Question 1

A chemist mixes two solutions. The first contains $$\dfrac{3}{4}$$ liters of acid, and the second contains $$\dfrac{2}{3}$$ liters of acid. What is the total amount of acid in both solutions, expressed as a simplified fraction?

Accepted Answer

$$\dfrac{17}{12}$$

Question 2

A company’s profit $$P (in $$thousands of dollars) after $$x$$ years is modeled by $$P(x) = 2x^2$ - 5x + 3. $$What is the degree of this polynomial, and is it a monomial, binomial, trinomial, or none of these?

Accepted Answer

Degree 2, trinomial

Question 3

Simplify the expression using the laws of exponents: $$\left( x^3$ y^2$ \$$right)^2$$

Accepted Answer

$$x^6$$ $$y^4$$

Question 4

A hiker descends from a mountain peak at 1,200 feet above sea level to a valley at -350 feet. What is the total change in elevation?

Accepted Answer

$$1,550$$ feet

Question 5

Which of the following numbers is both a rational and an integer?

Accepted Answer

$$-7$$

Question 6

A rectangular garden has a length of $$2x + 5$$ meters and a width of $$x - 3$$ meters. What is the area of the garden, expressed as a simplified polynomial?

Accepted Answer

$$2x^2 - x - 15$

Question 7

Solve for $$x$$: $$5(x - 2) = 3x + 8$$

Accepted Answer

$$x = 6$$

Question 8

Which of the following expressions is equivalent to $$\dfrac{2}{3} \div \dfrac{4}{9}$$?

Accepted Answer

Question 9

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. Write an algebraic expression for the total cost $$C of $$renting a car and driving $$m$$ miles.

Accepted Answer

$$C = 0.2m + 25$$

Question 10

Simplify the expression: $$-3[2x - (4 - x)]$$

Accepted Answer

Question 11

Which of the following is the additive inverse of $$-15$$?

Accepted Answer

$$15$$

Question 12

A biologist observes that a bacteria population triples every hour. If the initial population is $$P_0$$, which expression models the population after $$t$$ hours?

Accepted Answer

$$P_0$$ \cdot 3^t$$

Question 13

Which of the following is a solution to the equation $$2x^2 - 8 = 0$?

Accepted Answer

$$x = 2$$

Question 14

Simplify the expression: $$\dfrac{5}{8} - \dfrac{1}{4}$$

Accepted Answer

$$\dfrac{3}{8}$$

Question 15

Which of the following is the reciprocal of $$-\dfrac{7}{3}$$?

Accepted Answer

$$-\dfrac{3}{7}$$

Question 16

A rectangular field has an area of $$60$$ square meters and a width of $$5$$ meters. What is the length of the field?

Accepted Answer

$$12$$ meters

Question 17

Simplify the expression: $$2x^2 + 3x$$ - $$4x^2 + x$

Accepted Answer

Question 18

Which of the following is a solution to the equation $$x + 5 = 2x - 3$$?

Accepted Answer

$$x = 8$$

Question 19

Evaluate $$(-2)^3.$$

Accepted Answer

$$-8$$

College Algebra Fundamentals: Equations, Expressions, and Polynomials

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