Chapter 7 Answers - Poudre School District

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Chapter 7 Answers

Practice 7-1

1. 12 2. -5 3. not a real number 4. 0.1 5. 0.3 6. 3

7. -3

8. 0.3

9. 6

10. -7

11. -0.4

12.

10 3

13. -20, 20

14. no real square roots 15. -100, 100 16. -0.25, 0.25

17. no real fourth roots 18. -4, 4 19. -0.1, 0.1 20. -5, 5 21. 9x2 22. 11 y5? 23. 2g2 24. 5x3 25. 3xy3

26. x - 9

27. 5(x + 2)2

28.

4x3 7

29. -2, 2

30. -3, 3

31. -0.4, 0.4

32.

247,

4 7

33. 20 cm

34a. about 25.30 ft/sec

34b. about 10.48 ft/sec

Practice 7-2

1. 2"6 2. 9xy2"y 3. 5yz2"3 6x2 4. 48x 5. 2xy

6. 27"2y

7.

3"2x 2

8.

"3y 3

"3 9x2y2 9. 3y

10.

"4 54x3 3x

11.

"2xy 4y

12. "3 6abc2 2bc

13. 10

14. 54

15. 9

16. -3

17. 3x2"2 18. 2xy3 19. 6x"x 20. 5z"3 y2z

21. 3k3"2 22. 22a4"3 2 23. xy5"z 24. 4st3"4 s3

25. 6xy"3 x 26. 5r"3r 27. 5uv2"4 u 28. "2 29. "3 4x

30.

3 k

31.

2x 25y2

"3 12y 32. 2

33.

3"3 a

34a.

r

5

3

?

34Vp ;

r

5

"3 6p2V 2p

34b. 2.88 in.

Practice 7-3

1. -63 2. -6 3. 73 4. 11"3 5. 5"2 + 2"3 6. 3"7 - 7"3 x 7. 11"3 xy 8. -2 - "3 9. 10 - 5"3

10.

-3

1 "5 2

11.

22

1 14"3 13

12. 22"2

13. 4"2

14. 0 15. 13"4 3 16. -3 - "5 17. -38 + 7"10

18. 67 - 15"7 19. 28 - 16"3 20. 9 + 2"14

21. 30 + 12"6 22. 12"7 23. 18"10 24. 41"3 - 3"6 25. 6"3 3 + 4"3 9 26. 105"x

27. 26y"5 28. 6y + 13"5y - 25 29. x - 3

30.

"5

2 3

2"2

31. "2

32.

x

1

2"3 x2 x

33a. (900 1 300"3 1 300"6) ft or about 2154 ft

33b.

270,000

1 90,000"3 2

ft2

or

about

212,942

ft2

Practice 7-4

1. 3 2. 81 3. 32 4. 256 5. 1 6. 4 7. -1 8. 9 9. 2

10.

x

5 6

11.

3

2y2

12. 4

13. 1

14.

1 2

15.

9 4

16. 0

17.

7

12x6

18.

3

1

y6

19.

2

9ab3

20.

1 y6

21.

b3 a4

22.

31

y40

23.

1

2

x21

24.

3

8a4

25.

1 9

26.

13

12x20

27.

3x2 y

28. 10.1% 29. "3 x4 30. "3 2y 31. "a3 32. "5 b

33. "3 z2 34. "4 ab

35. "5 m12

36.

1 "7 t2

37.

1 "5 a8

38.

3

x2

39.

1

m3

40.

1

(5y)2

41.

12

23y3

42.

3

b4

43.

1

(26)2

44. 36a2

45.

4

n5

3

46. (5ab)4

Practice 7-5

1. 127 2. -8, 8 3. 9 4. 3 5. no solution 6. 25 7. 9 8. -14 9. 1 10. 27 11. 4, 2 12. 9 13. 7 14. 2 15. 4 16. 29,-25 17. 10 18. 16 19. 4 20. 13 21. 4 22. -27, 27 23. 64 24. 0, -1 25. no solution 26. 64 27. 23 28. 0 29. no solution 30. -2 31. 1 32. -123 33. 8 34. 12 35. 1 36. 16 37. 8 38. -6, 2 39. 2 40. 1 41. 2 42. 66

Practice 7-6

1a. (x) = 1.8x 1b. g(x) = 0.75x 1c. g(f(150)) = $202.50

1d. No; it doesn't matter whether you first multiply by 0.75 or by 1.8. 2. 2x2 + 4x + 2; all real numbers

3. -2x2 + 4x - 4; all real numbers 4. 8x3 - 2x2 + 12x - 3; all real numbers

5.

4x 2 2x2 1

1; 3

all

real

numbers

6. 2x2 - 4x + 4; all real

numbers

7.

2x2 4x

1 2

13;

all

real

numbers

except

1 4

8. -4

9. -2

10. 7

11.

23a 1 5

2

12. -4x + 7

13. 2x2 - 3x - 7

14.

17 5

15.

16 5

16. -8x

+6

17. 245

18.

23x 1 5

2

19.

7 5

20. 3x2 - 13

21. 3x3 + 2x2 - 15x - 10 22. -2x2 + 3x + 12

23a. (x) = 0.75x 23b. g(x) = x - 5

23c. g((50)) = $32.50 23d. Yes; multiplying by 0.75 and

then subtracting by 5 is different than subtracting by 5 and

then multiplying by 0.75.

Practice 7-7

1.

y

6

2.

y

6

4

4

2

x

2O

x

4 O 2 4 6

642 2 2 6

4

6

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Algebra 2 Chapter 7

Answers

39

All rights reserved.

Chapter 7 Answers (continued)

3.

y

4.

y

5

4

2O

3

642 2 4 x

4 6

O

x 45

5. 32

y 3

2

1

x

O 123

2 3

6. 2

y 4

3

2

1

x

O 1234

2

7. y 5 4"x 2 2; no 8. y = x - 2; yes

9.

y

5

1 3

x

2

1;

yes

10. y 5 4"2x 2 3; no

11.

y

5

12 x

1

1 2

;

yes

12.

y

5

4?

1

2 3

x;

no

13. y 5 4? x5; no 14. y 5 4"x 2 3; no

15.

y

5

4?

x

1 6

4;

no

16.

y

5

4?

x

1 3

2;

no

17. y 5 4"x 1 4 2 4; no 18. y 5 4"4 2 x; no

19. f21(x) = 6x; The domain and range of f and f21 is the set of all real numbers; f21 is a function.

20. f21(x) 5 25x 1 10; The domain and range of f and f21 is the set of all real numbers; f21 is a function.

21. f21(x) 5 4"x 1 2; Domain of f = all real numbers = range of f21; Range of f = the set of real numbers greater than or equal to -2 = domain of f21; f21 is not a function.

22. f21(x) 5 4"x 2 4; Domain of f = all real numbers = range of f21; Range of f = all real numbers greater than or equal to 4 = domain of f21; f21 is not a

function.

23. f21(x) 5 x2 1 1; Domain of f = all real numbers greater than or equal to 1 = range of f21; Range of f = all real numbers greater than or equal to 0 = domain of f21; f21 is a function.

24. f21(x) 5 31x2; The domain and range of f and f21 is the set of all real numbers greater than or equal to 0; f21 is a function.

25. x ?3 ?2 ?1 0 y ?2 ?1 0 1

y

2

2 O 2

x 2

26. x ?3 ?1 0 ?2 y 0 12 3

y

2

2 O 2

x 2

27. -1 28. 3 29. 212 30. f21(x) 5 x 21986,3950,0600; in 2009

Practice 7-8

1.

y

6

4

2O

x

642 2 2 4 6

4

6

2.

y

6

4

2O

x

2 2 2 4 6 8 10

4

6

3.

y

6

4

2O

x

2 2 2 4 6 8 10

4

6

4.

y

6

4

2O

x

2 2 2 4 6 8 10

4

6

5.

y

6

4

2O

x

2 2 2 4 6 8 10

4

6

6.

y

6

4

2O

2

4 6

68 x

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40

Answers

Algebra 2 Chapter 7

All rights reserved.

Chapter 7 Answers (continued)

7.

y

4

2O

x

42 2 2 4 6 8

4

6

8

8.

y

6

4

2O

x

2 2 2 4 6 8 10

4

6

9.

y

6

10.

y

6

4

4

2O

x

2O

2 2 2 4 6 8 10

4 2 2 4 6 x

4

4

6

6

11.

y

6

4

2O

x

2 2 2 4 6 8 10

4

6

12.

y

6

4

2O

x

2 2 2 4 6 8 10

4

6

13.

y

6

14.

y

6

4

4

2O

x

O

x

2 2 2 4 6 8 10

2 2 2 4 6 8

4

6

6

15.

y

6

4

2O

x

2 2 2 4 6 8 10

4

6

16.

y

4

3

2

1O

x

1 1 2 3 4 5

2

17.

3y

18. 5 y

2

4

1O 321

2 3

x 23

3

2

1O

x

1 1 2 3 4 5

19.

6y

4

3

2

1O

x

21 1 2 3 4

20. 5 y

4

3

2

1O

x

123456

21.

3y

2

1O

x

21 1 2 3 4

2 3

22. 3 y 2 1O

1

2 3

x 2345

23.

2y

1O x

4321 1 2

2 3 4

24.

3y

2

1O x

4321 1 2

2 3

25.

1

y O

x

1 1 2 3 4 5

2 3 4 5

26.

4y

3

2

1O

x

321 1 2 3

2

27. 5 y

4

3

2

1O

x

1 1 2 3 4 5

28a. r 12

28b. about 10.6 ft

8

4

O

A

100 200 300

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Algebra 2 Chapter 7

Answers

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All rights reserved.

Chapter 7 Answers (continued)

29. 75

30. 7

31.

no

solution;

3 2

is

extraneous

32. 2.36

33. y 5 9"x 1 2; graph of y 5 9"x shifted left

2 units 34. y 5 22"x 1 5; graph of y 5 22"x shifted left 5 units 35. y 5 5"3 x 2 2; graph of y 5 5"3 x

shifted right 2 units 36. y 5 28"x 1 3; graph of y 5 28"x shifted left 3 units 37. y 5 22"3 x 2 7 1 4; graph of y 5 22"3 x shifted right 7 units and up 4 units

38. y 5 5"x 1 3 2 1; graph of y 5 5"x shifted left

3 units and down 1 unit

39.

y

2

2 O 2 2

40.

y

2

x

x

4 2 O 2

4

2

4

41.

y

42.

y

2

2 O 2

x 2

2

2 O 2

2x

43.

y

44.

y

2

2

2 O 2

2x

4 2 O 2 x 2

Reteaching 7-1

1. 6 u x u

2. 6y

3.

1 10 ux

u

4.

x10 y4

5.

x (x

1 2

3 4)2

6. x2y3z

7.

(z

3z 1 12)2

8. 7 u x3 u

9.

11 x

(y 2 4)2 10. u z 1 9 u

11.

a2b2 c

12. -xy2

Reteaching 7-2

1.

"5x x

2.

"3 3b a

"4 9x3y 3. x

"30xy 4. 6

5.

k"3 k 4

6.

x2"15xy 5y

7.

"4 10z2 z

8.

"3 19ac2 c2

Reteaching 7-3

1. 3

2.

"3 1 2

1

3. 20 1 15"6

4.

211

1 3

4"7

5. 40 2 28"2 6. 2"5 2 "15

Reteaching 7-4

1.

19

y15

2.

1 4xy4

3.

1

1

z3

4. 16x

5.

7 3x4

5y 6. x3

7.

1 x

8.

4b6 a2

9.

5x4 4z2

3

10. a2

1

14.

2r2 s

15. 27z15

21

11. x5y5

12.

n2 9m6

1

13. 6x2

Reteaching 7-5

1. 169 2. 8 3. 2 4. no solution 5. 3 6. 9 7. 16 8. 7 9. 5

Reteaching 7-6

1. 5 2. 15 3. 10 4. 10 5. 10 6. 100 7. 102 8. 102 The first input should be one color. Answers 3 and 4 should be a second color. Answers 7 and 8 should be a third color. 9. 77 10. 35.5 11. 13 12. 21

Reteaching 7-7

1.

y

5

x

1 4

5

2.

y

5

3x ?

2 3

2

3. y 5 "3 x 2 1

4. y 5 2x 2 4

5. -1(x) = x - 3

6. 21(x)

5

x

1 2

4

7. -1(x) = 5x

8. 21(x)

5

x

2 4

2

9. y = x

10. y = x + 3 11. y = 2x + 1 12. y 5 "3 x 1 8

13. -1(x) = x2 - 2

14.

21(x)

5

3 2

(x

1

1)

15. -1(x) = 5x - 3

16.

21(x)

5

5

4

x ?2

17. y = (x - 4)2

18.

y

5

x

2 8

1

Reteaching 7-8

1. y

2.

4

2

x

O

246

2

y

x

2 O

2

2

4

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42

Answers

Algebra 2 Chapter 7

All rights reserved.

Chapter 7 Answers (continued)

3.

y

4.

y

2 2 O

x 2

x 4 2 O

2

2

5.

y

6.

y

6

2

x

4

2 O 2

2

2

x

4 2 O

7.

y

2

O2 2

4

8.

x 4

4 2

y x

O

2

4

9.

y

6

10. y

2

4

x

2

O 24

x

2

O 24

11. y 2

O 24 2

12. x

y

4

4 O 4

x 4

Enrichment 7-2

The Goldbach Conjecture

2"3 xy 1. y

"4 x3y3 2. y2

3. "3 y

"5 xy4 4. y

5.

x2 y2

6. xy

7. "6 x4y

"4 x3y2 8. x

9.

4"x 3y

10. "6 xy

11.

2"xy y

"4 x3y3

"5 xy4

2"xy

2"5 x2y2

12. y2 13. y 14. y 15. xy 16. y

17. x

18. "3 y

19.

2"xy y

2"3 xy 20. y

21. x"4 y

22.

5x2"y y

23. "3 y

Enrichment 7-3

A 23 2 2"2 C 0 1 4"5 E 22 2 3"30 E 1 1 5"3 I 21 1 3"5 P 21 2 4"61 R 22 1 2"5 S 24 2 "7

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10

R1

S

R2

A

R3

E

R

R4 P

I

R5

C

R6

E

Enrichment 7-4

11111

1. final r 5 "x

2.

122222

a a a a ax2b b b b b ;

1

x64;

26;

210;

212;

1; yes 3. 2 4. 2 5. 1 6. "3 2

Enrichment 7-1

11483, 11.483; 13271.8, 13272.3, 13272, 132.72; 349.99, 350.49, 350, 35.0; 2.000001, 2.000000; 1.999, 2.000; 2.0, 2.2

Enrichment 7-5

1. 3;C 2. 1, 3; H 3. -2; A 4. 0, 4; R 5. -1; L 6. 2, 4; E 7. -2, -1; S 8. 2; blank 9. 4; D 10. 3, 4; O 11. -3; D 12. 1, 5; G 13. -1; S 14. -2; O 15. 6; N Charles Dodgson

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Algebra 2 Chapter 7

Answers

43

Chapter 7 Answers (continued)

All rights reserved.

Enrichment 7-6

1. B = D 2. g(x) = Cx + B 3. A + B = C + B 4. A = C 5. when the coefficients of x are equal and the constant

terms are equal

6. ACx + BC + D 7. linear 8. AC 9. BC + D 10. ACx + AD + B 11. BC + D = AD + B 12. AC = A and AD + B = B 13. AC = C and AD + B = D 14. AC = 0 and AD + B = 0 15. constant 16a. if h(x) = k(x) 16b. if h(x) = k(x) 16c. h + k always equals h 16d. if h(x) = 0

Enrichment 7-7

5(F 2 32)

1. K 5

9

1 273

2. F 5 59(K 2 273) 1 32

3. Kelvin; Fahrenheit 4. F 5 95C 1 32 5. C 5 K 2 273

6. F 5 59(K 2 273) 1 32

7. c = 10,000 + 2000(y - 1940);

y

5

c

2 10,000 2000

1

1940;

find the year given the cost of a house 8. h = 2(a - 5) + 42;

a

5

h

2 2

42

1

5;

compute Mary's age given her height 9. a = 200(-T + 110); find the altitude of the airplane given the temperature 10. W 5 L 02.250.5; find the weight attached to the spring given the length of the stretched spring

Enrichment 7-8

1. reflect across the x-axis, stretch by a factor of 3, shift right 5 units and shift up 7 units 2. y 5 2"3 x 2 4 2 6

3.

y

4. g(x) = f(x + 1) - 3

4

4 O 4

x 4

Chapter Project

Activity 1: Creating Check students' work.

Activity 2: Investigating Check students' work.

Activity 3: Analyzing

t 5 2p? 98/0; Check students' work; The weight of the bob is not a factor in the period of a pendulum; Check students' work.

Checkpoint Quiz 1

1. -3x2 2. a2 u b3 u 3. -2s3t2 4. 4y2 5. -1 6. 2a2

7. 25

8.

27

1

7"3 2

9. 6"2

10. 90x2y2"2y

Checkpoint Quiz 2

1.

1 8x6

2. 256a12

3.

7 4

4.

5 6

5. 227, 217

6. -2

7. 12

8. 257 9. 15 10. 120

Chapter Test, Form A

1. 20 u xy3 u 2. -5a3 3. 3 u x u y2"4 xy 4. 4a2"3 b2

5. 5 u s u t2"2

6. 4x4 u y7 u

7.

10x y2

8. 46

9.

5

2 "3 22

10. 4x4

11. 2"7

12.

"3 4

1 2

"3 2

13. 22 1 2"2

14.

"4 20 2

15. "15 2 15"3

8x3y6 16. 27

17.

1 16

7

18. a6

19.

x 2y2

20. 1

21.

9

s10

5

t6

22. 4

23. 2

24. 4

25. 13 26. 4"21 27. -9, 7

28.

x2 x

1 2

75;

all

real

numbers

except

7

29. x2 - 2x + 19; all real numbers 30. x3 - 7x2 + 5x - 35; all real numbers 31. 3x2 + 8; 9x2 + 30x + 26 32. 4x2 - 10x + 2; 2x2 - 10x + 4

33. "10x 1 5; 5"2x 2 1 1 3 34. 22x2 2 16x 2 32; 22x2 1 4

35. y 5 3"x 2 7 1 4; graph of y 5 3"x shifted right

7 units and up 4 units 36. y 5 2"3 x 2 8 2 5; graph of y 5 2"3 x shifted right

8 units and down 5 units 37. y 5 23"3 x 1 1 1 4; graph of y 5 23"3 x shifted left

1 unit and up 4 units 38. y 5 4"x 2 2; graph of y 5 "4 x shifted right 2 units

39.

y

4

2

x O 24

domain: x $ 1; range: y $ 2

44

Answers

Algebra 2 Chapter 7

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Chapter 7 Answers (continued)

All rights reserved.

40.

y

x

4 2 O

2

4

domain: x $ 23; range: y # 21

41.

y

4

2

x O 24

domain: x $ 0; range: y $ 3

42.

y

x

4 2 O

2

4

domain: x $ 24; range: y # 21 43. 80 44. 11 45. 15 46. 21 47. -9 48. -1 49. f21(x) 5 4"x 1 4 2 2; not a function

50.

f21(x)

5

3x ?

1 4

1; function

51. f21(x) 5 x2 2 4; function

52.

f21(x)

5

x

2 3

2; function

53. f21(x) 5 4"x 1 5; not a function

54. f21(x) 5 x3 2 2; function

55a. 360 ft 55b. 360 ft 56. Check students' work.

Chapter Test, Form B

1. 30a2 u b3 u 2. -4x4 3. 4s2 u t u "2 4. 3 u x3y9 u 5. 37

6. 6x2y

7. 2"5

8. 23 2 3"2

9.

"4 12 2

10. "6 2 6"2

1 11. 27x6

5

12. b4

13.

x2 3y

14. 1

15. 211

16. 4

17. 34 18. 43"5 19. 4x3 + 20x2; all real numbers

20.

x

1 4

5;

all

real

numbers

except

0

21. 25x2 - 10x; 5x2 - 10x 22. 2x2 + 5; 4x2 - 4x + 4

23. y 5 3"3 x 2 2 1 2; graph of y 5 3"3 x shifted right

2 units and up 2 units 24. y 5 7"x 2 3 1 1; graph of y 5 7"x shifted right 3 units and up 1 unit

25. D 26. B 27. A 28. C 29. 31 30. -1 31. 49 32. -1

33. f21(x) 5 4"x 2 3 1 1; not a function

34. f21(x) 5 x3 1 5; function

35.

f21(x)

5

x

1 4

5; function

36. f21(x) 5 4"x 2 7; not a function

Alternative Assessment, Form C

TASK 1 Scoring Guide:

3 Student writes three original expressions correctly. Student shows the steps in simplifying.

2 Student writes two of the three original expressions correctly. Student shows the steps in simplifying, making only minor errors.

1 Student writes one original function correctly, with errors in the others. Student has some errors in simplifying.

0 Response is missing or inappropriate.

TASK 2 Scoring Guide:

3 Student writes a correct equation and shows all steps in its solution. Student gives clear and thorough explanations to the other questions.

2 Student writes an equation with a minor error but shows all steps in the solution. Student gives good explanations to the other questions.

1 Student writes an equation that does not satisfy the criteria or does not show the solution to the equation. Student gives an explanation with some conceptual errors.

0 Response is missing or inappropriate.

TASK 3 Scoring Guide:

a.

x2

x 1

2 x

2 2

; 12

all

real

numbers

except

3

and

-4

b. x2 + x - 14; x2 - 3x - 10; no

c. when f and g are inverses

3 Student performs all calculations correctly and gives a thorough explanation to the questions.

2 Student performs most calculations correctly and gives a satisfactory explanation to the questions.

1 Student performs some calculations correctly. Explanations are unclear or incomplete.

0 Response is missing or inappropriate.

Algebra 2 Chapter 7

Answers

45

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Chapter 7 Answers (continued)

TASK 4 Scoring Guide: a. f21(x) 5 (x 2 5)2 1 2; domain: x $ 5 b. (f + f21)(a) 5 (f21 + f)(a) 5 a

c.

y

6

f

;

4

f1

2

x

O

246

The graphs are a reflection of each other across the line y = x.

3 Student performs all calculations correctly and gives a thorough explanation to the questions.

2 Student performs most calculations correctly and gives a satisfactory explanation to the questions.

1 Student makes some errors in calculations and/or makes conceptual errors in the explanation.

0 Response is missing or inappropriate.

Cumulative Review

1. B 2. J 3. C 4. G 5. B 6. F 7. C 8. F 9. C 10. G 11. C 12. F 13a. 4x + 7 13b. x2 + 6x + 5

14a. -13 14b. -4 401

15. ? 4 4 1 ?

510

16.

625a16b4 16

17. -59

18. Check students' work. 19. Answers may vary. Sample: (x) = (x + 2)2 + 3

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? Pearson Education, Inc., publishing as Pearson Prentice Hall.

46

Answers

Algebra 2 Chapter 7

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