Question 1

Which property is illustrated by the equation $$6(-2 + 7) = -12 + 42$$?

Accepted Answer

Distributive property of multiplication over addition

Question 2

Solve the equation $$2x^4$$ - $$98x^2 = 0$ by factoring and using the zero product principle.

Accepted Answer

$$\{-7, 0, 7\}$$

Question 3

Simplify the exponential expression $$\$$left(7x^4$$\$$right)^{-2}$$.

Accepted Answer

$$\frac{1}{49x^8$}$$

Question 4

Write $$9 	imes 10^4$ in decimal notation without exponents.

Accepted Answer

90,000

Question 5

Simplify the expression $$\frac{-21x^3$}{7x$$^{13}$$}.$$

Accepted Answer

$$-\frac{3}{x$$^{10}$$}$$

Question 6

A store charges $$1.75 to send the first page and 0.45 $$for each subsequent page by fax. The total price $$P$$ for faxing $$x$$ pages is $$P = 0.45(x - 1) + 1.75. $$How many pages can be faxed for $4.00?

Accepted Answer

6 pages

Question 7

Solve for $$t in $$the formula $$I = Prt.$$

Accepted Answer

$$t = \frac{I}{Pr}$$

Question 8

Find the product and write the result in standard form: $$(9 + 3i)(9 - 3i).$$

Accepted Answer

90

Question 9

Divide and express the result in standard form: $$\frac{7 - 2i}{2 + 7i}.$$

Accepted Answer

$$-i$$

Question 10

Solve the equation $$4x^2 = 60$.

Accepted Answer

$$\left\{-\sqrt{15}, \sqrt{15}\right\}$$

Question 11

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

Accepted Answer

$$\frac{-1 - \sqrt{17}}{4}, \frac{-1 + \sqrt{17}}{4}$$

Question 12

Solve the radical equation $$\sqrt{2x + 3} - \sqrt{x + 1} = 1$$ and check all proposed solutions.

Accepted Answer

$$\{-1, 3\}$$

Question 13

Solve and check the equation $$\sqrt[3]{6x - 5} - 6 = 2.$$

Accepted Answer

$$\frac{517}{6}$$

Question 14

Which of the following is the correct equation for the sentence: 'The y-value is three more than five times the x-value'?

Accepted Answer

$$y = 5x + 3$$

Question 15

Given the equation $$x + 9 = 9$$, solve for $$x in $$the context of absolute value equations.

Accepted Answer

$$\{-18, 0\}$$

Question 16

A chemical reaction requires the temperature $$T (in $$Celsius) to be at least 5 degrees more than twice the concentration $$C (in $$mol/L). Which equation models this relationship?

Accepted Answer

$$T = 2C + 5$$

Question 17

If the graph of a line passes through the points $$(0, 6)$$ and $$(2, 0)$$, what is the equation of the line in slope-intercept form?

Accepted Answer

$$y = -3x + 6$$

Question 18

Which of the following numbers is NOT a real number: $$16, \frac{7}{8}, 0, 9, -0.9, 0.48, -19, \sqrt{-4}$$?

Accepted Answer

$$\sqrt{-4}$$

Question 19

A car rental company charges a flat fee of $$25 plus 0.20 $$per mile driven. Write a formula for the total cost $$C$$ for driving $$m$$ miles, and find the cost for 150 miles.

Accepted Answer

$$C = 25 + 0.20m;\ C = 55$$

College Algebra Practice: Properties, Equations, Graphs, and More

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