All Questions ⁺⁰236405 Questions

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Counting

In how many ways can you distribute $8$ indistinguishable balls among $6$ distinguishable boxes, if at least three of the boxes must be empty?

crimefightingvigiI Jan 12, 2025

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Counting

Find the number of solutions to
x_1 + x_2 + x_3 + x_4 + x_5 \le 1
in nonnegative integers.

crimefightingvigiI Jan 12, 2025

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+2729

Algebra

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

LiIIiam0216 Jan 12, 2025

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Algebra

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does read more ..

LiIIiam0216 Jan 12, 2025

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Geometry

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $90^\circ.$ Find the area of the rhombus.

LiIIiam0216 Jan 12, 2025

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Geometry

The perimeter of a rectangle is $40,$ and the length of one of its diagonals is $10 \sqrt{2}.$ Find the area of the rectangle.

LiIIiam0216 Jan 12, 2025

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+837

Geometry

A pole of height 50 units has broken into two pieces, and the top of the pole is now at a point that is 25 units from the base of the pole. Find the difference between the lengths of the two pieces.

booboo44 Jan 12, 2025

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+837

Geometry

Rectangle ADEH is divided into rectangles ABGH, BCFG, and CDEF. If $AC = 15,$ $GE = 15,$ $[ABGH] = 8,$ and $[CDEF] = 8,$ find $[BCFG].$

booboo44 Jan 12, 2025

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+837

Geometry

In the diagram, XY = 2\cdot AX = 2\cdot YB and $\dfrac{AZ}{BX} = \dfrac{2}{5}$. Find $\dfrac{[YBC]}{[ZYC]}$.

booboo44 Jan 12, 2025

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+553

Help help

Find all values of $x$ such that $x^2 - 5x + 4 = -x^2 - 25x - 14$. If you find more than one value, then list your solutions, separated by commas.

crimefightingvigiI Jan 12, 2025

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+553

Help me plz

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator read more ..

crimefightingvigiI Jan 12, 2025

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I need help

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

crimefightingvigiI Jan 12, 2025

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Help plz

Suppose a does not equal 0. Compute log base 8a (4^b) in terms of a and b.

crimefightingvigiI Jan 12, 2025

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+28

Please help ASAP

Hi I need help solving:
The sum
is equal to a polynomial for all Write as a polynomial with terms in descending order of n.
Thank you!!

crimefightingvigil Jan 12, 2025

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+27

Hard Counting Problem Please Help

When two standard 6-sided dice are rolled, there are 36 possible outcomes for the sum of the two rolls: one sum of 2, two sums of 3, and so on, up to one sum of 12.
Find all possible ways of numbering a 4-sided die and a 9-sided die with positive read more ..

Halplz Jan 12, 2025

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+697

Geometry

In triangle $ABC$, point $D$ is on side $\overline{AC}$ such that line segment $\overline{BD}$ bisects $\angle ABC$. If $\angle A = 45^\circ$, $\angle C = 45^\circ$, and $AC = 12$, then find the area of triangle $ABD$.

cooIcooIcooI17 Jan 12, 2025

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+697

Geometry

In triangle $ABC,$ $\angle B = 90^\circ.$ Point $X$ is on $\overline{AC}$ such that $\angle BXA = 90^\circ,$ $BC = 15,$ and $CX = 5$. What is $BX$?

cooIcooIcooI17 Jan 12, 2025

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Geometry

There are four cities: Capital City, Little Village, Mytown, and Yourtown. The distance from Capital City to Little Village is $5$ miles. The distance from Capital City to Mytown is $2$ miles. The distance from Mytown to Yourtown is $3$ read more ..

cooIcooIcooI17 Jan 12, 2025

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+697

Geometry

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

cooIcooIcooI17 Jan 12, 2025

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+2729

HALP ME Plz

In parallelogram EFGH, let M be the point on \overline{EF} such that FM:ME = 1:1, and let N be the point on \overline{EH} such that HN:NE = 1:1. Line segments \overline{FH} and \overline{GM} intersect at P, and line segments \overline{FH} and GN intersect read more ..

LiIIiam0216 Jan 12, 2025

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+2729

HALP ME HALP ME

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 ..

LiIIiam0216 Jan 12, 2025

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+2729

I need halp

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.

LiIIiam0216 Jan 12, 2025

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+2729

Plz halp

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.

LiIIiam0216 Jan 12, 2025

Jan 11, 2025

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+363

HALP PLZ

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 2$, $BY = 16$, $\angle ACB = 90^\circ$, and $CY = 2 \cdot CX$, then find $AB$.

Lilliam0216 Jan 11, 2025

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+363

Help plz.

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $BY = 2$ and $AZ = 4$, then what is the area of rectangle $WXYZ$?

Lilliam0216 Jan 11, 2025

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