Intermediate Algebra (11th edition)

Simplify each expression. Assume that all variables represent positive real numbers.

8. 
   
   
   
   9. 
      
      
      
      10. 
          
      
      
      
      
   
   
   
   

11. 12. 13.

14.Use the Pythagorean theorem to find the exact length of side bin
the figure.

a 7 3/4# 7 - 1/4 23 a^4 # 23 a^7

x-^4 y-^6

x-^2 y^3

b

• 2/3

3 2/5x-1/4y2/5

3 - 8/5x7/4y1/10

a 1 - 642 - 4/3

16

25

b

• 3/2

CHAPTER 8 Test 491

b

a = 12

c = 17

90 °

15.Find the distance between the points and

Simplify each expression. Assume that all variables represent positive real numbers.

16. 
    
    
    
    17. 
        
    
    
    
    


17. (Express as a radical.) 19.


18. 
    
    
    
    21. 
        
    
    
    
    

22. 23.

24. 25.

26.Write in lowest terms.

27.The following formula is used in physics, relating the velocity Vof sound to the tempera-
ture T.

(a)Find an approximation of Vto the nearest tenth if and

Use a calculator.

(b)Solve the formula for T.

Solve each equation.

28. 
    
    
    
    29. 
        
    
    
    
    


29. 
    

In Exercises 31–33, perform the indicated operations. Give the answers in standard form.

31. 
    
    
    
    32. 
        
    
    
    
    


32. 34.Simplify

35.Concept Check Answer trueor falseto each of the following.

(a)i^2 =- 1 (b)i= 2 - 1 (c)i=- 1 (d) 2 - 3 =i 23

i^37.

7 +i

1 - i

1 - 2 + 5 i 2 - 13 + 6 i 2 - 7 i 11 + 5 i 213 +i 2

2 x+ 4 - 21 - x=- 1

235 x= 232 x- 3 x+ 2 x+ 6 = 9 - x

V 0 =50,k=0.01, T=30.

V=

V 0

21 - kT

6 + 224

2

- 4

27 + 25

2

235

- 5

240

A 23 - 225 B^2

2316 t^3 s^5 - 2354 t^6 s^2 A 725 + 4 BA 225 - 1 B

22 # 235 3220 - 5280 + 42500

254 x^5 y^62432 a^7 b^13

1 - 4, 2 2 1 2, 10 2.