Question 1

Given the equation $$-2x + 7y = -21$$, what is the slope and y-intercept of the line?

Accepted Answer

Slope: $$\frac{2}{7}$$, y-intercept: $$-3$$

Question 2

Find the x- and y-intercepts of the line $$4x - 5y + 12 = 0.$$

Accepted Answer

x-intercept: $$(-3, 0)$$, y-intercept: $$(0, 2.4)$$

Question 3

What is the slope of the line passing through the points $$(-3, 5)$$ and $$(-1, -1)$$?

Accepted Answer

Slope: $$-3$$

Question 4

Write the equation of the line in slope-intercept form that passes through $$(1, 6)$$ and has slope $$-\frac{3}{5}.$$

Accepted Answer

$$y = -\frac{3}{5}x + \frac{33}{5}$$

Question 5

The number of adults living alone in the U.S. increased from 7.5 million in 1960 to 36 million in 2020. Let $$x=60$$ correspond to 1960. Assuming a linear trend, what is the equation for the number of adults living alone, $$N(x)$$, in millions, as a function of $$x$$?

Accepted Answer

$$N(x) = 0.475(x - 60) + 7.5$$

Question 6

Using your equation from the previous question, estimate the number of adults living alone in 2025.

Accepted Answer

$$38.75$$ million

Question 7

A company has fixed costs of $$200 and it costs 2000$ to produce 50$ items. What is the cost function C(x$$)$?

Accepted Answer

$$C(x) = 36x + 200$$

Question 8

Given the cost function $$C(x) = 36x + 200$$, what is the marginal cost?

Accepted Answer

$$36$$

Question 9

Given the cost function $$C(x) = 36x + 200$$, what is the average cost to produce $$150$$ items?

Accepted Answer

$$37.33$$

Question 10

A home supply outlet has revenue $$R(x) = 0.21x (in $$millions) and profit $$P(x) = 0.084x - 1.5 (in $$millions). What is the cost equation $$C(x)$$?

Accepted Answer

$$C(x) = 0.126x + 1.5$$

Question 11

Using the cost equation $$C(x) = 0.126x + 1.5$$, what is the cost of producing $$7$$ units (in millions)?

Accepted Answer

$$2.382$$ million

Question 12

Given the supply and demand equations for bananas: $$p = 25q ($$supply) and $$p = 100 - 25q ($$demand), what is the equilibrium quantity?

Accepted Answer

$$q = 2$$

Question 13

Given the supply and demand equations for bananas: $$p = 25q ($$supply) and $$p = 100 - 25q ($$demand), what is the equilibrium price?

Accepted Answer

$$p = 50$$

Question 14

For $$f(x) = 3(x - 2)^2$ - 3$$, does the parabola open upward or downward, and what is its vertex?

Accepted Answer

Opens upward; vertex at $$(2, -3)$$

Question 15

A store owner sells $$x$$ units at price $$p(x) = -2x + 900$$ dollars. The cost function is $$C(x) = 100x + 5000. $$What is the revenue function $$R(x)$$?

Accepted Answer

$$R(x) = (-2x + 900)x$$

Question 16

Given the cost function $$C(x) = 100x + 5000$$ and revenue function $$R(x) = (-2x + 900)x$$, what is the profit function $$P(x)$$?

Accepted Answer

$$P(x) = -2x^2$ + 800x - 5000$$

Question 17

For the profit function $$P(x) = -2x^2$ + 800x - 5000$$, how many items should be sold to maximize profit?

Accepted Answer

$$x = 200$$

Question 18

What is the maximum profit for the function $$P(x) = -2x^2$ + 800x - 5000$$?

Accepted Answer

$$75,000$$

Question 19

For the profit function $$P(x) = -2x^2$ + 800x - 5000$$, what are the break-even points (values of $$x$$ where $$P(x) = 0$$)?

Accepted Answer

$$x = 7$$ and $$x = 357$$

College Algebra Test 1 Review – Step-by-Step Guidance

스터디 가이드 - 연습 문제

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