Question 1

Solve the inequality $$10x - 4x + 3 \u003c 3(x + 5). $$Write the solution set in interval notation.

Accepted Answer

$$( -\infty, 4 )$$

Question 2

Solve the compound inequality $$2x - 5 \u003c 3 \u003c 7. $$What is the solution set in interval notation?

Accepted Answer

$$( -2, 3 ]$$

Question 3

Solve the quadratic inequality $$x^2 - 4x - 12$$ \u003e 0$$. Write the solution set in interval notation.

Accepted Answer

$$( -\infty, -2 ) \cup (6, \infty )$$

Question 4

A company has a fixed cost of $$90,000 and a variable cost of 150$ per bicycle. Write the total cost function C(x$$)$$ and find C(110$$)$$. What does C(110$$)$ represent?

Accepted Answer

$$C(x) = 90,000 + 150x$$; $$C(110) = 106,500$$; It costs $106,500 to produce 110 bicycles.

Question 5

Given the points $$P(-22, 22)$$ and $$Q(-15, 27)$$, find the distance $$d(P, Q)$$ and the coordinates of the midpoint $$M of $$the segment $$PQ.$$

Accepted Answer

Distance: $$\sqrt{74}$$; Midpoint: $$(-18.5, 24.5)$$

Question 6

Find the slope of the line passing through the points $$(1, 3)$$ and $$(3, 7).$$

Accepted Answer

$$2$$

Question 7

Determine whether the relation $$\{ (4, 2), (5, 2), (4, 1) \} is a $$function.

Accepted Answer

No

Question 8

Evaluate the function $$f(x) = x^2$ - 4x + 1 at$$ $$f(-1).$$

Accepted Answer

$$6$$

Question 9

A car was purchased for $$22,500. Its value decreases by 3$$,300 per year for the first six years. Write a function $$V(x)$$ for the value after $$x$$ years $$(0 \leq x \leq 6)$$ and find $$V(2). $$What does $$V(2)$$ represent?

Accepted Answer

$$V(x) = 22,500 - 3,300x$$; $$V(2) = 15,900$$; The value of the car after 2 years is $15,900.

Question 10

Find the equation of the line passing through $$(6, 3)$$ with slope $$-2. $$Write your answer in standard form.

Accepted Answer

$$2x + y = 15$$

Question 11

Given the function $$f(x) = \frac{5x^2$ - 1}{x^2$}$$, what is $$f(-5)$$?

Accepted Answer

$$\frac{124}{25}$$

Question 12

Given the equation $$3x + y - 4 = 0$$, rewrite it in slope-intercept form and state the slope and $$y-$$intercept.

Accepted Answer

Slope-intercept form: $$y = -3x + 4$$; Slope: $$-3$$; $$y-$$intercept: $$4$$

Question 13

Find the average rate of change per year in the number of high school dropouts from 1975 ($$5,217$$ thousand) to 2003 ($$3,121$$ thousand).

Accepted Answer

$$-74.9$$ thousand per year; the number of high school dropouts decreased by an average of about $$74.9$$ thousand each year from 1975 to 2003.

Question 14

Which of the following equations represents a vertical line passing through $$(-13, 15)$$?

Accepted Answer

$$x = -13$$

Question 15

Given the lines $$y = 3x - 7$$ and $$y = \frac{4}{5}x - 1$$, are the lines parallel, perpendicular, or neither?

Accepted Answer

Neither

Question 16

Given the function $$f(x) = x^2$ + 4x + 6$$, what is $$f(-6)$$?

Accepted Answer

$$4$$

Question 17

Find the equation of the line passing through $$(2, -11)$$ with slope $$0. $$Write your answer in standard form.

Accepted Answer

$$y = -11$$

Question 18

Suppose the velocity of an object is given by $$v = 2t^2$ + 7t - 9. $$For which interval is the velocity negative?

Accepted Answer

Between $$t = -4.5 sec $$and $$t = 1 sec$$

Question 19

Given the rational inequality $$\frac{x - 3}{x + 2} \leq 0$$, what is the solution set in interval notation?

Accepted Answer

$$( -2, 3 ]$$

College Algebra Test 2 Review: Step-by-Step Study Guidance

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