Intermediate Algebra (11th edition)

57.about 68,600 calls 59.Answers will vary. 61. 8 63.

65.not a real number

Chapter 7 Review Exercises (pages 420–423)

1. (a) (b) 2. (a)2, 5 (b)


2. (a) 9 (b) 4. 5. 6.

7.The reciprocal of a rational expression is another rational expression

such that the two rational expressions have a product of 1.

8. 
   
   
   
   9. 
      
      
      
      10. 
          
          
          
          11. 1 12.
          
          
          
          
      
      
      
      
   
   
   
   


9. 
   
   
   
   14. 
       
   
   
   
   


10. 
    
    
    
    16. 
        
        
        
        17. 12 18.
        
        
        
        
    
    
    
    


11. 20.Both students got the correct

answer. The two expressions obtained are equivalent. 21.

22. 
    
    
    
    23. 
        
        
        
        24. 
            
            
            
            25. 
                
                
                
                26. 27.{0}
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


23. 
    
    
    
    29. (a) (b) is not in the domain. 30.In
    
    
    
    

simplifying the expression, we are combining terms to get a single frac-
tion with a denominator of 6x. In solving the equation, we are finding a

value for xthat makes the equation true. 31.C; 32.

33. 
    
    
    
    34. 35.6000 passenger-km per day
    
    
    
    

36.16 km per hr 37. 38. 39.C 40.430 mm

41.5.59 vibrations per sec 42. 43. 44.

45. 
    
    
    
    46. , or 47. 48.
    
    
    
    


46. 
    
    
    
    50. 
        
        
        
        51. 
            
            
            
            52. 
                
            
            
            
            
        
        
        
        
    
    
    
    


47. 
    
    
    
    54. 
        
        
        
        55. 
            
        
        
        
        
    
    
    
    


48. , or 57. 58.


49. (a)about 8.32 mm (b)about 44.9 diopters 60.

61.$36.27 62. 63. 64.480 mi 65.150 mi

Chapter 7 Test (pages 423–424)

[7.1]1. 2. 3.

4. 
   
   
   
   5. 
      
      
      
      6. [7.2]7.
      
      
      
      
   
   
   
   


5. 
   
   
   
   9. 
      
      
      
      10. 
          
          
          
          11. 
              
          
          
          
          
      
      
      
      
   
   
   
   

[7.3]12. 13. 14.

[7.4]15. (a)expression; (b)equation;

16. 
    
    
    
    17. 
        
        
        
        18. , or /=
            2 S-na
            n
            /=
            2 S
            n
            E^12 F 556 - a
        
        
        
        
    
    
    
    

566

111 x- 62

12

2 y^2 +x^2

xy 1 y-x 2

• 1
  a+b

72

11

4

x+ 2

11 x+ 21

1 x- 3221 x+ 32

9 a+ 5 b

21 a^5 b^3

7 - 2 t

6 t^2

t^21 t+ 321 t- 22

x+ 5

x

• 2

y+ 4

y- 5

31 x+ 32

4

2 x- 5

x 13 x- 12

• 2,^43 ;Ex|xZ-2,^43 F

12 ft^2412 mi

847 min

r= 5 1, 4 (^6) E-^143 F

• AR
  A-R
  r=
  AR
  R-A

E^13 F

acd+b^2 d+bc^2

bcd

5 a^2 + 4 ab+ 12 b^2

1 a+ 3 b 21 a- 2 b 21 a+b 2

x 19 x+ 12

3 x+ 1

k- 3

36 k^2 + 6 k+ 1

s^2 +t^2

st 1 s-t 2

1

3

3 - 5 x

6 x+ 1

x^2 - 6

212 x+ 12

• 11
  x- 3

11

3 - x

6 m+ 5

3 m^2

x+ 5

x+ 2

1

x- 2 y

22.5 ft^3

445 min 335 hr

M=

mm

n-m

m=

Fd^2

GM

15

x=0;y= (^02)
0 5 x|xZ- 36 - 3
5 - 36 5 - 26
y+x
xy
1
3 q+ 2 p

• 2

3 + 2 t

4 - 7 t

13 r^2 + 5 rs

15 r+s 212 r-s 21 r+s 2

71

301 a+ 22

15 y^2 - 8 x^2

9 x^6 y^7

31 x- 4221 x+ 22

9 r^213 r+ 12 13 x- 1212 x+ 5213 x+4)

96 b^5

z 1 z+ 22

z+ 5

• 31 w+ 42
  w

3 y^212 y+ 32

2 y- 3

• 1
  2 +r

5 m+n

5 m-n

x

2

5 x|xZ 96

• 
  

  6 5 x|xZ- 66 5 x|xZ2, 5 6

  
  


• 
  

  (^4) 19. ; [7.5]20. hr
  21.15 mph 22.48,000 fish

  
  

23. (a)3 units (b) 0
    [7.6]24.200 amps 25.0.8 lb

Chapters 1–7 Cumulative Review Exercises

(pages 425–426)

[1.3]1. [2.1]2. [2.7]3.

[2.5]4. [2.7]5.

[2.3]6.$4000 at 4%; $8000 at 3% 7.6 m

[3.1]8.x-intercept: y-intercept:

[3.2]9. 10. [3.3]11.

[3.4]12. 13.

[3.5]14.function; domain: range:

[3.6]15. (a) , or (b) [4.1, 4.4]16.

[4.2, 4.4]17. 18. [4.3]19.automobile: 42 km per hr;

airplane: 600 km per hr [5.1]20. [5.2]21.

[5.4]22. 23.

[5.5]24. [5.3]25. (a)

(b) (c) (d)

[6.2]26. [6.3]27.

28. [6.5]29. [7.1]30.


29. 
    
    
    
    32. [7.2]33. 3
    
    
    
    

[7.4]34. [7.5]35. hr [7.6]36.$9.92

ROOTS, RADICALS, AND ROOT FUNCTIONS

Section 8.1 (pages 433– 435)

1.E 3.D 5.A 7. 9. 6 11. 13. 15. 6 17.

19.It is not a real number. 21. 2 23.It is not a real number. 25.

27. 
    
    
    
    29. 
        
        
        
        31. 3 33.0.5 35. 37.0.1
        
        
        
        
    
    
    
    


28. (a)It is not a real number. (b)negative (c) 0
    In Exercises 41–47, we give the domain and then the range.

(^43) - (^12) - 0.7
8
9

• 9 - 4 - 8 - 2

8

6

5 - (^465)
21 x+ 32
1 x+ 221 x^2 + 3 x+ 92
a 1 a-b 2
21 a+b 2
y+ 4
E y- 4
12 p+ 5214 p^2 - 10 p+ 252 -^73 , 1F
12 x+ 521 x- 92 2512 t^2 + 1212 t^2 - 12
2 x^3 - 4 x^2 + 2 x+ 2 - 14 x^4 + 2 x^2 - 3
x^2 + 4 x- 7 2 x^3 - 2 x^2 + 6 x- 4
1
16 x^2 +
5
12ƒ^2 +5ƒ- 3 2 x+ 25
4 y^2 - 7 y- 6
m
n
51 - 2, 3, 1 26 0

• 1 51 - 1, 3 26
  5
  3
  x-
  8
  3

5 x- 8

3

3 - 2,q 2 ; 1 - q, 0 4

3

34

–3

0

y

x

x – y≥ 3 and

3 x + 4y≤ 12

2

0 5

y

x

2 x + 5y > 10

-^32 - 43 y=- 23 x+^12

–2

4

0

y

x

–4x + 2y = 8

1 - 2, 0 2 ; 1 0, 4 2

A-q,^24013 D^1 - q,-^24 ́C^23 ,qB

• 199 E-^154 F E^23 , 2F

3143

x

y

–1

2

f(x) =x–2 + 1

x=- 1 y= 0

Answers to Selected Exercises A-17

41. 
    
    
    
    43. 
        
    
    
    
    

x

y

0

–2^49

f(x) = √x – 2

3 0,q 2 ; 3 - 2,q 2

x

y

0

2

–3 1

f(x) = √x + 3

3 - 3,q 2 ; 3 0,q 2