Q: If $$A = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \\ 4 & 2 \end{pmatrix}$$, what is $$A + B$$?

$$\begin{pmatrix} 3 & 1 \\ 4 & 5 \end{pmatrix}$$

Question 1

Which of the following best describes the main objective of applying algebra in economics?

Accepted Answer

To analyze and solve real-world economic problems using mathematical models.

Question 2

Given the linear function $$y = 3x + 5$$, what is the value of $$y$$ when $$x = -2$$?

Accepted Answer

$$y = -1$$

Question 3

A company’s cost function is given by $$C(x) = 50 + 10x. $$What does the number 50 represent in this context?

Accepted Answer

The fixed cost, independent of the number of units produced.

Question 4

If the demand function for a product is $$Q_d = 100 - 2P$$, what is the quantity demanded when the price $$P = 30$$?

Accepted Answer

$$Q_d = 40$$

Question 5

Which of the following equations represents a straight line with a slope of $$-4$$ and a $$y-$$intercept of $$8$$?

Accepted Answer

$$y = -4x + 8$$

Question 6

Suppose the supply function is $$Q_s = 5P - 10. At $$what price does the quantity supplied equal zero?

Accepted Answer

$$P = 2$$

Question 7

Which of the following best describes the solution set of the inequality $$2x - 3 \u003e 7$$?

Accepted Answer

$$x \u003e 5$$

Question 8

A business’s revenue function is $$R(x) = 20x. If $$the cost function is $$C(x) = 5x + 60$$, what is the break-even quantity?

Accepted Answer

$$x = 4$$

Question 9

If $$f(x) = x^2$ - 4x + 3$$, what is the value of $$f(5)$$?

Accepted Answer

$$f(5) = 8$$

Question 10

Which of the following is the correct solution to the system of equations: $$\begin{cases} x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (4, 3)$$

Question 11

A quadratic function models the profit of a company: $$P(x) = -2x^2$ + 8x + 10. $$What is the maximum profit?

Accepted Answer

$$P_{max} = 18$$

Question 12

If the price elasticity of demand is calculated as $$E = \frac{\Delta Q/Q}{\Delta P/P}$$, what does it mean if $$|E| \u003e 1$$?

Accepted Answer

Demand is elastic.

Question 13

Which of the following best represents the domain of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$x 
eq 2$$

Question 14

A bank offers compound interest modeled by $$A = P(1 + r)^t. If $$you invest $$P = 1000 at$$ $$r = 0.05$$ for $$t = 3$$ years, what is the final amount $$A$$?

Accepted Answer

$$A = 1157.63$$

Question 15

If $$g(x) = 2x + 1$$ and $$h(x) = x^2$, what is (g$$ \circ h)(2)$$?

Accepted Answer

$$g(h(2)) = 9$$

Question 16

Which of the following is the solution to the equation $$\log_{2}(x) = 3$$?

Accepted Answer

$$x = 8$$

Question 17

A firm’s total revenue is given by $$TR = 5Q$$, and total cost is $$TC = 2Q + 30. $$What is the profit when $$Q = 10$$?

Accepted Answer

$$Profit = 20$$

Question 18

If $$A = \begin{pmatrix} 2 & 1 \ 0 & 3 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \ 4 & 2 \end{pmatrix}$$, what is $$A + B$$?

Accepted Answer

$$\begin{pmatrix} 3 & 1 \ 4 & 5 \end{pmatrix}$$

Question 19

Which of the following best describes the solution to the quadratic equation $$x^2 - 6x + 9 = 0$?

Accepted Answer

$$x = 3$$

Question 20

If the function $$f(x) = 2x - 5$$ represents the cost in dollars to produce $$x$$ units, what is the cost to produce 12 units?

Accepted Answer

$$f(12) = 29$$

Fundamental Concepts in College Algebra for Applied Economics

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