Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Solve.

9. 3 x + 3 = 15 3 square root of x plus 3 equals 15
10. 4 x − 1 = 3 4 square root of x minus 1 equals 3
11. x + 3 = 5 square root of x plus 3 end root , equals 5
12. x + 1 = 4 square root of x plus 1 end root , equals 4
13. 2 x − 1 = 3 square root of 2 x minus 1 end root . equals 3
14. x + 2 − 2 = 0 square root of x plus 2 end root , minus 2 equals 0
15. 3 x + 4 = 4 square root of 3 x plus 4 end root . equals 4
16. 2 x + 3 − 7 = 0 square root of 2 x plus 3 end root . minus 7 equals 0
17. 6 − 3 x − 2 = 0 square root of 6 minus 3 x end root . minus 2 equals 0

See Problem 2.

Solve.

18. ( x + 5 ) 2 3 = 4 open , x plus 5 , close super 2 thirds end super . equals 4
19. ( x + 2 ) 2 3 = 9 open , x plus 2 , close super 2 thirds end super . equals 9
20. 3 ( x − 2 ) 3 4 = 24 3 . open , x minus 2 , close super 3 fourths end super . equals 24
21. 3 ( x + 3 ) 3 4 = 81 3 . open , x plus 3 , close super 3 fourths end super . equals 81
22. ( x + 1 ) 3 2 − 2 = 25 open , x plus 1 , close super 3 halves end super . minus 2 equals 25
23. 3 + ( 4 − x ) 3 2 = 11 3 plus . open , 4 minus x , close super 3 halves end super . equals 11

    See Problem 3.

24. Volume A spherical water tank holds 9000  ft  3 9000 , ft cubed of water. What is the diameter of the tank? (Hint: d = 6 V π 3 d equals . cube root of fraction 6 v , over pi end fraction end root , )
25. Hydraulics The formula d = 4 Q π v d equals . square root of fraction 4 q , over pi v end fraction end root  models the diameter of a pipe where Q is the maximum flow of water in a pipe, and v is the velocity of the water. What is the diameter of a pipe that allows a maximum flow of 30  ft/min 3 30 , ftslashmin cubed of water flowing at a velocity of 400 ft/min? Round your answer to the nearest inch.

See Problem 4.

Solve. Check for extraneous solutions.

26. 3 x + 7 = x − 1 square root of 3 x plus 7 end root . equals x minus 1
27. ( 5 − x ) 1 2 = x + 1 open , 5 minus x , close super 1 half end super . equals x plus 1
28. − 3 x − 5 = x + 3 square root of negative 3 x minus 5 end root . equals x plus 3
29. 11 x + 3 − 2 x = 0 square root of 11 x plus 3 end root . minus 2 x equals 0
30. ( 5 x − 4 ) 1 2 − x = 0 open , 5 x minus 4 , close super 1 half end super . minus x equals 0
31. 3 x + 13 − 5 = x square root of 3 x plus 13 end root . minus 5 equals x
32. x + 7 + 5 = x square root of x plus 7 end root , plus 5 equals x
33. ( x + 3 ) 1 2 − 1 = x open , x plus 3 , close super 1 half end super . minus 1 equals x
34. x + 7 − x = 1 square root of x plus 7 end root , minus x equals 1

See Problem 5.

Solve. Check for extraneous solutions.

35. 3 x = x + 6 square root of 3 x end root , equals , square root of x plus 6 end root
36. ( 2 x ) 1 2 = ( x + 5 ) 1 2 open , 2 x , close super 1 half end super . equals . open , x plus 5 , close super 1 half end super
37. ( 7 x + 6 ) 1 2 − ( 9 + 4 x ) 1 2 = 0 open , 7 x plus 6 , close super 1 half end super . minus . open , 9 plus 4 x , close super 1 half end super . equals 0
38. 3 x + 2 − 2 x + 7 = 0 square root of 3 x plus 2 end root . minus . square root of 2 x plus 7 end root . equals 0
39. ( x + 5 ) 1 2 − ( 5 − 2 x ) 1 4 = 0 open , x plus 5 , close super 1 half end super . minus . open , 5 minus 2 x , close super 1 fourth end super . equals 0
40. ( x − 2 ) 1 2 − ( 28 − 2 x ) 1 4 = 0 open , x minus 2 , close super 1 half end super . minus . open . 28 minus 2 x . close super 1 fourth end super . equals 0
41. 5 − x − x = 1 square root of 5 minus x end root , minus square root of x equals 1
42. 3 x + 1 − x + 1 = 2 square root of 3 x plus 1 end root . minus , square root of x plus 1 end root , equals 2
43. 2 x + 6 − x − 1 = 2 square root of 2 x plus 6 end root . minus , square root of x minus 1 end root , equals 2
44. 3 − x + x + 2 = 3 square root of 3 minus x end root , plus , square root of x plus 2 end root , equals 3

B Apply

45. Think About a Plan A hexagonal tray of vegetables has an area of 450  cm  2 . 450 , cm squared . . What is the length of each side of the hexagon?
    • What is the area of the triangle at the bottom in terms of the side length?

    • How can you use the diagram below to find the formula for the area of the hexagon? (Hint: Six triangles make one hexagon.)

      

46. Traffic Signs A stop sign is a regular octagon, formed by cutting triangles off the corners of a square. If a stop sign measures 36 in. from top to bottom, what is the length of each side?

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