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$$x \gt 90$$

Quantity A

The area of triangular region $$ABC$$

Quantity B

$$12$$


A sales representative' s monthly earnings consist of a base salary of $$ $3,500$$ plus a commission equal to $$5$$ percent of monthly sales in excess of $$ $50,000$$. If monthly sales total $$s$$ dollars and $$s \gt 50,000$$, what are the sales representative' s monthly earnings in terms of $$s$$, in dollars?
A total of $$ $72,000$$ was invested for one month in a new money market account that paid simple annual interest at the rate of $$r$$ percent. If the investment earned $$ $360$$ in interest for the month, what is the value of $$r$$?
James and Ellie are two of $$32$$ people standing in a line for move tickets. There are $$12$$ people, including Ellie, behind James, and there are $$4$$ people between James and Ellie. How many people are in front of Ellie in the line?


If the algebraic expression $$(a+b+c)^2$$ is represented geometrically by the square above, then the expression $$2ab+2bc$$ is represented by which of the following sets of regions?
$$n \gt 4$$

Quantity A

$$n^2-5n+4$$

Quantity B

$$n^2-6n+9$$


$$x \lt 0 \lt y$$

Quantity A

$$y-x^2$$

Quantity B

$$y+x$$


Which of the following integers CANNOT be expressed as $$x^2+y^2+z^2$$, where $$x, y$$, and $$z$$ are integers?
$$x$$ and $$y$$ are integers, $$x \leq 6$$ and $$y \gt 3-2x$$

Quantity A

The least possible value of $$y$$

Quantity B

$$-8$$


If $$a$$, $$b$$, and $$c$$ are positive numbers, which of the following could be the graph in the xy-plane of the equation $$ax+by-c=0$$?


Quantity A

$$(b-1)+(a-3)$$

Quantity B

$$\sqrt{(b-1)^2+(a-3)^2}$$




Quantity A

$$\frac{s}{r}$$

Quantity B

$$\frac{u}{t}$$


In the xy-plane, circle $$C$$ has radius $$4$$ and is centered at the origin, and parabola $$P$$ has the equation $$y=-(\frac{x}{2})^2+4$$. Which of the following points are on both circle $$C$$ and parabola $$P$$?
Indicate all such points.


Quantity A

$$x+y$$

Quantity B

$$z$$


Quantity A

The number of possible integers $$x$$ for which $$x, 2$$, and $$6$$ are the respective lengths of three sides of a triangle

Quantity B

$$4$$


A garden in the shape of a triangle has two sides that measure $$35$$ feet and $$20$$ feet, respectively. Which of the following values could be the perimeter, in feet, of the garden?
Indicate all such values.


The area of triangular region $$PQR$$ is $$16$$.

Quantity A

The length of $$PQ$$

Quantity B

$$8$$




$$OM=OA$$
$$ON=OB$$

Quantity A

The length of line segment $$OC$$

Quantity B

The length of line segment $$OP$$




In order to adequately heat or cool a house, a contractor must determine the number of cubic meters of space inside the house. A floor plan of a house with two sections, $$A$$ and $$B$$, is shown above. Each section of the house has a rectangular floor and is shaped like a rectangular solid. Section $$A$$ is $$1$$ story high, section $$B$$ is $$2$$ stories high, and the distance from the floor to the ceiling for each story is $$2.7$$ meters. Disregarding the dimensions of interior walls and structures, approximately how many cubic meters of space are inside the house?


In the circle shown, point $$O$$ is the center, and the length of arc $$ABC$$ is $$12$$.

Quantity A

The area of the shaded region

Quantity B

$$144π$$


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