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A circle in the $xy$-plane has its center at $(-4,5)$ and the point $(-8,8)$ lies on the circle. Which equation represents this circle?

MathGeometry and Trigonometry

What is the perimeter, in inches, of a rectangle with a length of 4 inches and a width of 9 inches?

MathGeometry and Trigonometry

A right triangle has sides of length $2\sqrt{2}$, $6\sqrt{2}$, and $\sqrt{80}$ units. What is the area of the triangle, in square units?

MathGeometry and Trigonometry

A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of 75 cm$^{2}$, and the height of the can is 10 cm. If 110 cm$^{3}$ of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?

MathGeometry and Trigonometry

In a right triangle, the measure of one of the acute angles is $51^{\circ}$. What is the measure, in degrees, of the other acute angle?

MathGeometry and Trigonometry

Right triangles $LMN$ and $PQR$ are similar, where $L$ and $M$ correspond to $P$ and $Q$, respectively. Angle $M$ has a measure of $53^{\circ}$. What is the measure of angle $Q$?

MathGeometry and Trigonometry

A circle in the $xy$-plane has equation $(x+3)^{2}+(y-1)^{2}=25$. Which of the following points does NOT lie in the interior of the circle?

MathGeometry and Trigonometry

What is the area of a rectangle with a length of 4 centimeters (cm) and a width of 2 cm?

MathGeometry and Trigonometry

In a right triangle, the tangent of one of the two acute angles is $\frac{\sqrt{3}}{3}$. What is the tangent of the other acute angle?

MathGeometry and Trigonometry

Circle $A$ has a radius of $3n$ and circle $B$ has a radius of $129n$, where $n$ is a positive constant. The area of circle $B$ is how many times the area of circle $A$?

MathGeometry and Trigonometry

A square is inscribed in a circle. The radius of the circle is $\frac{20\sqrt{2}}{2}$ inches. What is the side length, in inches, of the square?

MathGeometry and Trigonometry

The length of a rectangle's diagonal is $5\sqrt{17}$, and the length of the rectangle's shorter side is 5. What is the length of the rectangle's longer side?

MathGeometry and Trigonometry

What is the area of a rectangle with a length of 17 centimeters (cm) and a width of 7 cm?

MathGeometry and Trigonometry

The area of a rectangle is 630 square inches. The length of the rectangle is 70 inches. What is the width, in inches, of this rectangle?

MathGeometry and Trigonometry

The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?

MathGeometry and Trigonometry

Two identical rectangular prisms each have a height of 90 centimeters (cm). The base of each prism is a square, and the surface area of each prism is $\bm{K}$ $cm$${}^{2}$. If the prisms are glued together along a square base, the resulting prism has a surface area of $\frac{92}{47}\bm{K}$ $cm$${}^{2}$. What is the side length, in cm, of each square base?

MathGeometry and Trigonometry

The equation $x^{2}+\left(y-2\right)^{2}=36$ represents circle A. Circle B is obtained by shifting circle A down 4 units in the $xy$-plane. Which of the following equations represents circle B?

MathGeometry and Trigonometry

$(x-6)^{2}+(y+5)^{2}=16$

In the $xy$-plane, the graph of the equation above is a circle. Point $P$ is on the circle and has coordinates $(10,-5)$. If $\overline{PQ}$ is a diameter of the circle, what are the coordinates of point $Q$ ?

MathGeometry and Trigonometry

What is the area, in square centimeters, of a rectangle with a length of 36 centimeters and a width of 34 centimeters?

MathGeometry and Trigonometry

Which of the following equations represents a circle in the $xy$-plane that intersects the $y$-axis at exactly one point? 

MathGeometry and Trigonometry

Triangles $ABC$ and $DEF$ are congruent, where $A$ corresponds to $D$, and $B$ and $E$ are right angles. The measure of angle $A$ is $18^{\circ}$. What is the measure of angle $F$?

MathGeometry and Trigonometry

In the $xy$-plane, a circle with radius 5 has center ($-8$,$6$). Which of the following is an equation of the circle?

MathGeometry and Trigonometry

A circle has center $O$, and points $A$ and $B$ lie on the circle. The measure of arc $AB$ is $45^{\circ}$ and the length of arc $AB$ is $3$ inches. What is the circumference, in inches, of the circle?

MathGeometry and Trigonometry

The equation $x^{2}+\left(y-1\right)^{2}=49$ represents circle A. Circle B is obtained by shifting circle A down $2$ units in the $xy$-plane. Which of the following equations represents circle B? 

MathGeometry and Trigonometry

Triangle $ABC$ is similar to triangle $DEF$, where $A$ corresponds to $D$ and $C$ corresponds to $F$. Angles $C$ and $F$ are right angles. If $\tan(A)=\sqrt{3}$ and $DF=125$, what is the length of $\overline{DE}$?

MathGeometry and Trigonometry