All Questions ⁺⁰237783 Questions

0

30

1

+613

Geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

Pythagorearn Jan 23, 2025

0

27

1

+900

Geometry

In triangle $ABC$, $AB = 7$, $AC = 17$, and the length of median $AM$ is $12$. Find the area of triangle $ABC$.

eramsby1O1O Jan 23, 2025

0

32

0

+900

Geometry

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

eramsby1O1O Jan 23, 2025

0

34

0

+900

Geometry

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

eramsby1O1O Jan 23, 2025

0

37

0

+900

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

eramsby1O1O Jan 23, 2025

0

42

0

+381

Geometry

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

cwimie Jan 23, 2025

0

43

0

+381

Geometry

The equation of the line below can be expressed in the form
\frac{x}{a} + \frac{y}{b} = 1.
Find a. read more ..

cwimie Jan 23, 2025

0

42

0

+381

Geometry

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length AB.

cwimie Jan 23, 2025

0

27

1

+381

Geometry

A semicircle is inscribed in triangle XYZ so that its diameter lies on YZ, and is tangent to the other two sides. If XY = 10, XZ = 10, and YZ = 10*sqrt(2), then find the area of the semicircle.

cwimie Jan 23, 2025

0

15

1

+1855

Algebra

Find the minimum value of 9^x - 2 \cdot 3^x + 1 over all real numbers x.

ABJeIIy Jan 23, 2025

0

32

0

+1855

Algebra

Find one ordered pair $(x,y)$ of real numbers such that $x + y = 10$ and $x^3 + y^3 = 162 + x^2 + y^2.$

ABJeIIy Jan 23, 2025

0

29

0

+1855

Algebra

Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

ABJeIIy Jan 23, 2025

0

27

0

+1855

Algebra

Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$

ABJeIIy Jan 23, 2025

0

25

1

+823

Counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

crimefightingvigiI Jan 23, 2025

0

42

0

+823

Counting

The entries in a certain row of Pascal's triangle are
1, n, \dots, n, 1.
The average of the entries in this row is 2. Find $n$.

crimefightingvigiI Jan 23, 2025

0

32

1

+519

Algebra

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

bIueb3rry Jan 23, 2025

0

45

0

+519

Algebra

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

bIueb3rry Jan 23, 2025

0

34

0

+519

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

bIueb3rry Jan 23, 2025

0

35

0

+1844

Geometry

In triangle PQR, M is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If PQ = 36, find the area read more ..

blackpanther Jan 23, 2025

0

26

1

+1844

Geometry

A quadrilateral has angles of $q$, $4q + 17^\circ $, $8q + 21^\circ$, and $15q + 148^\circ $. Find the largest angle of the quadrilateral, in degrees.

blackpanther Jan 23, 2025

0

34

0

+1844

Geometry

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

blackpanther Jan 23, 2025

0

12

2

+28

Help please

Ms. Q gave Grogg the following problem: "License plates in Aopslandia consist of six upper-case letters. For example, two possible Aopslandian license plates are $ABCDEF$ and $AAAOPS.$ No two license plates are the same. How many possible Aopslandian license read more ..

dogsrule Jan 23, 2025

0

15

2

+1022

Geometry

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?

gnistory Jan 23, 2025

0

39

0

+1022

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

gnistory Jan 23, 2025

0

42

0

+1022

Geometry

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

gnistory Jan 23, 2025

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