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*1. Disregard

2. Simplify the following expression:

3.
The surface area of a right prism is given by
,
where is the area of the base, is the perimeter of the base, and is the height of the prism.
Solve for .
4. Solve the following equation for .

5. Graph the line.

6. Disregard

7. Find the values of and that solve the following system of equations:

.

8. Express the following product of powers of as a single power of :
.

9. Simplify the following:

10. Write without parentheses:
.

11. Rewrite the following without an exponent:
.

12. Simplify.

*13. Disregard

14. Simplify the following:

15. Perform the following multiplications.

16. Write the product below in simplest form without parentheses:
.

17. Rewrite without parentheses and simplify.

18. Multiply:
.

19. Factor
.

20. Factor.

21. Factor:

22. Factor:

23. Factor:
.

25. Express the following compound fraction in lowest terms:
.

28. Reduce the following expression to lowest terms:

29. Solve for :
.

30.
Find all values of satisfying the equation
.
(If there is more than one solution, separate them with commas.)

31. Solve the following proportion for .

32. Heather drove miles using gallons of gas. At this rate, how many miles would she drive using gallons of gas?

33. Rewrite the following in simplified radical form.

34.
Simplify:

Assume that the variable represents a positive real number.

35. Simplify.

36. Write without exponents:
.

37. Rewrite the following in simplified radical form.

Assume that all variables represent positive real numbers.

38. Simplify the following expression as much as possible:

Assume that all variables represent positive real numbers.
39. Simplify.

Assume that all variables represent positive real numbers.

40. Rationalize the denominator and simplify:
.

41. Solve for :
,
where is a real number.
(If there is more than one solution, separate them with commas.)

42. Solve the following equation for :
,
where is a real number.
(If there is more than one solution, separate them with commas.)

*43. Disregard

44. Compute the following:
.
45. Write the following expression in simplified radical form.

46. Find the roots of the quadratic equation:
.
(If there is more than one root, separate them with commas.)

47. Find the roots of the quadratic equation:
.
(If there is more than one root, separate them with commas.)

48. Solve where is a real number.
(If there is more than one solution, separate them with commas.)

49. Solve the following equation for by using the quadratic formula:
.
(If there is more than one solution, separate them with commas.)

50. Disregard

#### Solution Preview

Hi,

Please find the solutions/explanations attached herewith.

*1. Disregard

2. Simplify the following expression:

Solution:
Open the parenthesis, we will get
= -10t - 2y + 30y + 36t
combine similar terms, we will get
= 26t + 28y
3.
The surface area of a right prism is given by
,
where is the area of the base, is the perimeter of the base, and is the height of the prism.
Solve for .
Solution:
We can write it as
Ph = S - 2B
Divide each side by h, we will get

4. Solve the following equation for .

Solution:
Open the parenthesis, we will get
2x + 10 = -4x + 4
Bring all the variables to left side and numbers to right side, we will get
2x + 4x = 4 - 10
6x = -6
Divide each side by 6, we will get
=> x = -1
5. Graph the line.

Solution:
Let us find the x and y -intercepts of the given equation.
For finding x-intercept, put y = 0

x-intercept is ( ,0)
For finding y-intercept, put x = 0

y-intercept is (0, 3)
Plot the x and y-intercepts and join through line.
The graph is shown below:

6. Disregard

7. Find the values of and that solve the following system of equations:
-------(i)
-----------(ii)
Solution:
Multiply equation (i) by 2 and add to equation (ii), we will get
11y = -36 + 14 = -22
=> y = -22/11 = -2

Now substitute value of y in equation (i), we will get
-4x + 3(-2) = -18
=> -4x - 6 = -18
=> -4x = -18 + 6 = -12
divide each side by -4, we will get
=> x = 3
The solution is x = 3, y = -2. ...

#### Solution Summary

The expert examines the problems on radical, exponents, linear and quadratic equations.Step by step detailed solution is provided to all the problems.

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