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# Basic Algebra

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1. Express 775% as a decimal.

A) 775 B) 77,500 C) 77.5 D) 7.75

2. Evaluate. | -7 | + | 13 |

A) 20 B) -20 C) 6 D) -6

3. Evaluate. 81 ÷ 9 - 16 ÷ 8

A) 7 B) 9 C) 6 D) 8

4. Express 9.41 as a percent.

A) 94.1% B) 941.0% C) 0.0941% D) 9.41%

5. Find the GCF for 14 and 21.

A) 7 B) 1 C) 42 D) 6

6. Subtract. 12.537 - 9.21

A) 3.327 B) 3.516 C) 1.1616 D) 11.616

7. Use the distributive property to remove the parentheses in the following expression. Then simplify your result if possible.
3(6 + 7)

A) 16 B) 39 C) 126 D) 25

8. Evaluate if m = -2, n = 4, and p = -1.

A) 16 B) -24 C) 24 D) -16

9. Multiply.
2y3 &#61655; 5y6

A) 10y18 B) 7y9 C) 10y9 D) 7y18

10. Use your calculator to evaluate the following expression if x = -3.07, and y = 8.77, and z = -6.66. Round your answer to the nearest tenth.
x - yz

A) 55.3 B) 54.0 C) 53.9 D) 56.4

11. Which property of the real numbers is illustrated by the following statement?
7 + 8 = 8 + 7

A) Distributive property C) Associative property of addition

A) -15.1 B) 4.3 C) 15.1 D) -4.3

13. Solve. -8x + 8 + 10x = 2x + 1

A) No solution B) Identity C) 0 D) 1

14. Identify the base in the statement "20% of 500 is 100."

A) 500 B) 100 C) 20%

15. A principal of \$5000 was invested in a savings account for 4 years. If the interest earned for the period was \$400, what was the interest rate?

A) 2.5% B) 2% C) 1% D) 1.5%

16. Solve. -7x = -14

A) -98 B) 98 C) 2 D) -2

17. Convert 0.32 to a percent.

A) 32% B) 3.2% C) 0.32% D) 0.0032%

18. A television is marked down from \$350 to \$308. What is the discount rate?

A) 12% B) 87% C) 11% D) 13%

19. Which of the ordered pairs is a solution for the equation 5x - 4y = 20?

A) (-4, -5) B) (0, 5) C) (0, -5) D) (-4, 0)

20. Find the slope of the graphed line.

A) 1 B) -2 C) Undefined D) 0

21. Find the slope of the graphed line.

A) B) 4 C) -4 D)

22. Give the coordinates of the point graphed below.

A) (-2, 3) B) (3, -2) C) (-3, 2) D) (2, -3)

23. Find the slope of the graphed line.

A) -2 B) - C) 2 D)

24. Rewrite the equation 4x - 10y = 11 as a function of x.

A) B) C) D)

25. Write the equation of the line that passes through point (1, -8) with a slope of 0.

A) x = -8 B) y = 1 C) y = -8 D) x = 1

26. One day, the temperature at 9:00 A.M. was 42°F, and by 2:00 P.M. the temperature was 57°F. What was the hourly rate of temperature change?

A) 3°F/h B) 4°F/h C) 5°F/h D) 2°F/h

27. Given f(x) = 5x2 - 3x + 1, find f(-2).

A) 15 B) 27 C) -13 D) -25

28. Write the equation of the line passing through (-6, -3) and (-6, 1).

A) y = 4x B) y = x - 6 C) x = -6 D) y = -6

29. The length of a rectangle is 1 in. more than twice its width. If the perimeter of the rectangle is 26 in., find the width of the rectangle.

A) 4 in. B) 5 in. C) 6 in. D) 3 in.

30. Solve the following system of linear inequalities by graphing.
x - 2y &#61619; 4
x &#61603; 4

A)
B)
C)
D)

31. One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number.

A) 7 B) 17 C) 34 D) 5

32. Solve the following system of linear inequalities by graphing.
x + 2y &#61603; 3
2x - 3y &#61603; 6

A) C)
B) D)

33. Janet invested \$25,000, part at 5% and part at 2%. If the total interest at the end of the year is \$980, how much did she invest at 5%?

A) \$16,000 B) \$9,000 C) \$15,000 D) \$17,000

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## The solution of basic algebra problems

Use Equation Editor to write mathematical expressions and equations.

1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C = 6,000/(200 - 2x)

a. What is the cost to remove 75% of the pollutant?

b. What is the cost to remove 90% of the pollutant?

c. What is the cost to remove 99% of the pollutant?

d. For what value is this equation undefined?

e. Do the answers to sections a. through d. match your expectations? Explain why or why not.

2. Biologists want to set up a station to test alligators in the lake for West Nile Virus. Suppose that the costs for such a station are \$2,500 for setup costs and \$3.00 to administer each test.

a. Write an expression that gives the total cost to test x animals.

b. You can find the average cost per animal by dividing total costs by number of animals. Write the expression that gives the average cost per animal.

c. Find the average cost per animal for 10 animals, 100 animals, and 1,000 animals.

d. As the number of animals tested increases, what happens to the average cost to test the animals? Would the average cost ever fall below \$3.00? If so, identify a value that supports your answer. If not, explain how you know.

e. How many animals should be tested for the average cost to be \$5.00 per animal?

3. To estimate animal populations, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat (in acres) polled.

a. Write an equation using only one variable that could be used to solve for the constant of variation k.

b. A biologist counted 12 white tail deer in a 100-acre parcel of land in a nature preserve. Find the constant of variation k.

c. If the entire nature preserve is 2,500 acres, then what is the total white tail deer population in the preserve? Describe how you arrived at your answer.

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