All Questions ⁺⁰236343 Questions

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+1234

semicircles

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

Akhain1 Mar 13, 2024

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36

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+1234

geometry

In triangle ABC, point X is on side BC such that AX=13,BX=10,CX=10, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

Akhain1 Mar 13, 2024

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34

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+1234

Triangle

Triangle DEF is equilateral. Find AE.

DA = 3, AF = 2

Akhain1 Mar 13, 2024

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33

1

+1234

help geometry

In triangle PQR, let X be the intersection of the angle bisector of angle P with side QR, and let Y be the foot of the perpendicular from X to side PR. If PQ = 9, QR = 9, and PR = 12, then compute the length of X read more ..

Akhain1 Mar 13, 2024

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25

5

+85

Geometry

I am confused by these problems
1.

2.

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Akhaim1 Mar 13, 2024

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25

3

+2653

Arithmetic Series

Let a1, a2, a3, ..., a10, a11, a12 be an arithmetic sequence. If a1 + a2 = 4 and a2 + a3 = 5, then find a1.

LiIIiam0216 Mar 13, 2024

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36

1

+2653

Arithmetic Series

Laverne starts counting out loud by 5's. She starts with 1. 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 sends Shirley screaming read more ..

LiIIiam0216 Mar 13, 2024

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29

0

+2653

Arithmetic Series

Let a1, a2, a3, ... be an arithmetic series. Let Sn denote the sum of the first n terms. If S1 = 5 and S2 = 15, then find S15.

LiIIiam0216 Mar 13, 2024

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20

1

+1839

Algebra

Let x be a real number such that 625x = 9. Then 125x = ____

ABJeIIy Mar 13, 2024

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29

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+1839

Domain and Range

Find the domain and range of the function f(x) = 2(2 - 3x).

ABJeIIy Mar 13, 2024

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35

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+1839

Exponential Function

The graph of the exponential function f(x) is shown below. Find f(x).
f(0) = 1 and f(1) = 2.

ABJeIIy Mar 13, 2024

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24

1

+1560

help counting

A baking club wants to form an executive committee. There are $18$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $2$ people?
A baking club wants to form read more ..

blackpanther Mar 13, 2024

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29

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+1560

Distributions

In how many ways can $4$ balls be placed in $8$ boxes if the balls and boxes are both distinguishable?
In how many ways can $4$ balls be placed in $8$ boxes if neither the balls nor the boxes are distinguishable?
In read more ..

blackpanther Mar 13, 2024

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41

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+1560

help counting

I run a book club with $n$ people, not including myself. Every day, for $100$ days, I invite $14$ members in the club to review a book. What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of $14$ members read more ..

blackpanther Mar 13, 2024

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47

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+478

geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

ChiIIBill Mar 13, 2024

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34

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+478

Triangle

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 $BD$?

ChiIIBill Mar 13, 2024

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30

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+478

triangle problem

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

ChiIIBill Mar 13, 2024

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31

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+478

help with triangle

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?

ChiIIBill Mar 13, 2024

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34

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+478

Geometry

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

ChiIIBill Mar 13, 2024

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22

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+478

rectangle

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

ChiIIBill Mar 13, 2024

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26

0

+823

Triangles

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 45^\circ,$ $\angle ABC = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

booboo44 Mar 13, 2024

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30

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+823

Altitudes

In triangle $ABC,$ $AB = 15,$ $BC = 10,$ and $AC = 12.$ Find the length of the shortest altitude in this triangle.

booboo44 Mar 13, 2024

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29

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+823

Triangle

Find the area of triangle $ABC$ if $AB = 6,$ $BC = 8,$ and $\angle ACB = 30^\circ$.

booboo44 Mar 13, 2024

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