All Questions ⁺⁰235749 Questions

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31

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+359

Triangle

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

falafronk Mar 24, 2024

0

21

1

+16

Please Help

How many real solutions are there to the equation √x+5= |2x|? (Note: Both x and 5 are under the same square root symbol)

Arhantio Mar 24, 2024

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17

1

+359

help 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?

falafronk Mar 24, 2024

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31

0

+359

counting

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?

falafronk Mar 24, 2024

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19

0

+1443

help 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.

blackpanther Mar 24, 2024

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19

1

+1443

Trapezoid

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 Mar 24, 2024

0

23

1

+1443

Polygons

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

blackpanther Mar 24, 2024

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30

0

+1246

need help

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle PBA$, and $\angle ABC - \angle ACB = 24^\circ$. Find $\angle PBC$ in degrees.

Akhain1 Mar 24, 2024

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19

1

+1246

Circle sector

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle? read more ..

Akhain1 Mar 24, 2024

0

26

1

+359

help geometry

Let $A$, $B$, $C$, and $D$ be points on a circle such that $AB = 11$ and $CD = 19.$ Point $P$ is on segment $AB$ with $AP = 7$, and $Q$ is on segment $CD$ with $CQ = 8$. The line through $P$ and $Q$ intersects the circle at $X$ and $Y$. If $PQ = 25$, find read more ..

falafronk Mar 24, 2024

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18

1

+359

help!! need help

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

falafronk Mar 24, 2024

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21

4

+70

halp!

Find the area of triangle ABC, given that AH=11 and HD=5 read more ..

faiafronk Mar 24, 2024

0

37

0

+359

Need help

Joanna has seven beads that she wants to assemble into a bracelet. Five of the beads have the same color, and the other two all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical read more ..

falafronk Mar 24, 2024

0

30

0

+359

Help Probability

Raina places the following balls into a bag. She draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?
There are 6 orange balls and 6 purple read more ..

falafronk Mar 24, 2024

0

15

1

+1246

Square

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

Akhain1 Mar 24, 2024

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22

0

+1768

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 $AB = 20$, $AC = 20$, read more ..

bader Mar 24, 2024

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32

1

+1768

Geometry

Points $T$ and $U$ lie on a circle centered at $O$, and point $P$ is outside the circle such that $\overline{PT}$ and $\overline{PU}$ are tangent to the circle. If $\angle TOP = 45^{\circ}$, then what is the measure of minor arc $TU$, in deg read more ..

bader Mar 24, 2024

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24

0

+359

Probability

Three cards are randomly drawn from a standard deck of $52$ cards, without replacement. Find the probability that the first card is spades or an Ace, the second card is red, and the third card is a nine.

falafronk Mar 24, 2024

0

22

1

+359

Counting

Syd chooses two different primes, and multiplies them. If both primes are greater than 4, and the resulting product is less than 600, then how many different products could Syd have ended up with?

falafronk Mar 24, 2024

0

27

0

+359

help counting

In the array below, in how many different ways can we start with the letter A and move from letter to letter (horizontally, vertically, or diagonally), to spell the word ARCH?
A
RRR read more ..

falafronk Mar 24, 2024

0

19

3

+118

PLEASE HELP ASAP!!!!

Let

Evaluate (This sum has terms, one for the result when we input each integer from to into .)

CPhill ●●●

SilviaJendeukie Mar 24, 2024

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15

1

+359

Counting

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.)

falafronk Mar 24, 2024

0

27

0

+359

Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

falafronk Mar 24, 2024

0

22

1

+359

Probability

The following cards are split into three piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
There are two queens, two kings, and two aces.

falafronk Mar 24, 2024

0

22

0

+359

Probability

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both have read more ..

falafronk Mar 24, 2024

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