Q: Which of the following ordered pairs correctly represents the relationship between the category 'transportation' and the amount spent, according to the example in the study material?

$$(\text{transportation}, 9728)$$

Question 1

Which of the following ordered pairs correctly represents the relationship between the category 'transportation' and the amount spent, according to the example in the study material?

Accepted Answer

$$(	ext{transportation}, 9728)$$

Question 2

What is the formula for the distance $$d$$ between two points $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$) in $$the rectangular coordinate plane?

Accepted Answer

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

Question 3

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

Accepted Answer

$$\sqrt{194}$$

Question 4

If the sides $$a$$, $$b$$, and $$c of a $$triangle satisfy $$a^2$$ + $$b^2$$ = $$c^2$$, what type of triangle is it?

Accepted Answer

A right triangle

Question 5

What is the midpoint of the line segment with endpoints $$(-7, -5)$$ and $$(2, 13)$$?

Accepted Answer

$$(-2.5, 4)$$

Question 6

Which equation represents a circle with center $$(1, -2)$$ and radius $$3$$?

Accepted Answer

$$(x-1)^2$$ + $$(y+2)^2 = 9$

Question 7

Given the general form of a circle $$x^2$$ + $$y^2 + Dx + Ey + F = 0$, what is the center-radius form?

Accepted Answer

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

Question 8

If the equation of a circle is $$x^2 + 4x$$ + $$y^2 - 8y = 45$, what are the coordinates of its center?

Accepted Answer

$$(2, 4)$$

Question 9

Which of the following relations is NOT a function?

Accepted Answer

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

Question 10

What is the domain of the function $$x = \sqrt{y+1}$$?

Accepted Answer

$$y \geq -1$$

Question 11

Which graph best represents the equation $$y = -x^2$ + 1$$?

Accepted Answer

A parabola opening downwards with vertex at $$(0, 1)$$

Question 12

If the equation of a circle is $$(x-3)^2$$ + $$(y+1)^2 = -2$, what can be said about its graph?

Accepted Answer

It does not represent any real points; the graph is nonexistent

Question 13

Which of the following is the correct midpoint formula for points $$P(x_1$, y_1$)$$ and $$Q(x_2$, y_2$)$$?

Accepted Answer

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

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 the total revenue in 2014?

Accepted Answer

$$(228.8)$$ billion

Question 15

Which of the following best describes the rectangular coordinate system?

Accepted Answer

A system with two perpendicular axes called the $$x-$$axis and $$y-$$axis

Question 16

What is the equation of a circle with center $$(0, 0)$$ and radius $$2$$?

Accepted Answer

$$x^2$$ + $$y^2 = 4$

Question 17

If a function $$f is $$defined by $$f(x) = x^2$ - 3x - 9$$, what is $$f(3)$$?

Accepted Answer

$$-9$$

Question 18

Which of the following statements is true about the domain of the square root function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$x \geq 0$$

Question 19

If the graph of a circle is $$x^2$$ + $$y^2 + Dx + Ey + F = 0$ and D = 0$, E = 0$, F = -4$, what is the radius of the circle?

Accepted Answer

$$2$$

Rectangular Coordinates, Graphs, and Introduction to Functions

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