Question 1

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

Accepted Answer

$$(-\infty, 4)$$

Question 2

Solve the compound inequality $$2x - 5 \u003c 3 \u003c x + 7$$ and write the solution set in interval notation.

Accepted Answer

$$(-4, 2)$$

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

$$V(x) = 22,500 - 3,300x;\ V(2) = 15,900$$ and it represents the value of the car after 2 years.

Question 5

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

Accepted Answer

$$2$$

Question 6

Given the function $$f(x) = x^2$ - 4x + 1$$, evaluate $$f(-1).$$

Accepted Answer

$$6$$

Question 7

A company has a fixed cost of $$90,000$$ and a variable cost of $$150$$ per bicycle produced. 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 8

Find the equation of the line in standard form that passes through $$(6, 3)$$ with slope $$m = -2.$$

Accepted Answer

$$2x + y = 15$$

Question 9

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

Accepted Answer

No

Question 10

Find the average rate of change per year in the number of high school dropouts from $$1975$$ ($$5217$$ thousand) to $$2003$$ ($$3121$$ thousand).

Accepted Answer

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

Question 11

Rewrite the equation $$3x + y - 4 = 0 in $$slope-intercept form and state the slope and y-intercept.

Accepted Answer

$$y = -3x + 4$$; slope $$= -3$$, y-intercept $$= 4$$

Question 12

Find the slope of the line passing through $$(-7, 9)$$ and $$(5, 9)$$ and indicate whether the line rises, falls, is horizontal, or is vertical.

Accepted Answer

Slope $$= 0$$; the line is horizontal.

Question 13

Given the function $$f(x) = \frac{5x^2$ - 1}{x^2$}$$, evaluate $$f(5).$$

Accepted Answer

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

Question 14

Find the equation of the line in standard form that passes through $$(-3, 1)$$ and $$(5, 2).$$

Accepted Answer

$$x - 8y = -11$$

Question 15

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

Accepted Answer

Neither

Question 16

Solve the rational inequality $$\frac{30}{x + 6} \leq 5$$ and write the solution set in interval notation.

Accepted Answer

$$(-\infty, -12) \cup [0, \infty)$$

Question 17

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

Accepted Answer

Between $$-4.5 sec $$and $$1 sec$$

Question 18

Find the midpoint of the segment with endpoints $$(-22, 22)$$ and $$(-15, 27).$$

Accepted Answer

$$(-18.5, 24.5)$$

Question 19

Given the function $$f(r) = \frac{r + 4}{r + 6}$$, evaluate $$f(-6).$$

Accepted Answer

$$-\frac{1}{2}$$

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

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