Q: Which of the following ordered pairs correctly represents the relationship between the category 'transportation' and the amount spent $$5796$$ from the provided table?

$$(\text{transportation}, 5796)$$

Question 1

Which of the following ordered pairs correctly represents the relationship between the category 'transportation' and the amount spent $$5796$$ from the provided table?

Accepted Answer

$$(	ext{transportation}, 5796)$$

Question 2

Given points $$P(3, -5)$$ and $$Q(-2, 8)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(3 - (-2))^2$ + (-5 - 8)^2$} = \sqrt{25 + 169} = \sqrt{194}$$

Question 3

Which formula is used to find the midpoint $$M of a $$line segment with endpoints $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$)$$?

Accepted Answer

$$M = (\frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2})$$

Question 4

If the equation of a circle is $$(x-1)^2$$ + $$(y+2)^2 = 9$, what are the center and radius?

Accepted Answer

Center $$(1, -2)$$, radius $$3$$

Question 5

Which of the following relations is NOT a function?

Accepted Answer

$$P = \{(4, -3), (0, 6), (2, 8), (-4, -3)\}$$

Question 6

What is the general form of the equation of a circle?

Accepted Answer

$$x^2$$ + $$y^2 + Dx + Ey + F = 0$

Question 7

Given the equation $$y = -2x + 5$$, which of the following is an ordered pair solution?

Accepted Answer

$$(2, 1)$$

Question 8

If the graph of $$x = \sqrt{y+1} is $$plotted, which of the following points lies on the graph?

Accepted Answer

$$(0, -1)$$

Question 9

Which of the following describes the domain of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 10

If the equation of a circle is $$x^2$$ + $$y^2 = 4$, what is the radius?

Accepted Answer

$$2$$

Question 11

Which formula is used to determine if three points $$A$$, $$B$$, and $$C$$ are collinear?

Accepted Answer

Check if the area of the triangle formed by the points is zero

Question 12

What is the center and radius of the circle given by $$x^2 + 4x$$ + $$y^2 - 8y = 45$?

Accepted Answer

Center $$(-2, 4)$$, radius $$7$$

Question 13

Which of the following is the correct center-radius form for a circle with center $$(h, k)$$ and radius $$r$$?

Accepted Answer

$$(x-h)^2$$ + $$(y-k)^2$$ = $$r^2$$

Question 14

If the total revenue for full-service restaurants increased from $$194.6$$ billion in $$2011 to$$ $$263.0$$ billion in $$2017$$, what is the midpoint estimate for $$2014$$?

Accepted Answer

$$(2014, 228.8)$$

Question 15

Which of the following is NOT a step in graphing equations as described in the study material?

Accepted Answer

Calculate the area under the curve

Question 16

If $$d(P, Q) is $$the distance between points $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$)$$, which formula is correct?

Accepted Answer

$$d(P, Q) = \sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Rectangular Coordinates, Distance, Midpoint, Circles, and Functions: Precalculus Study Notes

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