Math 120 Exam 3 Review

1. Simplify the following expression. Assume that each variable may be positive or negative.

2. Simplify the following expression. Assume that each variable is positive.

3. Divide and simplify the radicals by using the quotient rule for radicals.

4. Divide and simplify the above radicals by using the quotient rule for radicals. Please rationalize the denominator before entering your answer.

5. Simplify the following expression.

6. Simplify the following expression.

7. Simplify the following expression.

7. Simplify the following expression.

9. Simplify the following expression. Enter the solution using rational exponents. Assume that the variables are positive.

10. Simplify the following expression. Assume that the variables are positive.

11. Change the following expression to an equivalent expression in exponential notation, and then simplify. Assume that the variable is positive.

12. Change the following expression to an equivalent expression in exponential notation, and then simplify. Assume that the variable is positive.

13. Change the following expression to an equivalent expression in exponential notation, and then simplify. Assume that the variable is positive.

14. Divide and simplify the above radicals by using the quotient rule for radicals. Please rationalize the denominator before entering your answer

15. Simplify the expression by combining the radical terms using the indicated operation(s).

16. Simplify the expression above by combining the radical terms using the indicated operation(s).

17. Simplify the expression above by combining the radical terms using the indicated operation(s). Assume all variables are positive.

18. Simplify the expression above by combining the radical terms using the indicated operation(s). Assume all variables are positive.

19. Multiply and simplify the radical expressions.

20. Simplify the expression by rationalizing the denominator

21. Simplify the expression by rationalizing the denominator.

22. Multiply and simplify the radical expressions. Assume all variables are positive.

23. Givenfind f (7). Your answer should be written in radical notation.

24. Givenfind g(7). Your answer should be written in radical notation.

25. Givenuse interval notation to indicate the domain. Note: Round any decimal values to two decimal places.

26. Given

Select the correct graph.

27. Given

Select the correct graph

28. Find the sum of the following expressions

29. Find the difference of the following expressions.

30. Find the sum of the following expressions.

31. Simplify the following expression:

32. Find the product:

33. Find the product:

34. Find the quotient:

35. Find the quotient:

36. Simplify the following:

37. Solve the quadratic equation by extracting roots and enter the solutions in radical form . Simplify the solutions before entering.

38. Consider the following quadratic equation:

39. Consider the following quadratic equation:

40. Consider the following quadratic equation:

41. Solve the quadratic equation above by completing the square. Simplify the solutions and rationalize the denominators before entering your answer.

42 Solve the quadratic equation above by completing the square. Simplify the solutions and rationalize the denominators before entering your answer.

43. Solve the quadratic equation above by completing the square. Simplify the solutions and rationalize the denominators before entering your answer.

44. Solve the quadratic equation using the quadratic formula.

45. Solve the quadratic equation using the quadratic formula.

46. Solve the quadratic equation using the quadratic formula.

47. Solve the quadratic equation using the quadratic formula.

48. A rectangle has a length of 19 feet less than 5 times its width. If the area of the rectangle is 66 square feet, find the length of the rectangle.

49. A small motorboat travels 12 mph in still water. It takes 6 hours longer to travel 36 miles going upstream than it does going downstream. Find the rate of the current. ( Hint: 12 + x = rate going downstream and 12 - x  = rate going upstream.)( Round off your answer to the nearest tenth. )

50. Two companies working together can clear a parcel of land in 9 hours. Working alone, it would take Company A 4 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone? (Round off your answer to the nearest tenth.)

51. Two pipes can fill a tank in 99 minutes if both are turned on. If only one is used, it would take 45 minutes longer for the smaller pipe to fill the tank than the larger pipe. How long will it take for the smaller pipe to fill the tank? (Round off your answer to the nearest tenth.)

52. A plane travels at a speed of 220 mph in still air. Flying with a tailwind, the plane is clocked over a distance of 750 miles. Flying against a headwind, it takes 1 hour more time to complete the return trip. What was the wind velocity? (Round off your answer to the nearest tenth.)

53. A rectangular auditorium seats 2820 people. The number of seats in each row exceeds the number of rows by 13. Find the number of seats in each row.

54. The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $3200, which was to be divided equally among the members going. Prior to the trip, 10 members decided not to go. If the cost per person increased by $16, how many people went on the expedition?

55. An arrow is shot vertically upward from a platform 29 ft. high at a rate of 235 ft. per sec. When will the arrow hit the ground? Use the formula: h = -16t^2 + v0t + h0(Round off your answer to the nearest tenth.)

56. The hypotenuse of a right triangle is four times the length of one of the legs. The length of the other leg is feet. Find the lengths of the leg and hypotenuse.

57. Solve the radical equation.

58. Solve the radical equation.

59. Solve the radical equation.

60. Solve the radical equation.

61. Solve the radical equation.

62. Find the four solutions to the following equation. Simplify your answers

63. Find the two solutions to the following equation. Simplify your answers.

64. Find the two solutions to the following equation. Simplify your answers.

65. Find the two solutions to the following equation. Simplify your answers.

66. Find the two solutions to the following equation. Simplify your answers.

67. Find the solution(s) to the following equation. Simplify your answers.

68. Find the five solutions to the following equation. Simplify your answers.

69. Find the four solutions to the following equation. Simplify your answers.

70. Solve the following equation using the quadratic formula. Simplify your answers.