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Radicals and Quadratic Equations

Please see the attached file for the fully formatted problems.

1. Simplify.

2. Simplify. Write your answer with only positive exponents.

A)

B)

C) r10
D) r2

3. A triangle has sides 2x - 5, 3x + 1, and 4x + 2. Find the polynomial that represents its perimeter.
A) (2x - 5)(3x + 1)(4x + 2)
B) 24x - 10
C) 9x - 2
D) 10x - 8

4. Multiply. (2m - n)2

5. Divide.

A) x2 - x + 4
B) x2 + x + 4
C) x2 - x - 4
D) x2 + x - 4

6. Factor. 12x4y3 + 16x3y3 - 20x3y4

7. Factor completely. 3x2 + 15x + 18

8. Factor completely. 6x2 - xy - 5y2
A) (3x + 5y)(2x - y)
B) (3x - 5y)(2x + y)
C) (6x + 5y)(x - y)
D) (6x - 5y)(x + y)

9. Factor by grouping. x5 + 3x3 + 2x2 + 6

10. Factor completely. 5a2 - 125
A) 5(a + 5)(a - 5)
B) 5(a - 5)2
C) 5a(a - 25)
D) (5a - 1)(a - 125)

11. Write in simplest form.

12. Divide.

A)

B)

C)

D)

13. Subtract. Write your answer in simplest form.

14. Solve.

A) -8
B) -29
C) -17
D) No solution

15. A car uses 10 gallons of gasoline on a trip of 350 miles. At that rate, how much gasoline will a trip of 525 miles require?

16. Simplify.

17. Simplify.

18. Simplify.

19. Simplify.

20. The base of a ladder is 8 feet away from the wall. The top of the ladder is 17 feet from the floor. Find the length of the ladder to the nearest thousandth.
A) 18.788 feet
B) 16.656 feet
C) 21.089 feet
D) 17.767 feet

21. Solve. 5(x - 2)2 = 3
A)

B)

C)

D)

22. Solve by using the quadratic formula. x2 + 8x + 15 = 0

23. The area of a square is 82 ft2. Find the length of the side to the nearest hundredth.

24. How long must a guywire be to run from the top of a 18 ft pole to a point on the ground 12 fee away?

25. Solve.
2x2 - 8x + 5 = 0

26. A picture is 2.5 m long by 2.0 m wide. It is held by a frame of uniform width around its outside edge. If the picture itself (without the frame) is 4 m2, what is the width of the frame to the nearest centimeter?

27. Suppose the cost C, in dollars, of producing x tables is given by the equation
C = 2x2 - 40x + 2400. How many tables can be produced for $4650?

28. Match the graph with its equation.

A) y = -x2 - 1
B) y = -x2 + x
C) y = -x2 + 1
D) y = -x2 + 2x

29. Find the x-intercepts.
y = x2 + 2x - 3

30. The height h in feet of an object after t seconds is given by the function
h = -16t2 + 30t + 10.
How long will it take the object to hit the ground? Round your answer to the nearest thousandth.

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Solution Summary

Radicals and quadratic equations are investigated.

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