Q: A company has a demand function given by $p = 50 - 2x$, where $p$ is the price per unit and $x$ is the number of units sold. What is the total revenue $R$ when 10 units are sold?

$R = (50 - 2 \times 10) \times 10 = 300$

Q: Given the cost function $C(x) = 5x + 200$, what is the average cost per unit when 20 units are produced?

$\frac{C(x)}{x} = \frac{5 \times 20 + 200}{20} = 15$

Q: A business has a revenue function $R(x) = 20x$ and a cost function $C(x) = 8x + 120$. What is the profit when 15 units are sold?

$P = R - C = 20 \times 15 - (8 \times 15 + 120) = 300 - 240 = 60$

Q: Which of the following is the correct application of the quadratic formula to solve $2x^2 - 4x - 6 = 0$?

$x = \frac{4 \pm \sqrt{(-4)^2 - 4 \times 2 \times (-6)}}{2 \times 2}$

Question 1

A company has a demand function given by $p = 50 - 2x$, where $p$ is the price per unit and $x$ is the number of units sold. What is the total revenue $R$ when 10 units are sold?

Accepted Answer

$R = (50 - 2 	imes 10) 	imes 10 = 300$

Question 2

Given the cost function $C(x) = 5x + 200$, what is the average cost per unit when 20 units are produced?

Accepted Answer

$\frac{C(x)}{x} = \frac{5 	imes 20 + 200}{20} = 15$

Question 3

Which of the following correctly applies the difference of squares to factor $x^2 - 9$?

Accepted Answer

$x^2 - 9 = (x - 3)(x + 3)$

Question 4

A business has a revenue function $R(x) = 20x$ and a cost function $C(x) = 8x + 120$. What is the profit when 15 units are sold?

Accepted Answer

$P = R - C = 20 	imes 15 - (8 	imes 15 + 120) = 300 - 240 = 60$

Question 5

Simplify the expression $\frac{x^2 - 4}{x - 2}$ for $x 
eq 2$.

Accepted Answer

$x + 2$

Question 6

Find the real zeros of the polynomial $x^2 - 5x + 6$.

Accepted Answer

$x = 2$ and $x = 3$

Question 7

Which of the following is the correct domain of the function $f(x) = \frac{1}{x - 4}$?

Accepted Answer

All real numbers except $x = 4$

Question 8

Rationalize the denominator of $\frac{5}{\sqrt{3}}$.

Accepted Answer

$\frac{5\sqrt{3}}{3}$

Question 9

Given two points $(2, 5)$ and $(6, 13)$, what is the slope of the line passing through them?

Accepted Answer

$m = \frac{13 - 5}{6 - 2} = 2$

Question 10

If the supply and demand functions for a product are $S(x) = 2x + 10$ and $D(x) = 30 - x$, find the equilibrium quantity $x_0$.

Accepted Answer

$x_0 = 30 - x_0 = 2x_0 + 10 \Rightarrow x_0 = 10$

Question 11

Which of the following is the correct application of the quadratic formula to solve $2x^2 - 4x - 6 = 0$?

Accepted Answer

$x = \frac{4 \pm \sqrt{(-4)^2 - 4 	imes 2 	imes (-6)}}{2 	imes 2}$

Question 12

Simplify the expression $\frac{2x^2 - 8}{4x}$ for $x 
eq 0$.

Accepted Answer

$\frac{x^2 - 4}{2x}$

Question 13

A company’s cost function is $C(x) = 3x^2 + 12x + 100$. What is the fixed cost?

Accepted Answer

$100$

Question 14

Which of the following is the correct factorization of $x^2 + 6x + 9$?

Accepted Answer

$(x + 3)^2$

Question 15

Evaluate the function $f(x) = 2x^2 - x + 5$ at $x = -2$.

Accepted Answer

$f(-2) = 2(-2)^2 - (-2) + 5 = 8 + 2 + 5 = 15$

Question 16

Which of the following is the correct result of multiplying $\frac{3}{4}$ and $\frac{2}{5}$?

Accepted Answer

$\frac{6}{20}$

Question 17

If $a^2 = 25$, what are the possible values of $a$?

Accepted Answer

$a = \pm 5$

Question 18

A business sells a product at a price $p$ per unit. The demand function is $p = 100 - 4x$. What price should the company set to sell 15 units?

Accepted Answer

$p = 100 - 4 	imes 15 = 40$

Question 19

Which of the following is the correct point-slope form for a line with slope $m = -3$ passing through $(2, 7)$?

Accepted Answer

$y - 7 = -3(x - 2)$

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