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题目内容
The length of a diagonal of a certain rectangle is less than $$10$$.

Quantity A

The area of the rectangular region

Quantity B

$$50$$


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

$$144π$$


$$n$$ is an integer greater than $$1$$

Quantity A

The number of positive divisors of $$2n$$.

Quantity B

Twice the number of positive divisors of $$n$$




A triangle is inscribed in the circle with center $$O$$ as shown above. If the radius of the circle is $$5$$, what is the area of the shaded region? Give your answer to the nearest integer.
In a certain fire department, Adam works every third day, Branford works every fourth day, and Cathy works every fifth day. If all three work at the fire department today, in how many days will all three again work at the fire department on the same day?
The positive integer $$r$$ is a multiple of $$21$$.

Quantity A

The remainder when the integer $$20r$$ is divided by $$12$$

Quantity B

$$0$$


When integer $$n$$ is divided by $$8$$, the remainder is $$3$$. When integer $$n^2$$ is divided by $$8$$, the remainder is $$R$$.

Quantity A

$$R$$

Quantity B

$$1$$




$$E, F$$, and $$G$$ are midpoints of edges of the cube.

Quantity A

$$\frac{The area of triangular region EFG}{The surface area of the cube}$$

Quantity B

$$\frac{1}{6}$$


In 1995, for resident students attending public colleges in the United States, the average cost of room and board was approximately what percent of the average total cost of attending college?

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