All Questions ⁺⁰235721 Questions

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Sum

Compute the sum
1 + \frac{1}{5} + \frac{2}{5} + \frac{3}{5} + \frac{2}{25} + \frac{3}{25} + \frac{4}{25}

sandwich Jan 3, 2024

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22

1

+1364

Infinite series

Evaluate the infinite geometric series
0.4 + 0.036 + 0.0000324 + ...
Express your answer as a fraction with integer numerator and denominator.

sandwich Jan 3, 2024

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31

1

+1364

Sequences

Laverne starts counting out loud by ${}5$'s. She starts with $2$. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds $40,$ Shirley runs screaming from the room. What number does Laverne say that read more ..

sandwich Jan 3, 2024

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15

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+1439

Triangle

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $[DTM] = 20$. read more ..

kittykat Jan 3, 2024

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25

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+1439

Angles

As shown in the diagram $\angle BAC=90^\circ$. Let $X$ be the foot of the altitude from $A$ to $\overline {BC}$, $\overline{AY}$ be the bisector of $\angle BAC$, and $\overline{AZ}$ be the median of $\triangle ABC$. If $\angle XAY = 16^\circ$, then read more ..

kittykat Jan 3, 2024

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15

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+1439

Need help with coordinates

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

kittykat Jan 3, 2024

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15

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+1678

Length in Triangle

In the diagram, $\triangle PQR$ is right-angled at $P$ and has $PQ=2$ and $PR=5$. Altitude $PL$ intersects median $RM$ at $F$. What is the length of $PF$? read more ..

wiseowl Jan 3, 2024

Jan 2, 2024

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26

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+1678

Area of Quadrilateral

What is the area in square units of the quadrilateral $XYZW$ shown below? Also, find $WY$. read more ..

wiseowl Jan 2, 2024

+1

29

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+1911

Clock

What is the degree measure of the acute angle formed by the hands of a clock at $3:30$?

tomtom Jan 2, 2024

+1

22

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+1911

Circles

Stuart has drawn a pair of concentric circles, as shown. He draws chords $\overline{AB}$, $\overline{BC}, \ldots$ of the large circle, each tangent to the small one. If $m\angle ABC=65^\circ$, then how many segments will he draw before returning read more ..

tomtom Jan 2, 2024

+1

28

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+1911

Tangent

In the figure, $\angle{XYZ}$ is inscribed in circle $I$, $\angle{XYZ}=36^\circ$, $\angle{AZY}=44^\circ$, and $AB$ is tangent to circle $I$ at $Z$. What is the measure of $\angle YIZ$, in degrees? read more ..

tomtom Jan 2, 2024

+1

31

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+1911

Tangent

In the diagram below, triangle $ABC$ is inscribed in the circle and $AC = AB$. The measure of angle $BAC$ is $30$ degrees and segment $ED$ is tangent to the circle at point $C$. What is the measure of angle $ACD$? read more ..

tomtom Jan 2, 2024

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49

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+1768

Quadrilateral

In $\triangle ABC$ we have $AB=25$, $BC=39$, and $AC=42$. Points $D$ and $E$ are on $\overline{AB}$ and $\overline{AC}$ respectively, with $AD=15$ and $AE=12$. What is the ratio of the area of triangle $ADE$ to the area of the quadrilateral read more ..

bader Jan 2, 2024

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28

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+1768

rectangle

$AE$ divides rectangle $ABCD$ into two parts such that the ratio of the area of $\triangle ADE$ to the area of quadrilateral $ABCE$ is 1:4. Find the ratio of $DE$ to $EC$. Express your answer as a common fraction. read more ..

bader Jan 2, 2024

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+1768

triangle

An equilateral triangle has sides $8$ units long. An equilateral triangle with sides $2$ units long is cut off at the top, leaving an isosceles trapezoid. What is the ratio of the area of the smaller triangle to the area of the trapezoid? Express your answer read more ..

bader Jan 2, 2024

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32

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+4

Geometry Question

In the diagram, angles ABC and ADC are right angles. If AC = 35, AE=11, and , BE=10 then what is AD?

HWhelper44 Jan 2, 2024

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20

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+50

Unit circles

Let P, Q, R, and S be the terminal points on the unit circle below:

Let a, b, c, and d be angles such that P = Terminal point for a, Q = Terminal read more ..

helloworldhello Jan 2, 2024

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+50

Help with unit circles

Let P, Q, R, and S be the terminal points on the unit circle below:

Order the points P, Q, R, S so that the first point is the terminal point read more ..

helloworldhello Jan 2, 2024

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21

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+1768

Bisecting Lines

The line $y = mx$ bisects the angle between the two lines shown below. Find $m$.
The two lines are y = x and y = 2x.

bader Jan 2, 2024

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38

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+1768

Numbers

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
x^2 + y^2 = 4x + 2y
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

bader Jan 2, 2024

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34

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+1768

Coordinates

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 20.
The line is y = -4.

bader Jan 2, 2024

-1

27

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+1443

Pyramid

Let $ABCDE$ be a right square pyramid, with base $ABCD$ and apex $E.$ Find the volume of the pyramid. read more ..

blackpanther Jan 2, 2024

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