5, b ⴝ 4.0 11. m⬔C ⴝ 82ⴗ, a ⴝ 15.5, c ⴝ 21.4 12. m⬔ A ⴝ 75ⴗ, a ⴝ 82.9, c ⴝ 78.4 13. one; m⬔ B ⴝ 46.0ⴗ, m⬔C ⴝ 70.0ⴗ, c ⴝ 20.9 14. none

translation of 1 unit down y

2 1 0 –1

π 2

π

3π 2

2π

4. 0ⴗ

9. 兹23

5. ⴚ45ⴗ

Practice — Chapter 14 Note: Throughout Chapter 14, answers may vary slightly due to rounding, method of calculation, or order in which solutions were found. Lesson 14.1 1. 25.5 2. 24.8 3. 16.7 4. 29.7 5. 5.6 6. 28.9 7. m⬔C ⴝ 38ⴗ, b ⴝ 4.4, c ⴝ 3.1 8. m⬔ A ⴝ 35ⴗ, c ⴝ 21.7, a ⴝ 12.7 9. m⬔C ⴝ 45ⴗ, a ⴝ 25.8, c ⴝ 18.5

32

Lesson 14.2 1. SAS; a ⴝ 17.3 2. SAS; c ⴝ 28.2 3. SAS; a ⴝ 5.3 4. SSA; b ⴝ 9.8 5. SAS; c ⴝ 31.3 6. SAS; a ⴝ 13.9 7. m⬔ A ⴝ 44.7ⴗ, m⬔ B ⴝ 38.3ⴗ, m⬔C ⴝ 97.0ⴗ 8. m⬔ A ⴝ 78.3ⴗ, m⬔ B ⴝ 37.4ⴗ, m⬔C ⴝ 64.3ⴗ 9. m⬔ A ⴝ 73.0ⴗ, m⬔ B ⴝ 61.2ⴗ, m⬔C ⴝ 45.8ⴗ 10. m⬔ A ⴝ 45.8ⴗ, m⬔ B ⴝ 30.7ⴗ, m⬔C ⴝ 103.5ⴗ 11. m⬔ A ⴝ 41.1ⴗ, m⬔ B ⴝ 80.3ⴗ, m⬔C ⴝ 58.6ⴗ 12. SAS; b ⴝ 131.2, m⬔ A ⴝ 32.5ⴗ, m⬔C ⴝ 37.5ⴗ 13. SSS; m⬔ A ⴝ 50.0ⴗ, m⬔ B ⴝ 98.7ⴗ, m⬔C ⴝ 31.3ⴗ 14. SSS; m⬔ A ⴝ 104.5ⴗ, m⬔ B ⴝ 29.0ⴗ, m⬔C ⴝ 46.5ⴗ 15. SAS; a ⴝ 6.5, m⬔ B ⴝ 20.7ⴗ, m⬔C ⴝ 109.3ⴗ 16. SSA; not possible 17. 29.0ⴗ, 75.5ⴗ, and 75.5ⴗ Algebra 2

Copyright © by Holt, Rinehart and Winston. All rights reserved.

radians 11. ⴚ45ⴗ 12. π2 radians 13. 1.5459 radians 14. 0.0345 radians 15. 2.5173 radians 16. 0.6831 radians 17. ⴚ1.5446 radians 18. ⴚ0.5769 radians 19. 9.6ⴗ 20. 35.5ⴗ 21. 48.1ⴗ 10. π6

15. two; (1) m⬔ A ⴝ 46.2ⴗ, m⬔C ⴝ 105.8ⴗ, c ⴝ 53.3; (2) m⬔ A ⴝ 133.8ⴗ, m⬔C ⴝ 18.2ⴗ, c ⴝ 17.3 16. 1532.7 feet

–2

Lesson 13.6 1. ⴚ60ⴗ 2. 120ⴗ 3. 0ⴗ 6. ⴚ60ⴗ 7. 0 8. ⴚ1

x

Answers Lesson 14.3

19.

cot ␪ ⴝ x ⴜ x ⴝ x ⴢ r ⴝ r ⴝ csc ␪ 1. cos ␪ y r y x y 2. (sin ␪ ⴚ 1)(sin ␪ ⴙ 1) ⴝ

(

)(

)

y y y2 y2 ⴚ r2 ⴚ 1 ⴝ ⴚ 1 ⴙ 1 ⴝ 2 r r r r2 ⴝ x2 ⴚ r 2 ⴝ ⴚ cos2 ␪ x2

3. 1 ⴙ cot2 ␪ ⴝ 1 ⴙ y 2 ⴝ cos2 ␪ y2

4. 1 ⴙ tan 2 ␪ ⴝ 1 ⴙ x 2 ⴝ 5. sin ␪ 9. sin ␪

6. tan2 ␪

x 2 ⴙ y 2 r2 ⴝ 2 ⴝ sec 2 ␪ x2 x

7. ⴚ1

10. sec ␪

8. tan ␪

1 ⴚ sin ␪ sin ␪ 11. cos2 ␪ ⴝ sin ␪ sin2 ␪ 1 ␪ 12. sin ␪ ⴚ cos sin ␪ (1 ⴙ cos ␪) ⴝ sin ␪ ␪ 1 13. sin ␪ ⴙ (cos ␪) cos sin ␪ ⴝ csc ␪ ⴝ sin ␪

(

Copyright © by Holt, Rinehart and Winston. All rights reserved.

x2 ⴙ y 2 r 2 y2 ⴝ y 2 ⴝ

)

Lesson 14.4

1. 兹42 ⴚ 兹46 兹2

兹6

兹2

兹6

( ) 兹2

2. 4 ⴙ 兹46 兹2

兹6

3. ⴚ 4 ⴚ 4

4. ⴚ 4 ⴙ 4

5. ⴚ 4 ⴚ 4

6. 4 ⴚ 4

兹2

兹6

兹6

兹2

兹2

兹2

兹6

兹6

7. 4 ⴙ 4

8. 4 ⴚ 4

9. 4 ⴚ 4

10. 4 ⴙ 4

11. ⴚ兹42 ⴙ 兹46 兹2

兹6

14. ⴚ 4 ⴙ 4 兹2

兹6

16. 4 ⴙ 4

Algebra 2

兹2

兹2

12. 2

兹2

兹6

兹6

15. 4 ⴚ 4 兹3

17. ⴚ 2

兹3

13. ⴚ 2

兹2

兹6

18. ⴚ 4 ⴚ 4

20.

0.5 冤 ⴚ0.87

冤 ⴚ0.71 0.71

冥

ⴚ0.71 ⴚ 0.71

冥

0.71 ⴚ 0.71 冥 0.42 ⴚ0.91 22. 冤 0.91 0.42 冥 0.77 0.64 23. 冤 ⴚ0.64 0.77 冥 ⴚ0.37 ⴚ0.93 24. 冤 0.93 ⴚ0.37 冥 21.

冤 ⴚⴚ0.71 0.71

ⴚ0.87 ⴚ0.5

25. (ⴚ5.66, ⴚ1.41), (ⴚ9.19, ⴚ4.95), (ⴚ12.02, ⴚ2.12), (ⴚ8.49, 1.41)

Lesson 14.5 1–4. Check students’ work. 5–11. Answers may vary. Sample answers: 1 ⴚ cos ␪ 6. 1 ⴙ cos ␪ 7. 2 cos2 ␪ 5. 2 2 2 8. tan ␪ 9. tan ␪ 10. cot ␪ 11. 1 ⴙ sin ␪ 12. 27 feet Lesson 14.6 1. 30ⴗ ⴙ n(360ⴗ), 150ⴗ ⴙ n(360ⴗ), 210ⴗ ⴙ n(360ⴗ), and 330ⴗ ⴙ n(360ⴗ) 2. 45ⴗ ⴙ n(360ⴗ) 3. 120ⴗ ⴙ n(360ⴗ) 4. 120ⴗ ⴙ n(360ⴗ) 5. 120ⴗ and 240ⴗ 6. 210ⴗ, 270ⴗ, and 330ⴗ 7. 45ⴗ, 135ⴗ, 225ⴗ, and 315ⴗ 8. 30ⴗ, 150ⴗ, 210ⴗ, and 330ⴗ 5π 5π π π 9. 3 and 3 10. 4 and 4

33

Answers 11.

π

12.

π

9

2

π

,

5

9

π

,

7

9

π

,

11

π

,

7

6

π

,

9

13

9

π

, and

17

9

π

, and

11

6

13. 1.23, 1.91, 4.37, and 5.05 14. 0.34, 0.52, 2.62, and 2.80 15. 25.2ⴗ

Copyright © by Holt, Rinehart and Winston. All rights reserved.

34

Algebra 2