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The measure of angle $R$ is $\frac{2\pi}{3}$ radians. The measure of angle $T$ is $\frac{5\pi}{12}$ radians greater than the measure of angle $R$. What is the measure of angle $T$, in degrees?

MathGeometry and Trigonometry

In triangle $ABC$, the measure of angle $B$ is $52^{\circ}$ and the measure of angle $C$ is $17^{\circ}$. What is the measure of angle $A$?

MathGeometry and Trigonometry

A right triangle has legs with lengths of 28 centimeters and 20 centimeters. What is the length of this triangle's hypotenuse, in centimeters?

MathGeometry and Trigonometry

A rectangle has a length of 13 and a width of 6. What is the perimeter of the rectangle?

MathGeometry and Trigonometry

$RS=20$$ST=48$$TR=52$The side lengths of the right triangle $RST$ are given. Triangle $RST$ is similar to triangle $UVW$, where $S$ corresponds to $V$ and $T$ corresponds to $W$. What is the value of $\tan W$?

MathGeometry and Trigonometry

A right circular cone has a volume of $\frac{1}{3}\pi$ cubic feet and a height of $9$ feet. What is the radius, in feet, of the base of the cone?

MathGeometry and Trigonometry

$RS=440$$ST=384$$TR=584$The side lengths of right triangle $RST$ are given. Triangle $RST$ is similar to triangle $UVW$, where $S$ corresponds to $V$ and $T$ corresponds to $W$ . What is the value of $\tan W$?

MathGeometry and Trigonometry

An isosceles right triangle has a perimeter of $94+94\sqrt{2}$ inches. What is the length, in inches, of one leg of this triangle?

MathGeometry and Trigonometry

In the $xy$-plane, the graph of $2x^{2}-6x+2y^{2}+2y=45$ is a circle. What is the radius of the circle?

MathGeometry and Trigonometry

Triangle $ABC$ and triangle $DEF$ are similar triangles, where $\overline{AB}$ and $\overline{DE}$ are corresponding sides. If $DE=2AB$ and the perimeter of triangle $ABC$ is $20$, what is the perimeter of triangle $DEF$?

MathGeometry and Trigonometry

An isosceles right triangle has a hypotenuse of length $58$ inches. What is the perimeter, in inches, of this triangle?

MathGeometry and Trigonometry

In triangle $ABC$, the measure of angle $A$ is $50^{\circ}$. If triangle $ABC$ is isosceles, which of the following is NOT a possible measure of angle $B$ ?

MathGeometry and Trigonometry

Quadrilateral $P^{\prime}Q^{\prime}R^{\prime}S^{\prime}$ is similar to quadrilateral $PQRS$, where $P$, $Q$, $R$, and $S$ correspond to $P^{\prime}$, $Q^{\prime}$, $R^{\prime}$, and $S^{\prime}$, respectively. The measure of angle $P$ is $30^{\circ}$, the measure of angle $Q$ is $50^{\circ}$, and the measure of angle $R$ is $70^{\circ}$. The length of each side of $P^{\prime}Q^{\prime}R^{\prime}S^{\prime}$ is 3 times the length of each corresponding side of $PQRS$. What is the measure of angle $P^{\prime}$?

MathGeometry and Trigonometry

A manufacturer determined that right cylindrical containers with a height that is 4 inches longer than the radius offer the optimal number of containers to be displayed on a shelf. Which of the following expresses the volume, $V$, in cubic inches, of such containers, where $r$ is the radius, in inches?

MathGeometry and Trigonometry

A circle in the $xy$-plane has its center at $(-4,-6)$. Line $k$ is tangent to this circle at the point $(-7,-7)$. What is the slope of line $k$?

MathGeometry and Trigonometry

In $\bigtriangleup {XYZ}$, the measure of $\angle {X}$ is $23^{\circ}$ and the measure of $\angle {Y}$ is $66^{\circ}$ What is the measure of $\angle {Z}$?

MathGeometry and Trigonometry

Triangle $ABC$ is similar to triangle $XYZ$, such that $A$, $B$, and $C$ correspond to $X$, $Y$, and $Z$ respectively. The length of each side of triangle $XYZ$ is $2$ times the length of its corresponding side in triangle $ABC$. The measure of side $AB$ is $16$. What is the measure of side $XY$?

MathGeometry and Trigonometry

Triangle $XYZ$ is similar to triangle $RST$ such that $X$, $Y$, and $Z$ correspond to $R$, $S$, and $T$, respectively. The measure of $\angle Z$ is $20^{\circ}$ and $2XY=RS$. What is the measure of $\angle T$?

MathGeometry and Trigonometry

What is the diameter of the circle in the $xy$-plane with equation $\left(x-5\right)^{2}+\left(y-3\right)^{2}=16$?

MathGeometry and Trigonometry

A rectangle has an area of 63 square meters and a length of 9 meters. What is the width, in meters, of the rectangle?

MathGeometry and Trigonometry

$x^{2}+20x+y^{2}+16y=-20$The equation above defines a circle in the $xy$-plane. What are the coordinates of the center of the circle?

MathGeometry and Trigonometry

A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container

MathGeometry and Trigonometry

A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?

MathGeometry and Trigonometry

A cube has an edge length of 41 inches. What is the volume, in cubic inches, of the cube?

MathGeometry and Trigonometry

In triangles $LMN$ and $RST$, angles $L$ and $R$ each have measure $60^{\circ}$, $LN=10$, and $RT=30$. Which additional piece of information is sufficient to prove that triangle $LMN$ is similar to triangle $RST$?

MathGeometry and Trigonometry

The measure of angle $R$ is $\frac{2\pi}{3}$ radians. The measure of angle $T$ is $\frac{5\pi}{12}$ radians greater than the measure of angle $R$. What is the measure of angle $T$, in degrees?

In triangle $ABC$, the measure of angle $B$ is $52^{\circ}$ and the measure of angle $C$ is $17^{\circ}$. What is the measure of angle $A$?

A right triangle has legs with lengths of 28 centimeters and 20 centimeters. What is the length of this triangle's hypotenuse, in centimeters?

A rectangle has a length of 13 and a width of 6. What is the perimeter of the rectangle?

$RS=20$

$ST=48$

$TR=52$

The side lengths of the right triangle $RST$ are given. Triangle $RST$ is similar to triangle $UVW$, where $S$ corresponds to $V$ and $T$ corresponds to $W$. What is the value of $\tan W$?

A right circular cone has a volume of $\frac{1}{3}\pi$ cubic feet and a height of $9$ feet. What is the radius, in feet, of the base of the cone?

$RS=440$

$ST=384$

$TR=584$

The side lengths of right triangle $RST$ are given. Triangle $RST$ is similar to triangle $UVW$, where $S$ corresponds to $V$ and $T$ corresponds to $W$ . What is the value of $\tan W$?

An isosceles right triangle has a perimeter of $94+94\sqrt{2}$ inches. What is the length, in inches, of one leg of this triangle?

In the $xy$-plane, the graph of $2x^{2}-6x+2y^{2}+2y=45$ is a circle. What is the radius of the circle?

Triangle $ABC$ and triangle $DEF$ are similar triangles, where $\overline{AB}$ and $\overline{DE}$ are corresponding sides. If $DE=2AB$ and the perimeter of triangle $ABC$ is $20$, what is the perimeter of triangle $DEF$?

An isosceles right triangle has a hypotenuse of length $58$ inches. What is the perimeter, in inches, of this triangle?

In triangle $ABC$, the measure of angle $A$ is $50^{\circ}$. If triangle $ABC$ is isosceles, which of the following is NOT a possible measure of angle $B$ ?

A circle in the $xy$-plane has its center at $(-4,-6)$. Line $k$ is tangent to this circle at the point $(-7,-7)$. What is the slope of line $k$?

In $\bigtriangleup {XYZ}$, the measure of $\angle {X}$ is $23^{\circ}$ and the measure of $\angle {Y}$ is $66^{\circ}$ What is the measure of $\angle {Z}$?

Triangle $ABC$ is similar to triangle $XYZ$, such that $A$, $B$, and $C$ correspond to $X$, $Y$, and $Z$ respectively. The length of each side of triangle $XYZ$ is $2$ times the length of its corresponding side in triangle $ABC$. The measure of side $AB$ is $16$. What is the measure of side $XY$?

Triangle $XYZ$ is similar to triangle $RST$ such that $X$, $Y$, and $Z$ correspond to $R$, $S$, and $T$, respectively. The measure of $\angle Z$ is $20^{\circ}$ and $2XY=RS$. What is the measure of $\angle T$?

What is the diameter of the circle in the $xy$-plane with equation $\left(x-5\right)^{2}+\left(y-3\right)^{2}=16$?

A rectangle has an area of 63 square meters and a length of 9 meters. What is the width, in meters, of the rectangle?

$x^{2}+20x+y^{2}+16y=-20$

The equation above defines a circle in the $xy$-plane. What are the coordinates of the center of the circle?

A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container

A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?

A cube has an edge length of 41 inches. What is the volume, in cubic inches, of the cube?

In triangles $LMN$ and $RST$, angles $L$ and $R$ each have measure $60^{\circ}$, $LN=10$, and $RT=30$. Which additional piece of information is sufficient to prove that triangle $LMN$ is similar to triangle $RST$?