All Questions ⁺⁰231340 Questions

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Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $CY = 6$, find $BC$.

falafronk Mar 25, 2024

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7

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+357

Square

In the diagram below, P is a point inside square ABCD. Find x.

falafronk Mar 25, 2024

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10

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+357

Geometry

Two lines $p$ and $q$ intersect at $X$. The angle between lines $p$ and $q$ is $45^\circ$. Let $A$ be a point inside the $45^\circ$ angle formed by $p$ and $q$. Let $B$ be the reflection of $A$ through line $p,$ and let $C$ be the reflection read more ..

falafronk Mar 25, 2024

0

2

1

+1791

Algebra

Let a_1, a_2, a_3, \dots be a sequence. If
a_n = a_{n - 1} + a_{n - 2}
for all n \ge 3, and a_{11} = 4 and a_{10} = 1, then find a_6.

tomtom Mar 25, 2024

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5

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+624

Floor function

Find all values of t such that \lfloor t\rfloor = 3t + 4 - \lfloor 2t \rfloor. If you find more than one value, then list the values you find in increasing order, separated by commas.

bingboy Mar 25, 2024

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7

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+624

Function

The function f(x) is defined for 1 \le x \le 5 as follows:
-2x + 4 & \text{if }1 \le x \le 2, \\
5 - x & \text{if }2 < x \le 3, \\
9 - 2x & \text{if }3 < x \le 4, \\
6 - x & \text{if }4 < x \le read more ..

bingboy Mar 25, 2024

0

7

1

+624

help counting

I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row?

bingboy Mar 25, 2024

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4

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+88

counting

In how many ways can I arrange $3$ different math books and $4$ different history books on my bookshelf, if at least three of the history books are next to each other?

cooIcooIcooI17 Mar 25, 2024

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4

1

+1791

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 4 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 40 miles per hour, the trip takes 5 hours. How many read more ..

tomtom Mar 25, 2024

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+357

help how do you do this

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

falafronk Mar 25, 2024

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8

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+357

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.

falafronk Mar 25, 2024

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8

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+357

need help

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 ..

falafronk Mar 25, 2024

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9

1

+357

help geometry

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle ABC = 60^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

falafronk Mar 25, 2024

Mar 24, 2024

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10

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+357

Geometry

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 1 and QC = 4. Find sin angle PAQ.

falafronk Mar 24, 2024

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10

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+357

help with triangle

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

falafronk Mar 24, 2024

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+357

help plz

In triangle ABC, point X is on AC such that angle BXA=90 degrees, AX=12 and CX=5 What is BX?

falafronk Mar 24, 2024

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+1072

Area

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

kittykat Mar 24, 2024

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+4

Help

Point P is on the side of line AC of triangle ABC such that angle ACB =angle ABC, and angle ABC - angle ACB = 42 degrees. Find angle PBC in degrees.

Kyle111 Mar 24, 2024

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6

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+1072

Triangle

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 $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

kittykat Mar 24, 2024

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+1072

Triangle

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, then read more ..

kittykat Mar 24, 2024

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6

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+1072

Triangle

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

kittykat Mar 24, 2024

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+1072

need help

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length read more ..

kittykat Mar 24, 2024

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4

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+1072

help 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 $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid read more ..

kittykat Mar 24, 2024

0

4

1

+1072

geometry

In parallelogram EFGH, let M be the point on EF such that FM:ME = 3:5 and let N be the point on EH such that HN:NE = 2:5. Line segments FH and GM intersect at P, and line segments FH and GN intersect at Q. Find PQ/FH.

kittykat Mar 24, 2024

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