Question 1

Given the points $$A(-2, -3)$$ and $$B(4, 5)$$, what is the distance between them? Use the distance formula.

Accepted Answer

$$\sqrt{(4 + 2)^2$ + (5 + 3)^2$} = \sqrt{6^2$ + 8^2$} = \sqrt{36 + 64} = \sqrt{100} = 10$$

Question 2

Find the midpoint of the line segment joining the points $$P(-4, -3)$$ and $$Q(2, 1).$$

Accepted Answer

$$( -1, -1 )$$

Question 3

A family of four has a poverty threshold of $$24,257 in 2012. If $$their actual annual income is $$21,500$$, what is their ratio of income to the poverty threshold, rounded to two decimal places?

Accepted Answer

$$\frac{21,500}{24,257} \approx 0.89$$

Question 4

Which of the following equations represents a circle with center $$(1, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 1)^2$ + (y + 2)^2$ = 25$$

Question 5

Find the $$y-$$intercept of the equation $$y = 2x - 3.$$

Accepted Answer

$$(0, -3)$$

Question 6

Which equation is symmetric with respect to the $$y-$$axis?

Accepted Answer

$$y = x^2$

Question 7

A sound technician uses the equation $$y = x^2$ + y^2$ - 3x + 6 to $$model sound intensity. What is the $$x-$$intercept of this equation?

Accepted Answer

There is no $$x-$$intercept because the equation is not linear in $$x.$$

Question 8

Find the equation of the line passing through $$(1, -2)$$ and perpendicular to the line $$y = 3x + 4.$$

Accepted Answer

$$y + 2 = -\frac{1}{3}(x - 1)$$

Question 9

Which of the following is the correct formula for the distance between two points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 10

A business has fixed costs of $$800$$ and variable costs of $$5$$ per unit. What is the cost function $$C(x)$$ for producing $$x$$ units?

Accepted Answer

$$C(x) = 800 + 5x$$

Question 11

Find the midpoint of the segment joining $$(6, 2)$$ and $$(8, 4).$$

Accepted Answer

$$(7, 3)$$

Question 12

Which of the following equations is NOT symmetric with respect to the origin?

Accepted Answer

$$y = x^2$

Question 13

A satellite orbits the Earth with the center at $$(0, 0)$$ and a radius of $$6,400 km. $$What is the equation of its orbit?

Accepted Answer

$$x^2$$ + $$y^2 = 40$$,960,000$$

Question 14

Find the $$x-$$intercept of the equation $$y = 3x - 6.$$

Accepted Answer

$$(2, 0)$$

Question 15

Which of the following is the correct formula for the midpoint between two points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$)$$?

Accepted Answer

$$\left( \frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2} \right)$$

Question 16

If the equation of a line is $$y = -\frac{1}{2}x + 4$$, what is its slope and $$y-$$intercept?

Accepted Answer

Slope: $$-\frac{1}{2}$$, $$y-$$intercept: $$4$$

Question 17

Which of the following equations is symmetric with respect to the $$x-$$axis?

Accepted Answer

$$x = y^2$

Question 18

A circle has center $$(3, -2)$$ and radius $$7. $$What is its equation?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 49$$

Question 19

If a business has a cost function $$C(x) = 500 + 8x$$, what is the cost of producing $$50$$ units?

Accepted Answer

$$500 + 8 	imes 50 = 500 + 400 = 900$$

Question 20

Find the equation of the line passing through $$(2, 3)$$ with slope $$-4.$$

Accepted Answer

$$y - 3 = -4(x - 2)$$

Fundamental Concepts in College Algebra: Distance, Midpoint, Graphing, and Linear Equations

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