Question 1

A chemist is preparing a solution by mixing two chemicals. The equation $$2x + 3 = 11$$ models the number of milliliters of chemical $$x$$ needed. What is the value of $$x$$?

Accepted Answer

$$x = 4$$

Question 2

A company’s profit $$P (in $$dollars) is given by the formula $$P = 5n - 200$$, where $$n is $$the number of items sold. If the company wants a profit of at least $$100$$, what is the minimum number of items they must sell?

Accepted Answer

$$n \geq 60$$

Question 3

Which of the following is the solution set for the compound inequality $$-2 \u003c 3x + 1 \leq 7$$?

Accepted Answer

$$-1 \u003c x \leq 2$$

Question 4

Which of the following equations represents a line with slope $$m = -\frac{3}{2}$$ and $$y-$$intercept $$b = 4$$?

Accepted Answer

$$y = -\frac{3}{2}x + 4$$

Question 5

A biologist is tracking the population of a bacteria culture, which doubles every hour. If the initial population is $$P_0 = 100$, which function models the population after t$ hours?

Accepted Answer

$$P(t) = 100 \cdot 2^t$$

Question 6

Simplify the expression $$\frac{2x^2$ - 8}{4x}$$ and choose the correct answer.

Accepted Answer

$$\frac{x - 2}{2}$$

Question 7

Which of the following is the result of multiplying $$(x + 3)(x - 3)$$?

Accepted Answer

$$x^2 - 9$

Question 8

A pharmacist needs to dilute a $$20\%$$ saline solution to make $$100 mL of a$$ $$10\%$$ solution. How much of the $$20\%$$ solution should be used? (Let $$x be $$the amount in mL of $$20\%$$ solution.)

Accepted Answer

$$50 mL$$

Question 9

Simplify the radical expression $$\sqrt{50} + 2\sqrt{8}.$$

Accepted Answer

$$9\sqrt{2}$$

Question 10

Solve for $$x$$: $$\frac{1}{x} + \frac{2}{x} = 3$$

Accepted Answer

$$x = 1$$

Question 11

Which of the following is the correct simplification of $$\frac{3}{\sqrt{5}}$$ after rationalizing the denominator?

Accepted Answer

$$\frac{3\sqrt{5}}{5}$$

Question 12

Which of the following is equivalent to $$x^{\frac{3}$${2}}$$?

Accepted Answer

$$\sqrt{x^3$}$$

Question 13

Solve the quadratic equation $$x^2 - 5x + 6 = 0$ using the quadratic formula.

Accepted Answer

$$x = 2,\ 3$$

Question 14

Which of the following is the sum of $$2 + 5i$$ and $$3 - 2i$$?

Accepted Answer

$$5 + 3i$$

Question 15

A system of equations is given by $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}. $$What is the solution $$(x, y)$$?

Accepted Answer

$$(2, 3)$$

Question 16

Which of the following is the correct factorization of $$x^2 - 4x + 4$?

Accepted Answer

$$(x - 2)^2$

Question 17

A rectangular garden has a length that is $$3$$ meters more than twice its width. If the perimeter is $$36$$ meters, what is the width?

Accepted Answer

$$5$$ meters

Question 18

Which of the following is the solution to the equation $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 19

Simplify the complex fraction $$\frac{\frac{2}{x}}{\frac{4}{x^2$}}.$$

Accepted Answer

$$\frac{x}{2}$$

Question 20

Which of the following describes the graph of $$y = |x - 2|$$?

Accepted Answer

A $$V-$$shaped graph with vertex at $$(2, 0)$$

MAT 1033C Intermediate Algebra: Weekly Topic Overview and Study Guide

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