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
? Pearson Education, Inc., publishing as Pearson Prentice Hall.
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
? Pearson Education, Inc., publishing as Pearson Prentice Hall.
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
? Pearson Education, Inc., publishing as Pearson Prentice Hall.
Algebra 2 Chapter 7
Answers
41
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
? Pearson Education, Inc., publishing as Pearson Prentice Hall.
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
? Pearson Education, Inc., publishing as Pearson Prentice Hall.
Algebra 2 Chapter 7
Answers
43
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