All Questions ⁺⁰235735 Questions

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Geometry

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 13$, $SU = 14$, $TU = 4$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

kittykat Mar 15, 2024

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21

1

+1455

Angles

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 62^\circ$ and $\angle STU = 29^\circ$, read more ..

kittykat Mar 15, 2024

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22

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+4

…..

Billy purchased 100 shirts at a cost of $15 each and planned to resell them. The first week he sold some of them for $25 each. The second week he sold the rest for $20 each. If his total profit was $600, how many shirts did he sell the first week?
<read more ..

Serenah329 Mar 15, 2024

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27

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+1455

help triangle

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 20^\circ$, then what is $\angle ABH$ in degrees?

kittykat Mar 15, 2024

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21

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+1839

cozy numbers

We call a number cozy if every digit in the number is either even or next to an even digit. For example, a number is cozy if every digit in the number is either a 2 or next to a 2. For example, the number 222, 72, 45, and 810 and read more ..

ABJeIIy Mar 15, 2024

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8

2

+1839

cozy numbers

We call a number cozy if every digit in the number is either even or next to an even digit. For example, a number is cozy if every digit in the number is either a 2 or next to a 2. For example, the number 222, 72, 45, and 810 and read more ..

ABJeIIy Mar 15, 2024

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20

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+1839

Rolls

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $2000,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

ABJeIIy Mar 15, 2024

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+1839

need help

A coin is tossed $12$ times. How many different sequences of tosses could there have been, if the number of heads was at least $5?$

ABJeIIy Mar 15, 2024

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20

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+1839

Counting question

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

ABJeIIy Mar 15, 2024

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34

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+1839

help counting

You are given the 4 x 4 grid below.
(a) Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters.
(b) Find the number of ways read more ..

ABJeIIy Mar 15, 2024

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Help on counting

Hi I have a question
In how many ways can we distribute 13 pieces of identical candy to 5 kids, if the two youngest kids are twins and insist on receiving an equal number of pieces?
Thanks!

SOAPSTUDENT Mar 15, 2024

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25

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+1246

Hexagon

A regular hexagon has a perimeter of $p$ (in length units) and an area of $A$ (in square units). If $A = \frac{3}{2},$ then find the side length of the hexagon.

Akhain1 Mar 15, 2024

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32

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+1246

Polygon

In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.

Akhain1 Mar 15, 2024

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10

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+1246

Triangle

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $AX = 5,$ and $CX = 5$. What is $BX$?

Akhain1 Mar 15, 2024

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19

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+1246

Triangle

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

Akhain1 Mar 15, 2024

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39

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+1246

Altitudes

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

Akhain1 Mar 15, 2024

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+1246

help geometry

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 $ABC.$

Akhain1 Mar 15, 2024

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30

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+1246

Geometry

In the diagram, $ABCD$ is a square. Find $PR.$

The side length of the square is 10. L, M, N, O are midpoints.

Akhain1 Mar 15, 2024

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38

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+85

Geometry

Please solve these
1.

2.
<#> 3.<#> read more ..

Akhaim1 Mar 15, 2024

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14

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+1246

Equation of Circle

Find the coordinates of the center of the circle.
The points on the circle are (22,15), (-25,0), (22,-29).

Akhain1 Mar 15, 2024

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