All Questions ⁺⁰237796 Questions

Dec 16, 2025

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Number Theory

For a positive integer n, let \tau(n) be the sum of the positive integer divisors of n. Find the number of values of n, where 1 \le n \le 25, such that \tau(n) = 1.

AUnVerifedTaxPayer Dec 16, 2025, 2:37:32 PM

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Geometry

I is the incenter of triangle ABC. Find DE.

AUnVerifedTaxPayer Dec 16, 2025, 2:30:48 PM

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Geometry

Find the ratio of the area of the red region to the area of the yellow region. Enter your answer as a fraction.

AUnVerifedTaxPayer Dec 16, 2025, 2:30:36 PM

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Geometry

Triangle ABC has circumcenter O. What is \angle AOC, in degrees?

AUnVerifedTaxPayer Dec 16, 2025, 2:30:24 PM

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The Perfect Square of Balanced Binary Matrices

Let S be the set of 2n \times 2n matrices whose entries are 0 or 1. A matrix M \in S is called good if in every row and every column, the sum of the entries is exactly n.
Prove that the number of good matrices is a perfect square.

kotonarski Dec 16, 2025

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The Riemann Hypothesis Challenge

💥 The Ultimate Mathematical Challenge
The problem is to prove the Riemann Hypothesis (RH), a conjecture about the non-trivial zeros of the analytic continuation of the Riemann Zeta Function, \zeta(s).
The Equation and The Function read more ..

kotonarski Dec 16, 2025

Dec 15, 2025

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+1821

Geometry

Let XYZ be a triangle, and let XP, XQ, XR be the altitude, angle bisector, and median from X, respectively. If angle YQZ = 90^\circ and angle ZQX = 22^\circ, then what is the measure of angle RZP in degrees?

blackpanther Dec 15, 2025

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+1821

Geometry

Find the side length of the equilateral triangle.
AB = 1, CP = 4, PQ = 5, DA = 3, EP = 2

blackpanther Dec 15, 2025

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+1821

Geometry

In the diagram, ABCD is a square with side length 2, and BEF is an equilateral triangle with side length 3. Find DF.

blackpanther Dec 15, 2025

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+1821

Geometry

In the diagram, ABCD and AEFG are squares with side length 1. Find the area of the green region.

blackpanther Dec 15, 2025

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+4

Algabra

Graph the inequality on the axes below.
y, is greater than, minus, start fraction, 5, divided by, 6, end fraction, x, minus, 5
y>−65x−5

Isukathw Dec 15, 2025

Dec 12, 2025

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+869

Geometry

Shown below is rectangle $EFGH$. Its diagonals meet at $Y$. Let $X$ be the foot if an altitude is dropped from $E$ to $\overline{FH}$. If $FY = 24$ and $HX = 28$ and $EF = 10$, find the perimeter of rectangle $EFGH$.

cooIcooIcooI17 Dec 12, 2025

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+869

Geometry

In the diagram, \overline{BE} bisects \angle ABC, and \overline{CE} bisects \angle ACD. Compute \angle BAC, in degrees.

cooIcooIcooI17 Dec 12, 2025

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+869

Geometry

In pentagon ABCDE, \overline{AC} bisects \angle BCE and \overline{AD} bisects \angle CDA. If \angle CBD = 37^\circ and \angle CED = \angle ABC + 33^\circ, then find \angle BED, in degrees.

cooIcooIcooI17 Dec 12, 2025

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+995

Geometry

ABCD is a square. Find AM.

gnistory Dec 12, 2025

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+995

Geometry

Trapezoid ABCD has bases AB and CD. Line segment EF, which is parallel to the bases, divides trapezoid ABCD into two trapezoids of equal perimeter. If AM = 10, and BN = 5, find the length EF.

gnistory Dec 12, 2025

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Geometry

Find angle x, in degrees.
the angles of a triangle are x, 80, and 88.
Note: We say that a line bisects an angle if it splits it into two equal parts.

gnistory Dec 12, 2025

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+995

Geometry

FInd the value of x
Triangle with angles 50, 75, x

gnistory Dec 12, 2025

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+995

Geometry

Select the two triangles that must be congruent.
ABC
DEF
GHI read more ..

gnistory Dec 12, 2025

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Geometry

In the diagram, AD bisects BAC.
By adding one more condition, we can prove that triangles ABD and ACD are congruent. Which one of the following could be that condition? Select all that apply.
(a) BC read more ..

gnistory Dec 12, 2025

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Geometry

What kind of quadrilateral has the property that both pairs of opposite sides are parallel? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length? Select all that apply.
What read more ..

illrelyt Dec 12, 2025

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Geometry

What kind of quadrilateral has the property that both pairs of opposite sides are parallel? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length? Select all that apply.
What read more ..

illrelyt Dec 12, 2025

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Geometry

What kind of quadrilateral has the property that both pairs of opposite sides are parallel? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length? Select all that apply.
What read more ..

illrelyt Dec 12, 2025

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Geometry

What kind of quadrilateral has the property that both pairs of opposite sides are parallel? Select all that apply.
What kind of quadrilateral has the property that all four sides are equal in length? Select all that apply.
What read more ..

illrelyt Dec 12, 2025

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+1572

Geometry

Triangles RST and XYZ are congruent. Point P lies on ST, and point W lies on XY. Select all the true statements.
(a) If RST is isosceles, then XYZ is isosceles.
(b) If ST = 6, then WY = 6
(c) If RP \perp ST, read more ..

kittykat Dec 12, 2025

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Geometry

A straight line \ell divides a triangle \Delta into two congruent triangles. Select all the statements that must be true.
(a) If Delta is isoceles, then it is equilateral
(b) If Delta is right, then it is equilateral
(c) read more ..

kittykat Dec 12, 2025

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Geometry

Find AE
BE = 30, PE = 18, CP = 10

kittykat Dec 12, 2025

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Geometry

In triangle ABC, AB = AC. Find angle BAC in degrees.
AD = 5
DE = 7
BE = 3 read more ..

kittykat Dec 12, 2025

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+359

Geometry

In rectangle ABCD, \frac{[AEP]}{[DFP]} = 5. Find the ratio of the area of the red region to the area of the yellow region. Enter your answer as a fraction.

jaekg Dec 12, 2025

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+359

Geometry

In the diagram, ABCD is a rectangle, and BEFG is a square. Find AD.

jaekg Dec 12, 2025

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+359

Geometry

Which of the following conditions ensures that triangles ABC and DEF are similar? Select all that apply.
(1) A = B, D = C, F = E, B = A, AB/AD = BC/BE
(2) A = D, AB/EF = BC/DE
(3) AB perp CD, DE perp AE, AB = DE read more ..

jaekg Dec 12, 2025

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+359

Geometry

Find the perimeter of triangle XYZ.
YZ = 10, YP = 6, XQ = 4, XP = 8, PQ = 7

jaekg Dec 12, 2025

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+499

Geometry

In the diagram, AB is parallel to CD. Select the two products of lengths that must be equal.
AO \cdot BO
BO \cdot CE
CO \cdot AB read more ..

bIueb3rry Dec 12, 2025

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Geometry

Find length BC
AB = 13, AP = 12, BAC = 2*BPC, AC \perp BD

bIueb3rry Dec 12, 2025

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+499

Geometry

If ST = 2, QS = 4, and PT = 5, find PQ.

bIueb3rry Dec 12, 2025

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+499

Geometry

In rectangle ABCD, corner A is folded over crease DE to point F on BC. Find BC.

bIueb3rry Dec 12, 2025

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Im stuck on this. can u help

There are 3 red balls and 2 blue balls. A ball is randomly selected one at a time without replacement until a red ball is selected.Find the probability that it takes 3 times to select a red ball.

ilrelyt Dec 12, 2025

Dec 11, 2025

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Geometry

Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at P. If [APD]=3 and [BAD]=8, then what is [PAB]?

CInsbstnkng Dec 11, 2025

Dec 10, 2025

Dec 8, 2025

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Geometry

ABCD is a parallelogram. Find DG.

CInsbstnkng Dec 8, 2025

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Geometry

In trapezoid PQRS, Base PQ is parallel to base RS. Let point X be the intersection of diagonals PR and QS. The area of triangle PQR is 4 and the area of triangle QRX is 4. Find the area of trapezoid PQRS

CInsbstnkng Dec 8, 2025

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Geometry

In trapezoid ABCD, \overline{AB} \parallel \overline{CD}. Find the area of the trapezoid.

CInsbstnkng Dec 8, 2025

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Geometry

Let WXYZ be a trapezoid with bases \overline{XY} and \overline{WZ}. In this trapezoid, \angle XWZ = 81, angle WXY = 62, and angle ZYW = 137. Find \angle YWZ, in degrees.

CInsbstnkng Dec 8, 2025

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