Question 1

Which of the following is the correct way to express $$0.00056 in $$scientific notation?

Accepted Answer

$$5.6 	imes 10$$^{-5}$$

Question 2

A chemist mixes two solutions. The concentration of the first is modeled by $$2x^2 + 3x - 5$ and the second by x^2$ - 4x + 7. $$What is the resulting polynomial when the concentrations are added?

Accepted Answer

$$3x^2 - x + 2$

Question 3

Which of the following is the correct factored form of $$6x^2 + 11x + 3$?

Accepted Answer

$$(2x + 3)(3x + 1)$$

Question 4

A business’s profit $$P (in $$thousands of dollars) is modeled by $$P = 5x - 20$$, where $$x is $$the number of units sold. What is the break-even point?

Accepted Answer

$$x = 4$$

Question 5

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(2, 3)$$

Question 6

Simplify the expression $$\dfrac{3x^2$y}{6xy^2$}.$$

Accepted Answer

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

Question 7

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

Accepted Answer

$$x = 7, x = -2$$

Question 8

A company’s cost function is $$C(x) = 4x + 100$$ and revenue function is $$R(x) = 10x. $$For what value of $$x$$ does the company break even?

Accepted Answer

$$x = 25$$

Question 9

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

Accepted Answer

$$2\sqrt{5}$$

Question 10

Solve the quadratic equation $$x^2 - 6x + 8 = 0$ using the zero factor property.

Accepted Answer

$$x = 2, x = 4$$

Question 11

Which of the following is the correct application of the properties of exponents: $$\left( x^3$ \$$right)^2$$?

Accepted Answer

$$x^6$$

Question 12

A medical researcher is analyzing the growth of bacteria, modeled by $$N = 200 \cdot 2^t$$, where $$N is $$the number of bacteria and $$t is $$time in hours. How many bacteria are present after 3 hours?

Accepted Answer

$$1600$$

Question 13

Which of the following is the correct solution to the radical equation $$\sqrt{x + 3} = 5$$?

Accepted Answer

$$x = 22$$

Question 14

Which of the following is the correct solution to the quadratic equation $$2x^2 - 4x - 6 = 0$ using the quadratic formula?

Accepted Answer

$$x = 3, x = -1$$

Question 15

Which of the following is the correct simplified form of $$\dfrac{x^2$ - 9}{x + 3}$$?

Accepted Answer

$$x - 3$$

Question 16

A student is analyzing the graph of the equation $$y = -2x + 5. $$What is the slope and y-intercept?

Accepted Answer

Slope: $$-2$$, y-intercept: $$5$$

Intermediate Algebra: Course Syllabus and Study Guide

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