Question 1

Given a right triangle with legs $$a = 14$$, $$c = 50$$, and $$b$$ unknown, what is the value of $$b$$?

Accepted Answer

$$b = 48$$

Question 2

If $$M is $$the midpoint of $$PQ$$ with $$P(-8, 4)$$ and $$M(-2, 1)$$, what are the coordinates of $$Q$$?

Accepted Answer

$$Q = (-7, 6)$$

Question 3

Find the distance between $$P(-8, 4)$$ and $$Q(3, -2).$$

Accepted Answer

$$\sqrt{157}$$

Question 4

Given $$f(x) = 3x + 2$$, find $$f(2).$$

Accepted Answer

$$f(2) = 8$$

Question 5

A company charges a flat fee of $$20 plus 5 $$per hour. Which formula represents the cost $$f(x)$$?

Accepted Answer

$$f(x) = 5x + 20$$

Question 6

Find the slope of the line passing through $$(-2, 3)$$ and $$(1, 2).$$

Accepted Answer

$$m = -1$$

Question 7

What is the equation of the line through $$(-1, 3)$$ and parallel to $$3x + 2y = -5$$?

Accepted Answer

$$y = -\frac{3}{2}x + \frac{3}{2}$$

Question 8

Solve for $$x$$: $$\frac{3}{7}x - \frac{1}{5}x = 2.$$

Accepted Answer

$$x = 70$$

Question 9

How much pure alcohol should be added to $$20$$ liters of $$40\%$$ alcohol to increase the concentration to $$50\%$$ alcohol?

Accepted Answer

$$x = 4$$ liters

Question 10

Given $$f(x) = 3 - 4x$$ and $$g(x) = 2x + 4$$, find $$(f - g)(x).$$

Accepted Answer

$$3 - 4x - (2x + 4)$$

Question 11

Determine if $$f(x) = 6x^3$ - 9x is $$even, odd, or neither.

Accepted Answer

Odd

Question 12

Find the domain and range of the function $$f(x) = x^2$.

Accepted Answer

$$D = (-\infty, \infty), R = [0, \infty)$$

Question 13

Which of the following is NOT a function?

Accepted Answer

$$(0,5), (1,3), (0,-4), (3,1)$$

Question 14

Find the slope-intercept form of the line through $$(-2, 0)$$ and perpendicular to $$8x - 3y = 7.$$

Accepted Answer

$$y = -\frac{3}{8}x - \frac{3}{4}$$

Question 15

Solve $$|2x + 4| + 2 = 10.$$

Accepted Answer

$$x = 2 or$$ $$x = -6$$

Question 16

If $$f(x) = x^3$, what is the range of f$?

Accepted Answer

$$(-\infty, \infty)$$

Question 17

Given $$p = 2L + 2w$$, solve for $$w in $$terms of $$p$$ and $$L.$$

Accepted Answer

$$w = \frac{p - 2L}{2}$$

Question 18

Which transformation is represented by $$y = (x - 6)^2$ - 3$$?

Accepted Answer

Shift right 6 units, down 3 units

College Algebra: Essential Concepts and Problem-Solving Strategies

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