Question 1

Solve for $$x in $$the equation $$0.6x + 0.2(x + 0.3) = 15.26. $$What is the value of $$x$$?

Accepted Answer

$$x = 26$$

Question 2

A room is 14 feet long and 9 feet wide. What is the area of the room?

Accepted Answer

$$126$$ square feet

Question 3

A computer is on sale for $484 after a 20\% discount. What was the original price?

Accepted Answer

$$605$$

Question 4

Find the domain of the function $$f(x) = \dfrac{5x^2$ + 7x + 12}{x^2$ + 12x + 32}. $$Write your answer in interval notation.

Accepted Answer

$$(-\infty, -8) \cup (-8, -4) \cup (-4, \infty)$$

Question 5

Which of the following sets of points represents a function?

Accepted Answer

$$\{(-2, 3), (4, 5), (0, 8), (5, 3)\}$$

Question 6

Find the slope of the line passing through the points $$(-2, 3)$$ and $$(5, -11).$$

Accepted Answer

$$-2$$

Question 7

A vendor sells hot dogs and bags of potato chips. A customer buys 6 hot dogs and 4 bags of chips for $$8.70. Another customer buys 4 hot dogs and 3 bags of chips for 5.95. $$What is the cost of one hot dog?

Accepted Answer

$$1.15$$

Question 8

Factor the expression $$4x^2 - 49$ completely.

Accepted Answer

$$(2x + 7)(2x - 7)$$

Question 9

Solve the quadratic equation $$x^2 - 2x + 5 = 0$ using the quadratic formula.

Accepted Answer

$$x = 1 \pm 2i$$

Question 10

Simplify the expression $$\dfrac{x^2$ - 16}{x^2$ - 4x}.$$

Accepted Answer

$$\dfrac{x + 4}{x}$$

Question 11

An experienced bricklayer can build a wall in 8 hours, and an apprentice can do it in 10 hours. How long will it take them to build the wall together?

Accepted Answer

$$4\dfrac{4}{9}$$ hours

Question 12

Rationalize the denominator: $$\dfrac{7}{\sqrt{10} - 2}.$$

Accepted Answer

$$\dfrac{7(\sqrt{10} + 2)}{6}$$

Question 13

Solve the equation $$\sqrt{2x - 3} = x - 3$$ and check for extraneous solutions.

Accepted Answer

$$x = 6$$

Question 14

Which of the following is the correct factorization for $$x^3 - 27$?

Accepted Answer

$$(x - 3)(x^2$ + 3x + 9)$$

Question 15

A chemist needs to mix a 36\% alcohol solution with a 20\% alcohol solution to make 40 liters of a 30\% solution. How many liters of the 36\% solution should be used?

Accepted Answer

$$25$$ liters

Question 16

Simplify the expression $$\dfrac{3p$$^{-2}$$q^4$$}{$$(3p^4q$$^{-2}$$)^2$$}$ and write your answer with positive exponents only.

Accepted Answer

$$\dfrac{1}{9p$$^{10}$$q^8$$}$

Question 17

Solve the system of equations using the substitution method: $$-2x + 3y = 12$$ and $$4x + y = 5.$$

Accepted Answer

$$(-3, 2)$$

Question 18

Which of the following is the correct solution set in interval notation for the inequality $$3(2x - 1) - 5(x + 2) \u003e 3x - 9$$?

Accepted Answer

$$(-1, \infty)$$

Question 19

Simplify: $$\sqrt{32} + \sqrt{98} - \sqrt{50}.$$

Accepted Answer

$$39\sqrt{2}$$

Question 20

Multiply and simplify: $$(5 + \sqrt{2})(5 - \sqrt{2}).$$

Accepted Answer

$$23$$

Intermediate Algebra Final Exam Study Guide – Step-by-Step Guidance

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