Question 1

Which of the following is the correct simplification of the expression $$2(3x - 4) - 5(x + 2)$$?

Accepted Answer

$$x - 14$$

Question 2

A chemist mixes two solutions: one with 30% acid and another with 50% acid. If she wants to make 100 mL of a 40% acid solution, how many milliliters of the 50% solution should she use? (Let $$x be $$the amount of 50% solution.)

Accepted Answer

$$x = 50$$

Question 3

Which of the following is the solution to the equation $$\frac{2x}{3} - 4 = 6$$?

Accepted Answer

$$x = 15$$

Question 4

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. If a customer has $$\65$ to spend, what is the maximum number of miles they can drive? (Let x$ be the number of miles.)

Accepted Answer

$$x = 200$$

Question 5

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 6

If the line $$y = -2x + 5$$ represents the cost (in dollars) to produce $$x$$ units of a product, what does the slope of the line represent in this context?

Accepted Answer

The decrease in cost per additional unit produced

Question 7

Which of the following is the solution set for the inequality $$3x - 7 \u003c 2x + 5$$?

Accepted Answer

$$x \u003c 12$$

Question 8

A rectangle has a length that is 3 times its width. If the perimeter is 48 meters, what is the area of the rectangle?

Accepted Answer

$$144\ 	ext{m}^2$$

Question 9

Which of the following is the correct simplification of $$(-2)^3$$ \cdot $$(-2)^4$$?

Accepted Answer

$$128$$

Question 10

A system of equations is given by $$\begin{cases} 2x + y = 10 \ x - y = 1 \end{cases}. $$What is the solution $$(x, y)$$?

Accepted Answer

Question 11

Which of the following is the correct result of dividing $$x^5$$ $$y^3 by$$ $$x^2 y$?

Accepted Answer

$$x^3$$ $$y^2$$

Question 12

A student scored 80%, 85%, and 90% on three quizzes. What score must they get on the fourth quiz to have an average of at least 85%?

Accepted Answer

$$85$$

Question 13

Which of the following is the correct solution to the equation $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 14

Which of the following is the correct simplification of $$3(x - 2) + 4(x + 5)$$?

Accepted Answer

Question 15

A company’s profit $$P (in $$dollars) from selling $$x$$ units is given by $$P = 5x - 200. $$What is the minimum number of units the company must sell to make a profit?

Accepted Answer

$$40$$

Question 16

Which of the following is the correct factorization of $$x^2 - 16$?

Accepted Answer

$$(x + 4)(x - 4)$$

Question 17

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$15$$

Question 18

Which of the following is the correct solution to the system of equations $$\begin{cases} x + y = 8 \ x - y = 2 \end{cases}$$?

Accepted Answer

$$(5, 3)$$

Question 19

A medication is prescribed at a dosage of 2 mg per kg of body weight per day. If a patient weighs 75 kg, how many milligrams should they receive per day?

Accepted Answer

$$150 mg$$

Elementary Algebra (MATH 090) Syllabus and Course Structure – University of Indianapolis

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