Question 1

Given the equation of a line $$y = -\frac{6}{7}x - \frac{2}{3}$$, what are the slope and y-intercept of the line?

Accepted Answer

Slope: $$-\frac{6}{7}$$, y-intercept: $$(0, -\frac{2}{3})$$

Question 2

Solve for $$x$$: $$|x - 3| = 22.$$

Accepted Answer

$$x = 25 or$$ $$x = -19$$

Question 3

Divide and simplify: $$\frac{x^4$ - 7x^2$ + 10}{x^2$ - 2}.$$

Accepted Answer

$$x^2 - 7$$ + \frac{10}{$$x^2 - 2$$}$$

Question 4

Rewrite with positive exponents: $$\frac{1}{x$$^{-\frac{3}$${4}}}.$$

Accepted Answer

$$x^{\frac{3}$${4}}$$

Question 5

Find the equation of the line with slope $$9$$ passing through the point $$(3, 1). $$Write your answer in slope-intercept form.

Accepted Answer

$$y = 9x - 26$$

Question 6

Express in terms of $$i$$: $$2 - \sqrt{-28}.$$

Accepted Answer

$$2 - 2i\sqrt{7}$$

Question 7

Solve for $$z$$: $$\frac{z - 8}{z - 9} = \frac{1}{z - 9}.$$

Accepted Answer

$$z = 8$$

Question 8

Factor completely: $$147v^2 - 192$.

Accepted Answer

$$49v^2 - 64 = (7v - 8)(7v + 8$$)$$

Question 9

Find the equation of the line passing through $$(-4, -5)$$ and $$(-12, -15). $$Write your answer in slope-intercept form.

Accepted Answer

$$y = \frac{5}{4}x ($$since $$y-$$intercept is $$0)$$

Question 10

Write the equation of the line containing the point $$(5, 8)$$ and perpendicular to $$6x + y = 9. $$Express your answer in the form $$y = mx + b.$$

Accepted Answer

$$y = \frac{1}{6}x + \frac{43}{6}$$

Question 11

Rationalize the denominator: $$\frac{4}{4 - \sqrt{3}}.$$

Accepted Answer

$$\frac{4(4 + \sqrt{3})}{(4 - \sqrt{3})(4 + \sqrt{3})} = \frac{16 + 4\sqrt{3}}{13}$$

Question 12

For the quadratic function $$f(x) = 2x^2$ + 2x + 4$$, what is the vertex?

Accepted Answer

$$\left(-\frac{1}{2}, \frac{7}{2}\right)$$

Question 13

A rectangle has length twice its width and area $$72 yd$^2. $$What are the length and width?

Accepted Answer

Length: $$12 yd$$, Width: $$6 yd$$

Question 14

A car travels $$660$$ miles at a certain speed. If the speed had been $$5$$ mph faster, the trip would have taken $$1$$ hour less. What was the original speed?

Accepted Answer

$$55$$ mph

Question 15

Simplify: $$\frac{y^2$ - 1}{y} \div \frac{y - 1}{y + 1}.$$

Accepted Answer

$$\frac{(y + 1)^2$}{y}$$

Question 16

Find the $$x-$$intercepts and $$y-$$intercept of $$f(x) = -x^2$ + 4x + 12.$$

Accepted Answer

$$x-$$intercepts: $$(6, 0)$$ and $$(-2, 0)$$; $$y-$$intercept: $$(0, 12)$$

Question 17

Solve the system by elimination: $$3a + b = 14$$, $$a + 3b = -6.$$

Accepted Answer

$$(4, -6)$$

Question 18

Add and simplify: $$14\sqrt{48} + 2\sqrt{108}.$$

Accepted Answer

$$52\sqrt{3}$$

Question 19

Factor completely: $$-16 + a^2$.

Accepted Answer

$$(a - 4)(a + 4)$$

Question 20

Solve for $$x$$: $$7x^2 - 3 = 0$. Give the exact solutions.

Accepted Answer

$$x = \pm \sqrt{\frac{3}{7}}$$

Step-by-Step Guidance for Beginning-Intermediate Algebra Questions

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