Question 1

Which of the following is the correct equation of a line passing through the point $$(-2, 5)$$ with a slope of $$3$$?

Accepted Answer

$$y = 3x - 1$$

Question 2

A chemist is mixing two solutions. The first solution contains $$x$$ grams of salt per liter, and the second contains $$y$$ grams per liter. If the total amount of salt in $$3$$ liters of the first and $$2$$ liters of the second is $$20$$ grams, which equation models this scenario?

Accepted Answer

$$3x + 2y = 20$$

Question 3

Which of the following is the solution to the system of equations: $$\begin{cases} x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(4, 3)$$

Question 4

What is the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[2, \infty)$$

Question 5

A rectangle has a length that is two inches longer than its width. If the area is $$108$$ square inches, what is the width of the rectangle?

Accepted Answer

$$12$$ inches

Question 6

Which of the following is the solution set for $$|2x - 3| = 7$$?

Accepted Answer

$$\{-2, 5\}$$

Question 7

Simplify the expression $$\dfrac{2x^2$y}{4xy^2$}.$$

Accepted Answer

$$\dfrac{x}{2y}$$

Question 8

Which of the following is the solution to the equation $$\sqrt{x+5} = 4$$?

Accepted Answer

$$x = 11$$

Question 9

A vertical line passes through the point $$(4, -2). $$What is its equation?

Accepted Answer

$$x = 4$$

Question 10

Solve for $$x$$: $$2(x - 3) = 4x + 6$$

Accepted Answer

$$x = -6$$

Question 11

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 12

If $$f(x) = \dfrac{\sqrt{x-1}}{x-3}$$, what is the domain of $$f$$?

Accepted Answer

$$[1, 3) \cup (3, \infty)$$

Question 13

Which of the following is the solution to the inequality $$2x - 5 \u003c 7$$?

Accepted Answer

$$x \u003c 6$$

Question 14

A right triangle has legs of length $$x$$ and $$6$$, and hypotenuse $$20. $$What is the value of $$x$$?

Accepted Answer

$$x = 16$$

Question 15

Which of the following is the simplified form of $$\dfrac{\sqrt{50}}{\sqrt{2}}$$?

Accepted Answer

$$5$$

Question 16

Solve for $$x$$: $$\dfrac{x+2}{3} = 4$$

Accepted Answer

$$x = 10$$

Question 17

Which of the following is the solution set for $$|x + 1| \leq 4$$?

Accepted Answer

$$[-5, 3]$$

Question 18

Which of the following is the correct solution to $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$x = -3$$

Question 19

If $$g(x) = \dfrac{1}{x-2}$$, which value is not in the domain of $$g$$?

Accepted Answer

$$x = 2$$

Question 20

Which of the following is the solution to $$\dfrac{2x}{x-1} = 4$$?

Accepted Answer

College Algebra Final Exam Review: Key Concepts and Practice Problems

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