# Algebra Questions

See attached file for full problem description.

1. Use the five properties of exponents to simplify the expression

2. - 5x - 6, x = -3 and x = -2

3. What expression raised to the fourth power is 81x12y8z16?

4. The cost in dollars of manufacturing w wing nuts is given by the expression 0.07w + 13.3. Find the cost when 375 wing nuts are made.

5. Simplify each of the following expressions. Write your answer with positive exponents only.

6. Perform the indicated calculations. Write your results in scientific notation.

7. The U.S. population in 1990 was approximately 250 million, and the average growth rate for the past 30 years gives a doubling time of 66 years. The formula for the United States is P(in millions) = 250 2 . What will the population of the United States be in 2025, if this growth rate continues?

8. If there are 6 people on the Earth and there is enough freshwater to provide each person with 8.79 how much freshwater is on the Earth?

9. Add polynomials

10. Simplify: 8d - (-7c - 2d)

11. Subtract polynomials

12. Add polynomials using the vertical method

13. Subtract polynomials using the vertical method

14. A triangle has sides 3x + 7, 4x - 9, and 5x + 6. Find the polynomial that represents its perimeter.

15 - 19. Multiply polynomials

20. Multiply rational expressions

21. The price of an item is given by [see attachment]. Find the polynomial that represents the revenue generated from the sale of x items.

22. Simplify square of a polynomial

23. Simplify square of a rational expression

24. Find the product

Let x represent the number and then write an expression for the product.

25. The square of 5 more than a number.

26. A square has sides of length 3x - 2 cm. Express the area of the square as a polynomial.

27 - 29. Divide polynomials

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#### Solution Preview

Please see the attached file.

Use the five properties of exponents to simplify each of the following expressions

1.

(y15)(y6) = y21 = y5

y16 y16

When one exponent is raised to another, you multiply the exponents; when two exponents are multiplied together, you add them; and when one exponent is divided by another, you subtract them.

Find the values of each of the following polynomials for the given values of the variable.

2. - 5x - 6, x = -3 and x = -2

-(-3)2 - 5(-3) - 6 = -9 + 15 - 6 = -15 + 15 = 0

-(-2)2 - 5(-4) - 6 = -4 + 20 - 6 = -10 + 20 = 10

3. What expressions raised to the fourth power is

Take the 4th root of all the terms involved:

81 = 34

x12 = (x3)4

y8 = (y2)4

z16 = (z4)4

So, the expression is equal to (3x3y2z4)4.

4. The cost in dollars of manufacturing w wing nuts is given by the expression 0.07w + 13.3. Find the cost when 375 wing nuts are made. What is the average cost to manufacture one wing nut.

Plug w = 375 into 0.07w + 13.3:

0.07(375) + 13.3 = 26.25 + 13.3 = 39.55

The average cost is the total price divided by the number of ...

#### Solution Summary

The solution has complete answers and explanations to each of the problems.