All Questions +0 237750 Questions

Let theta be an acute angle such that sin 2 theta = sin 3 theta + sin 4 theta. What is the measure of theta in degrees?

kittykat Mar 19, 2026

+1609

Geometry

Two tangent circles are shown below. One common external tangent is the x-axis. The equation of the other external common tangent has the form y = mx + b. What is m?

kittykat Mar 19, 2026

Mar 18, 2026

+1609

Geometry

The line y = mx bisects the angle between the two lines shown below. Find m.
The two lines are y = 2x and y = x/2.

kittykat Mar 18, 2026

+1609

Geometry

Line \ell is shown below. The line y = 2x + k has a distance of 3 from line y = 5x + k. Find all possible values of k.

kittykat Mar 18, 2026

Mar 17, 2026

+1609

Geometry

Triangle PQR is rotated clockwise about P to triangle PQ'R', as shown in the diagram. We know the length of the path taken by vertex Q is the same as the length of the path takesn by P. What is the length of the path taken by vertex R?

kittykat Mar 17, 2026

Mar 16, 2026

+854

Geometry

Hi i offten face difficulties in coverting number into words. is there any reliable solution to this. or any advice.
Thanks.

cooIcooIcooI17 Mar 16, 2026

Mar 10, 2026

How to convert numbers to words?

Two circles C_1 and C_2 are shown below. Find the radius of the circle that is externally tangent to both $C_1$ and $C_2,$ and tangent to the $x$-axis.

jamesright22 Mar 10, 2026

Mar 7, 2026

Mar 5, 2026

+1609

Geometry

Triangle ABC is rotated clockwise about A to triangle $AB'C',$ as shown in the diagram. We know the length of the path taken by vertex $B$ is $6.$ What is the length of the path taken by vertex $C?$

kittykat Mar 5, 2026

Mar 2, 2026

+1609

Geometry

kittykat Mar 2, 2026

Mar 1, 2026

Feb 28, 2026

+1741

Geometry

Find XY if UV = 12

In the figure, triangles ABC$ and ACD are similar. What is \angle B in degrees?

parmen Feb 28, 2026

Feb 27, 2026

+1741

Geometry

A spherical orange is cut into 8 congruent slices. If the volume of the orange was 8, then what is the volume of each slice?

parmen Feb 27, 2026

Feb 26, 2026

+1609

Geometry

In unit square ABCD, E and F are the midpoints of \overline{AD} and \overline{AB}, respectively. The square is then folded along the edges of triangle CEF, so that triangles AEF, CDE, BCF, cover triangle CEF. read more ..

kittykat Feb 26, 2026

Feb 24, 2026

+1609

Geometry

Triangular pyramid BCDG is cut from cube ABCDEFGH. The triangular pyramid is then placed on a surface with triangle BCD as the base. Given that the side length of the cube is $12,$ find the height of the pyramid.

kittykat Feb 24, 2026

+1609

Geometry

In the diagram, a semicircle is centered at $O,$ and $\overline{AB}$ is tangent to the semicircle at $B.$ Find $\angle BCD,$ in degrees.

kittykat Feb 24, 2026

Feb 23, 2026

Feb 21, 2026

Feb 20, 2026

+199

Geometry

Given regular heptagon ABCDEFG, a circle can be drawn that is tangent to DC at C and to EF at F. What is radius of the circle if the side length of the heptagon is 1?

HumanBemg Feb 20, 2026

+199

Geometry

Hi friends,
it's been a couple of years since I've last been here, nice to see you guys are still around. Today please, I just need clarification on a solution. I hope supplying pictures will be okay.
This is the drawing: read more ..

HumanBemg Feb 20, 2026

Triangle ratios

Compute \angle AGD, in degrees.

Urimagic Feb 6, 2026

Jan 28, 2026

+962

Math

Find the radius of the quarter-circle.

booboo44 Jan 28, 2026

-2

+962

Math

Prove that for all numbers N;

booboo44 Jan 28, 2026

+123

Proof

Evaluate the derivative:
Using this derivative, find the slope of the graph at the x-values of 1, 2, and 3.

nerdboy Jan 28, 2026

Jan 27, 2026

+123

Easy Derivatives

nerdboy Jan 27, 2026

+123

Beginner limit

Evaluate the limit:

nerdboy Jan 27, 2026

+123

Beginning Integral

Evaluate

Two quarter-circles are drawn inside a unit square. A smaller square is inscribed in the two quarter-circles. Find the area of the smaller square.

nerdboy Jan 27, 2026

Jan 26, 2026

+1609

Math

The circle below centered at $O$ has a radius of $5.$ Find $CD.$

kittykat Jan 26, 2026

+1609

Math

Semicircles are drawn on diameters \overline{AB} and \overline{CD}, as shown below. Find AB.

kittykat Jan 26, 2026

+1609

Math

In equiangular octagaon EFGHIJKL, we know that EF = GH = IJ = KL = 1 and FG = HI = JK = LE = sqrt(2). Find the area of the octagon.

kittykat Jan 26, 2026

Jan 23, 2026

+962

Math

In the diagram below, chords $\overline{AB}$ and $\overline{CD}$ are perpendicular, and meet at $X.$ Find the diameter of the circle.

booboo44 Jan 23, 2026

Jan 22, 2026

+962

Math

In triangle $XYZ,$ circles are drawn centered at $X$, $Y$, and $Z$, so that all pairs of circles are externally tangent. If $XY = 2,$ $XZ = 2,$ and $YZ = 2$, then find the sum of the areas of all three circles.

booboo44 Jan 22, 2026

+962

Math

All the sides of a triangle have integer length. The perimeter of the triangle is 10, and the triangle is scalene. How many such non-congruent triangles are there?

booboo44 Jan 22, 2026

Jan 21, 2026

Jan 17, 2026

+1940

Math

In triangle ABC, let D be a point on side BC. Select all the true statements.
If AD is an altitude of triangle ABC, then AC > AD.
If AD is a median of triangle ABC, then BD > CD.
If AD is an angle bisector read more ..

tomtom Jan 17, 2026

+1940

Math

Bekah has three brass house number digits: 2, 3, 4, 5, and 6. How many distinct numbers can she form using one or more of the digits, if her number must be divisible by 4?

tomtom Jan 17, 2026

Jan 16, 2026

+404

Math

Ms. Lee has 12 boxes of crayons. Next year, she plans to buy 250% more boxes. How many boxes will she have in all?
Responses
15 boxes
15 boxes read more ..

Stanry Jan 16, 2026

Ms. Lee has 12 boxes of crayons. Next year, she plans to buy 250% more boxes. How many boxes will she have in all? Responses 15 boxes 15 bo

To win a game with a fair coin, you must flip n+1 heads in a row, where $n$ is the total number of tails flipped so far. So if your first flip is heads, you win and the game is over; if your first flip is tails but your next two in a row are heads, you read more ..

emmaisthebest Jan 16, 2026

Jan 15, 2026

+1289

Math

A train engine and carriages have a total mass of 750 tons
Its brakes fail, and it crashes into the barrier in the terminus with a force of 1,687,500 N.
The barrier stops the train in 15 s.
Calculate the velocity of the train in km/h just read more ..

AnswerscorrectIy Jan 15, 2026

Jan 14, 2026

+123

Easy Physics Problem

The sum of the prime numbers from 1-10, 11-20, 21-30, 31-40, and 41-50 are multiplied together with 997. What is the remainder when this result is divided by 97?

nerdboy Jan 14, 2026

+123

Modulo

Distinct prime numbers p, q, and r satisfy the equation p(q + r) = 16. Which of the following prime numbers must either q or r be equal to?
2 3 5 7 11

nerdboy Jan 14, 2026

Nov 3, 2025

Oct 29, 2025

Oct 26, 2025

Oct 24, 2025

+104

Math

ElectricPavlov ●●

BlackoutMiIkshake Oct 24, 2025

+104

Math

The triangle with vertices at (1,0), (0,1), and (k,k) has area 1/2. Find k.

Mrs. Monstrous Millie wants to throw a party for a group of monsters and aliens. The monsters each have 5 heads with 7 ears on each head, and the aliens each have 5 heads with 3 ears on each head. As party favors, Mrs. Millie wants to give each guest a read more ..

BlackoutMiIkshake Oct 24, 2025

-1

+104

Math

Siva starts at vertex A of square ABCD with side length 10. He walks towards vertex C, along the diagonal AC. He then walks towards B, then towards D. What is the length of his path?

BlackoutMiIkshake Oct 24, 2025

Oct 23, 2025

Oct 22, 2025

+104

Math

Bosco ●

BlackoutMiIkshake Oct 22, 2025

+104

Math

William writes the integers from 2 through 15 from left to right on a piece of paper, then does the following:

* He begins by circling the leftmost uncircled integer, then circles all its powers. Afterwards, he repeats this process until every read more ..

Two chords with length r are drawn on a circle of radius r. What is the maximum possible distance between their endpoints?

BlackoutMiIkshake Oct 22, 2025

+104

Math

asinus ●

BlackoutMiIkshake Oct 22, 2025

Oct 21, 2025

+104

Math

In the diagram below, AB = AC = 1, and arc BC is centered at A with \angle BAC = 60^\circ. Point D is on \overline{AB}, and point E is on arc BC so that BD = DE, and arc BE (centered at D) is tangent to \overline{AC}. Point F is on \overline{DB}, read more ..

Let ABC be a triangle with \angle B = 90^{\circ}. Suppose that point D lies on segment BC such that angle BAD = \angle CAD, and suppose that point E lies on segment AC such that angle EDA = 60^{\circ}. Given that AD = AC and that CE = 17, find BD.
<read more ..

BlackoutMiIkshake Oct 21, 2025

-1

+104

Math

A number is chosen at random from among all 9-digit numbers that use each of the digits 1 through 9 exactly once. What is the probability that this number is a multiple of 2?

BlackoutMiIkshake Oct 21, 2025

Oct 20, 2025

+104

Math

Bosco ●●

BlackoutMiIkshake Oct 20, 2025

+104

Math

Three squares of a 5 \times 5 grid are colored. Two colorings are conisdered equivalent if one coloring can be rotated to form the other coloring, such as the two colorings below, and the grid can be reflected as well. We also want the three read more ..

Selma multiplies the number 9 the two-digit number \overline{AB}, and the three-digit number \overline{CDE}. She finds that the product of all three numbers is the five-digit number 41409. Compute the sum \overline{AB} + \overline{CDE}. read more ..

BlackoutMiIkshake Oct 20, 2025

+104

Math

Given a positive integer N, a multiplication decomposition of N is a sequence of positive integers (d_1, d_2, \dots, d_k) such that
* d_1 \neq 1,
* d_i divides d_{i + 1} for 1 \le i \le k - 1, and
* d_1 d_2 \dotsm d_k = N.
The last read more ..

BlackoutMiIkshake Oct 20, 2025

+104

Math

A traffic light runs repeatedly through the following cycle: green for 40 seconds, then yellow for 5 seconds, then red for 35 seconds, which repeats indefinitely. Oliver picks a random time and watches the light for 75 seconds. What is the probability read more ..

BlackoutMiIkshake Oct 20, 2025

+104

Math

Consider a cube with side length 1, together with 14 congruent spheres each of radius r, with 8 of the spheres centered at the 8 vertices of the cube and the remaining $6$ spheres centered at the centers of the $6$ faces of the cube. Suppose $r$ is chosen read more ..

BlackoutMiIkshake Oct 20, 2025

+104

Math

What is the units digit of 1^1 + 2^2 + 3^4 + 4^8?

BlackoutMiIkshake Oct 20, 2025

Oct 18, 2025

+104

Math

A square has two of its vertices at (12, 34) and (-98, 56),$ and another vertex at (a, b). What is the sum of all possible values of the area of the square?

BlackoutMiIkshake Oct 18, 2025

+104

Math

At Patty the panda's pizza parlor, the possible pizza toppings are pesto, pepperoni, peppers, and pineapple, and the possible desserts are pumpkin pie, powdered-sugar pretzels, and papaya popsicles. If Prajwal the porcupine, Petunia the peacock, and Pete read more ..

BlackoutMiIkshake Oct 18, 2025

Oct 17, 2025

+104

Math

In a rectangular prism, the surface area is 24 and the sum of the lengths of all twelve edges is 24. What is the volume of the prism?

BlackoutMiIkshake Oct 17, 2025

+104

Math

For how many prime numbers p less than 100 is the sum of p's digits less than or equal to 2?

BlackoutMiIkshake Oct 17, 2025

+104

Math

In the game Nerdle, a player tries to guess a true equation made up of $8$ symbols, each of which is either $+,$ $-,$ $*,$ $/,$ $=,$ or one of the digits from $0$ to $9.$ A square turns teal if the symbol is correct and in the correct location, magenta read more ..

BlackoutMiIkshake Oct 17, 2025

+104

Math

Define the importance of a point (x, y) on the coordinate plane to be x^2 + y^2. There exist some points with positive, integer $x$- and $y$-coordinates whose importances are 5. Find the area of the convex polygon determined by those points.

BlackoutMiIkshake Oct 17, 2025

+104

Math

A set of 16 positive integers has mean, median, and unique mode all equal to 5. What is the largest possible value of one of the numbers in the set?

BlackoutMiIkshake Oct 17, 2025

+104

Math

Haoyu gives Mingze and Yihan two different positive integers, and tells them that the product of their numbers is less than 1000. They are also aware that they have two different positive integers. They have the following conversation:
Mingze: read more ..

BlackoutMiIkshake Oct 17, 2025

+104

Math

Sunita and Mohammed play a game where they start with a pile of candy and take turns eating a prime number of pieces of candy from the pile. A player who leaves 0 or 1 candies in the pile after their move wins. If Sunita and Mohammed both play perfectly read more ..

BlackoutMiIkshake Oct 17, 2025

+104

Math

The shaded region below has area a+b\pi where a and b are positive integers. What is a+b? (You may assume the boundary of each region is made up of straight lines and circular arcs, and the squares of the grid have side length $1.$) read more ..

BlackoutMiIkshake Oct 17, 2025

+104

Math

Jason is driving from his home to his office, which is 20 miles away. He normally drives at a constant speed of 60 miles per hour for the whole trip. However today, 15 minutes into his drive, his car breaks down. He calls a taxi, and it arrives 20 minutes read more ..

BlackoutMiIkshake Oct 17, 2025

+104

Math

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

BlackoutMiIkshake Oct 17, 2025

Oct 16, 2025

+854

Math

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

cooIcooIcooI17 Oct 16, 2025

+854

Math

cooIcooIcooI17 Oct 16, 2025

Oct 15, 2025

+12

Math

Area of compound figure

BlackoutMilkshake Oct 15, 2025

+12

Math

area of compound figure

I need help. What's the answer?

BlackoutMilkshake Oct 15, 2025

+12

Math

We define a formula that calculates both and . What formula would you create (or use)?

BlackoutMilkshake Oct 15, 2025

Oct 14, 2025

Oct 11, 2025

Math

For a positive integer n, let
a_n = 1 + \sqrt{\frac{1}{n}} - \sqrt{\frac{1}{n + 1}
Compute the product a_1 a_2 a_3 \dotsm a_{99}.

CharlieMathematical Oct 11, 2025

Oct 7, 2025

+1808

Math

Find the number of ways of arranging the numbers 1,2 ,3, 4, 5, 6 in a row so that the product of any two adjacent numbers is at least 5.

blackpanther Oct 7, 2025

+1808

Math

A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up four times in a row. What is the probability that the coin will be tossed more than 10 times? Express your answer as a common fraction.

blackpanther Oct 7, 2025

+267

Math

In triangle ABC, cos A=sqrt(7/10) and cos B=sqrt(3/10) Find cos C

CInsbstnkng Oct 7, 2025

-1

+267

Math

Some context:
Currently, I am in 9th grade and taking Calculus BC.
I can understand competition math problems and what they are asking for but I don't really have a sense for solving them.
I should have started preparing earlier and read more ..

CInsbstnkng Oct 7, 2025

Oct 6, 2025

AMC 10 I want to make AIME - PLEASE HELP

I’ve been working on this series and I’m not sure if I’m approaching it the right way:
At first glance it looks like it might behave similar to the alternating harmonic series, but the sine term is throwing me off. I’m wondering whether this read more ..

OOOOOOOO Oct 6, 2025

Oct 1, 2025

Stuck on a Tricky Series Problem

Let M⊂R∞×∞\mathcal{M} \subset \mathbb{R}^{\infty \times \infty}M⊂R∞×∞ be the set of all improperly convergent matrices whose entries are defined by the double integral:
Mij=∫0∞∫0∞sin⁡(ix)cos⁡(jy)x2+y2+ij dx dyM_{ij} = \int_0^{\infty} \int_0^{\infty} read more ..

skylerclooney Oct 1, 2025

Sep 29, 2025

Sep 28, 2025

plz help im cooked

Alex chooses a number at random from the set {1, 2, 3, 4, 5}. Winnie also chooses a number at random from the same set. (They can choose the same number.) What is the probability that the product of their numbers is at least 4? read more ..

fof.urmum Sep 28, 2025

Aug 25, 2025

+1289

Math

Bosco ●●●

AnswerscorrectIy Aug 25, 2025

+1289

Math

Suppose $f(x)$ is a function defined for all real $x$, and suppose $f$ is invertible (that is, $f^{-1}(x)$ exists for all $x$ in the range of $f$). If the graphs of $y=f(x)$ and $y=f(x^3)$ are drawn, at how many points do they intersect?

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

AnswerscorrectIy Aug 25, 2025

Aug 24, 2025

Aug 23, 2025

+962

Math

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 $BX$?

booboo44 Aug 23, 2025

+962

Math

Bosco ●

booboo44 Aug 23, 2025

+1289

Math

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

In rectangle , points and lie on so that and is the midpoint of . Also, intersects at and at . The area of rectangle is 70. Find the area of triangle .
read more ..

AnswerscorrectIy Aug 23, 2025

+67

Geometry Please answer with steps

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

bqimath Aug 23, 2025

+1289

Math

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

AnswerscorrectIy Aug 23, 2025

Aug 22, 2025

-1

+1289

Math

AnswerscorrectIy Aug 22, 2025

+1289

Math

Regular hexagon ABCDEF is inscribed in rectangle PQRS. If [AFP] = 20 and [ABC] = 25, then find [ABCDEF].

AnswerscorrectIy Aug 22, 2025

Aug 21, 2025

+970

Math

Point P lies in regular hexagon ABCDEF such that [ABP ] = 3, [CDP] = 3, and [EFP] = 3. Compute [BCP].

gnistory Aug 21, 2025

+970

Math

Suppose the domain of f is (-1,3). Define the function g by
g(x) = f((x + 1)(x - 2)).
What is the domain of g?

gnistory Aug 21, 2025

Aug 20, 2025

+490

Math

There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$

MeIdHunter Aug 20, 2025

+490

Math

The juniors at East HS drink a total of cartons of milk per -day week. If the average senior drinks milk at the same rate as the average junior, what is the average number of total cartons of milk the seniors drink read more ..

MeIdHunter Aug 20, 2025

Aug 19, 2025

+123

Alcumus

Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at $P$. If $[PBC] = 15$ and $CD = 3 \cdot AD,$ what is $[ABCD]$?

nerdboy Aug 19, 2025

-1

+267

Help me help

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

CInsbstnkng Aug 19, 2025

-1

+267

Need help

Let p(x) be defined on such that
where y is the greatest prime factor of . Express the range of p in interval notation.
Thanks and also please show the steps too!

CInsbstnkng Aug 19, 2025

+67

Algebra

●●●●●●

bqimath Aug 19, 2025

+490

Math

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

Given 5 colors to choose from, how many ways can we color the four unit squares of a 2\times 2 board, given that two colorings are considered the same if one is a rotation or reflection of the other? (Note that we can use the same color for more than one read more ..

MeIdHunter Aug 19, 2025

+294

how to solve

An equilateral triangle, a regular heptagon, a square, a 20-gon, a regular pentagon, a regular hexagon, and a regular n-gon, all with the same side length also completely surround a point. Find n.

AUnVerifedTaxPayer Aug 19, 2025

Aug 18, 2025

-1

+267

help me help me

Let ABCDE be an equilateral pentagon. If the pentagon is concave, and $\angle A = \angle B = 90^{\circ},$ then what is the degree measure of $\angle E$?

CInsbstnkng Aug 18, 2025

-1

+267

help me

Find all ordered pairs x, y of real numbers such that x+y=10 and x^3+y^3=300.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

CInsbstnkng Aug 18, 2025

Aug 17, 2025

-1

+267

Help help

For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.

CInsbstnkng Aug 17, 2025

-1

+267

Help me help