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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 $\bigtriangleup\bm{XYZ}$, the measure of $\bigtriangleup\bm{X}$ is 23${}^{*}$ and the measure of $\bigtriangleup\bm{Y}$ is 66${}^{*}$ What is the measure of $\bigtriangleup\bm{ZZ}$?

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 $XY$? ### $14$ ### $16$

MathGeometry and Trigonometry

Triangle $XYZ$ is similar to triangle $RSI$' such that $X$, $Y$, and $Z$ correspond to $R$, $S$, and $T$, respectively. The measure of $\angle Z$ is $20^{*}$ 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 $60^{*}$, $LN=10$, and $RT=30$. Which additional piece of information is sufficient to prove that triangle $LMN$ is similar to triangle $RST$?

MathGeometry and Trigonometry

In triangles _ABC_ and _DEF_, angles $B$ and $E$ each have measure 27${}^{*}$ and angles $C$ and $F$ each have measure 41${}^{*}$. Which additional piece of information is sufficient to determine whether triangle _ABC_ is congruent to triangle _DEF_?

MathGeometry and Trigonometry

Two nearby trees are perpendicular to the ground, which is flat. One of these trees is 10 feet tall and has a shadow that is 5 feet long. At the same time, the shadow of the other tree is 2 feet long. How tall, in feet, is the other tree?

MathGeometry and Trigonometry

In $\bigtriangleup\bm{XYZ}$, the measure of $\bigtriangleup\bm{X}$ is $\bm{24}^{*}$ and the measure of $\bigtriangleup\bm{Y}$ is $\bm{98}^{*}$. What is the measure of $\bigtriangleup\bm{ZZ}$?

MathGeometry and Trigonometry

In triangle $ABC$, the measure of angle $B$ is $90^{*}$ and $\overline{BD}$ is an altitude of the triangle. The length of $\overline{AB}$ is $15$ and the length of $\overline{AC}$ is $23$ greater than the length of $\overline{AB}$. What is the value of $\frac{BC}{BD}$?

MathGeometry and Trigonometry

A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere?

MathGeometry and Trigonometry

The area of a square is $64$ square inches. What is the side length, in inches, of this square?

MathGeometry and Trigonometry

Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

MathGeometry and Trigonometry

What is the length of one side of a square that has the same area as a circle with radius 2 ?

MathGeometry and Trigonometry

The side length of a square is 55 centimeters (cm). What is the area, in cm${}^{2}$, of the square?

MathGeometry and Trigonometry

In right triangle _RST_, the sum of the measures of angle $R$ and angle $S$ is 90 degrees. The value of $\sin(R)$ is $\frac{\sqrt{15}}{4}$. What is the value of $\cos(S)$?

MathGeometry and Trigonometry