All Questions +0 237741 Questions

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

BRAlNBOLT Dec 3, 2025

+224

Geometry

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

BRAlNBOLT Dec 3, 2025

+295

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?

CInsbstnkng Dec 3, 2025

Dec 2, 2025

+295

Geometry

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

CInsbstnkng Dec 2, 2025

+295

Geometry

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

CInsbstnkng Dec 2, 2025

+295

Geometry

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

CInsbstnkng Dec 2, 2025

+295

Geometry

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

CInsbstnkng Dec 2, 2025

+295

Geometry

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

CInsbstnkng Dec 2, 2025

+295

Geometry

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

CInsbstnkng Dec 2, 2025

Dec 1, 2025

+1301

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 ..

AnswerscorrectIy Dec 1, 2025

+1301

Geometry

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

AnswerscorrectIy Dec 1, 2025

+1301

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 ..

AnswerscorrectIy Dec 1, 2025

+1301

Geometry

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

AnswerscorrectIy Dec 1, 2025

Nov 27, 2025

+963

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.

booboo44 Nov 27, 2025

+963

Geometry

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

booboo44 Nov 27, 2025

+963

Geometry

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

booboo44 Nov 27, 2025

Nov 26, 2025

+963

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 ..

booboo44 Nov 26, 2025

+963

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 ..

booboo44 Nov 26, 2025

+1761

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 ..

parmen Nov 26, 2025

+1761

Geometry

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

parmen Nov 26, 2025

+1761

Geometry

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

parmen Nov 26, 2025

+1761

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.

parmen Nov 26, 2025

+1761

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.

parmen Nov 26, 2025

+1761

Geometry

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

parmen Nov 26, 2025

+1761

Geometry

web2.0calc features related questions:
1. What is the membership of a user and how do you pay it? (I don't want to pay, but just curious)
2. How is the score of a user calculated?
3. Is the "Top Users" column sorted by read more ..

parmen Nov 26, 2025

Nov 25, 2025

Nov 24, 2025

Nov 19, 2025

Nov 18, 2025

Nov 17, 2025

Nov 14, 2025

Nov 13, 2025

Nov 11, 2025

I'm new to web2.0calc.com (please answer)

Explore the relationship between speed and the other factors and plot a line for each. Only use linear, exponential and quadratics. Use the below assumptions Assumptions: Car, Car conditions, driver, driver conditions, road, road conditions, weather read more ..

ilovewolfoo Nov 11, 2025

Nov 10, 2025

Nov 7, 2025

PSMT Lines

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

MagicMan Nov 7, 2025

Nov 6, 2025

Nov 3, 2025

Oct 29, 2025

Oct 26, 2025

Oct 24, 2025

+109

Math

ElectricPavlov ●●

BlackoutMiIkshake Oct 24, 2025

+109

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

+109

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

+109

Math

Bosco ●

BlackoutMiIkshake Oct 22, 2025

+109

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

+109

Math

asinus ●●

BlackoutMiIkshake Oct 22, 2025

Oct 21, 2025

+109

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 ..

asinus ●

BlackoutMiIkshake Oct 21, 2025

-1

+109

Math

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 ..

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

+109

Math

Bosco ●●

BlackoutMiIkshake Oct 20, 2025

+109

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

+109

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

+109

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

+109

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

+109

Math

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

BlackoutMiIkshake Oct 20, 2025

Oct 18, 2025

+109

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

+109

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

+109

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

+109

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

+109

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

+109

Math

BlackoutMiIkshake Oct 17, 2025

+109

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.

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

+109

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

+109

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

+109

Math

BlackoutMiIkshake Oct 17, 2025

+109

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 ..

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

+109

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

+850

Math

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

cooIcooIcooI17 Oct 16, 2025

+850

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

+295

Math

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

CInsbstnkng Oct 7, 2025

-1

+295

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

+1301

Math

Bosco ●●●

AnswerscorrectIy Aug 25, 2025

+1301

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

+963

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

+963

Math

Bosco ●

booboo44 Aug 23, 2025

+1301

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

+68

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

+1301

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

+1301

Math

AnswerscorrectIy Aug 22, 2025

+1301

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

gnistory Aug 21, 2025

Aug 20, 2025

+490

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?

MeIdHunter 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

Aug 19, 2025

+85

Alcumus

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 ..

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

+295

Help me help

CInsbstnkng Aug 19, 2025

-1

+295

Need 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

+68

Algebra

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!

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 ..

bqimath Aug 19, 2025

+490

Math

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

+295

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

+295

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

+295

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

+295

Help me help

CInsbstnkng Aug 17, 2025

Aug 16, 2025

+850

CPhill answer me

Let $m$ and $n$ be positive integers. If $m$ has exactly $7$ positive divisors, $n$ has exactly $15$ positive divisors, and $mn$ has exactly $14$ positive divisors, then how many divisors does $m^2 n^2$ have?

Let $a$, $b$, $c$, and $n$ be positive integers. If $a + b + c = 19 \cdot 97$ and
a + 3n = b - 2n = \frac{c}{5n},
compute the value of $a$.

cooIcooIcooI17 Aug 16, 2025

+190

Help me CPhill Now

Let $A$, $B$, and $C$ be constants so that
\frac{1}{x^3-2x^2-5x+9}=\frac{A}{x+5}+\frac{B}{x-3} + \frac{C}{(x - 3)^2}
holds for all real numbers $x$ other than $-5$ and $3.$ What is $A$?

HumanBemg Aug 16, 2025

+483

Help me

For integers $a$ and $T$, $T \neq 0,$ a parabola whose general equation is $y = ax^2 + bx + c$ passes through the points $A = (0,0),$, $B = (2T,0)$, $C = (2T + 1,28).$ and $N$ Let be the sum read more ..

bIueb3rry Aug 16, 2025

+23

NEED HELP CPhill ASAP

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.

Dragononweb2.0calc Aug 16, 2025

Aug 15, 2025

+417

Geometry

I have to paint one side of a wall. The wall is $15$ meters tall and $60$ meters long. Each gallon of paint covers $400$ square feet. If a foot is approximately $0.3048$ meters, then what is the smallest whole number of gallons I can buy and read more ..

nathanl6656 Aug 15, 2025

+970

Math

Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$

gnistory Aug 15, 2025

+963

I need answer

In the diagram below, is a square. Find x[asy]
unitsize(1.5 cm);
pair A, B, C, D, P;
A = (0,3);
B = (0,0);<#> C = (3,0);<#> D = (3,3);<#> P = (0.8,1.8);<#> draw(A--B--C--D--cycle);<#> draw(A--P);<#> draw(B--P);<#> read more ..

booboo44 Aug 15, 2025

Aug 14, 2025

help me plz

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 EX = 24 and $GY = 30$, find the perimeter of rectangle $EFGH$.

askdjlkadjwl123 Aug 14, 2025

Aug 13, 2025

-1

+295

help me now

CInsbstnkng Aug 13, 2025

Aug 11, 2025

-1

+295

Help help help

Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

CInsbstnkng Aug 11, 2025

-1

+295

Help me

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

CInsbstnkng Aug 11, 2025

-1

+295

Help me!

Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

CInsbstnkng Aug 11, 2025

-1

+295

Help

Find one ordered pair $(x,y)$ of real numbers such that $x + y = 10$ and $x^3 + y^3 = 162 + x^2 + y^2.$

CInsbstnkng Aug 11, 2025

Aug 10, 2025

-1

+295

help help

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

CInsbstnkng Aug 10, 2025

Aug 9, 2025

-1

+295

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 ..

CInsbstnkng Aug 9, 2025

Aug 8, 2025

-1

+295

help me now

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

CInsbstnkng Aug 8, 2025

-1

+295

help!!!

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$ read more ..

CInsbstnkng Aug 8, 2025

-1

+295

help me plz

Lines $XQ$ and $XR$ are tangent to a circle, as shown below. If $\angle XTU = 47^\circ$ and $\angle QAU = 65^\circ,$ then find $\angle QXR,$ in degrees.

CInsbstnkng Aug 8, 2025

Aug 7, 2025

-1

+295

help me!

For an integer $n,$ let $f(n)$ be the remainder when $n^8 + n^{16}$ is divided by $5.$ Compute $f(0) + f(1) + f(2) + f(3) + f(4).$

CInsbstnkng Aug 7, 2025

-1

+295

help help help

For a certain positive integer $n$, the number $n^{6873}$ leaves a remainder of $3$ when divided by $23.$ What remainder does $n$ leave when divided by $23$?

CInsbstnkng Aug 7, 2025

Aug 5, 2025

-1

+295

I need help

Let a and b be positive real numbers such that a + b = 1. Find the set of all possible values of a/b.

CInsbstnkng Aug 5, 2025

-1

+295

Help me

The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XZ = 5$ and $YZ = 2,$ find $WX.$

CInsbstnkng Aug 5, 2025

Aug 3, 2025

-1

+295

Help help

CInsbstnkng Aug 3, 2025

-1

+295

Need help

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $AB = 2$, then find $AC.$

CInsbstnkng Aug 3, 2025

-1

+295

Help me help

Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

CInsbstnkng Aug 3, 2025

Aug 2, 2025

+68

Algebra

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

bqimath Aug 2, 2025

-1

+295

Plz help

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

CInsbstnkng Aug 2, 2025

-1

+295

Help

There is a group of five children, where two of the children are twins. In how many ways can I distribute $12$ identical pieces of candy to the children, if the twins must get an equal amount of candy?

CInsbstnkng Aug 2, 2025

-1

+295

Need help (it's really me!!!)

How many solutions are there to the equation
u + v + w + x + y + z = 6
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $8$ and $y$ is even?

CInsbstnkng Aug 2, 2025

-1

+295

Help!!! (really me)

In the complex plane, z, z2, z3, form, in some order, three of the vertices of a non-degenerate square. Enter all possible areas of the square, separated by commas.

CInsbstnkng Aug 2, 2025

+73

HELP!!! (From the real Clnsbstnkng)

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 ..

Clnsbstnkng Aug 2, 2025

Aug 1, 2025

-1

+295

HELP!!!

CInsbstnkng Aug 1, 2025

-1

+295

help

Find constants A and B such that
(2x + 11)/(x^2 - 6x + 5) = A/(x - 3) + B/(x + 4)
for all x such that x neq 7 and x neq 8

CInsbstnkng Aug 1, 2025

-1

+295

Help me

If z is a complex number such that z + 1/z = 3, what is the value of z^2 + 1/z^2?

Let z1 and z2 be two complex numbers such that |z1| = 5 and (z1/z2)+(z2/z1)=0.
Find z1+z2.

CInsbstnkng Aug 1, 2025

-1

+295

HELP HELP

George is planning a dinner party for three other couples, his wife, and himself. He plans to seat the four couples around a circular table for , and wants each husband to be seated opposite his wife. How many seating arrangements can he make, read more ..

CInsbstnkng Aug 1, 2025

+68

Counting & Probability

An ellipse has its foci at (-1, -1) and (-1, -3).
Given that it passes through the point (0, 2), its equation can be written in the form ((x-h)2/a2)/((y-k)2/b2)=1 where a, b, h, k are constants, and a and b are positive. Find a+k.

bqimath Aug 1, 2025

Jul 31, 2025

-1

+295

HELP ME

CInsbstnkng Jul 31, 2025

-1

+295

HELP

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 $WXYZ$?

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 $AB$.

CInsbstnkng Jul 31, 2025

-1

+295

help help

CInsbstnkng Jul 31, 2025

-1

+295

help me!

A sphere of radius 4 inches is inscribed in a cone with a base of radius 4 inches. In inches, what is the height of the cone? Express your answer as a decimal to the nearest tenth

CInsbstnkng Jul 31, 2025

-1

+295

HELP!!!

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

CInsbstnkng Jul 31, 2025

-1

+295

Help!

The ellipse shown below is defined by the equation PF1+PF2=d.
Find d.

CInsbstnkng Jul 31, 2025

Jul 30, 2025

+73

HELP!!!

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

Clnsbstnkng Jul 30, 2025

-1

+295

help help

CInsbstnkng Jul 30, 2025

-1

+295

help me

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

CInsbstnkng Jul 30, 2025

Jul 29, 2025

-1

+295

plz help

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

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

CInsbstnkng Jul 29, 2025

-1

+295

Help help!

Point X is on side \overline{AC} of triangle $ABC$ such that $\angle AXB =\angle ABX + 20^\circ$, and $\angle ABC - \angle BAC = 36^\circ$. Find $\angle XBC$ in degrees.

CInsbstnkng Jul 29, 2025

-1

+295

Help me

Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_8,$ $a_9,$ $a_{10}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 + a_7 + a_9 = 5$ and $a_2 + a_4 + a_6 + a_8 + a_{10} = -2$, then find $a_1$.

CInsbstnkng Jul 29, 2025

-1

+295

Help!! real

A sphere of radius inches is inscribed in a cone with a base of radius inches. In inches, what is the height of the cone? Express your answer as a decimal to the nearest tenth. read more ..

CInsbstnkng Jul 29, 2025

+68

Geometry from alcumus

●●●●●●●

bqimath Jul 29, 2025

-1

+295

Help me plz

Triangle DEF is the medial triangle of triangle ABC, and triangle $XYZ$ is the medial triangle of triangle $DEF.$ If the area of triangle $XYZ$ is $8$, what is the area of triangle $ABC?$

In triangle ABC, \angle A = 90^\circ. Altitude $\overline{AP},$ angle bisector $\overline{AQ},$ and median $\overline{AR}$ are drawn. If $PQ = 3$ and $QC = 4,$ find $AR.$

CInsbstnkng Jul 29, 2025

-1

+295

Need help now

An ellipse has its foci at (-1, -1) and (-1, -3).
Given that it passes through the point (4, -2), its equation can be written in the form ((x-h)2/a2)/((y-k)2/b2)=1 where a, b, h, k are constants, and a and b are positive. Find a+k.

CInsbstnkng Jul 29, 2025

+73

HELP!!! (From the real Clnsbstnkng)

●●●●●●●

Clnsbstnkng Jul 29, 2025

Jul 28, 2025

-1

+295

Help!

Find the coefficient of u^2*v^9 in (2u - 3*v^3)*5*(3u^3 - 2v^5)^3.

CInsbstnkng Jul 28, 2025

-1

+295

Help help

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

CInsbstnkng Jul 28, 2025

-1

+295

Help

Four cubes of volumes $1 \text{ cm}^3$, $2 \text{ cm}^3$, $3 \text{ cm}^3$, and $4 \text{ cm}^3$ are glued together at their faces. What is the number of square centimeters in the smallest possible surface area of the resulting solid figure?

CInsbstnkng Jul 28, 2025

-1

+295

Help!!

Triangle ABC is congruent to triangle DEF, but triangle ABC is not congruent to triangle XYZ. Which of the following relationships cannot hold?
ABC and DEF have the same area
ABC and DEF have the same perimeter
ABC read more ..

CInsbstnkng Jul 28, 2025

-1

+295

Help with geo

In pentagon ABCDE, \overline{AC} bisects \angle BCE and $\overline{AD}$ bisects $\angle BDE.$ If $\angle CBD = 30^\circ$ and $\angle CED = 60^\circ,$ then find $\angle CAD,$ in degrees.

CInsbstnkng Jul 28, 2025

-1

+295

Need help

Compute the smallest positive integer n such that n+i, (n+i)*2, and (n+i)*3 are the vertices of a triangle in the complex plane whose area is greater than 2015.

CInsbstnkng Jul 28, 2025

-1

+295

Plz help!!!

In the complex plane, z, z2, z3, form, in some order, three of the vertices of a non-degenerate square. Enter all possible areas of the square, separated by commas.

CInsbstnkng Jul 28, 2025

+73

HELP!!! (From the OG Clnsbstnkng)

In the complex plane, z, z2, z3, form, in some order, three of the vertices of a non-degenerate square. Enter all possible areas of the square, separated by commas.

Clnsbstnkng Jul 28, 2025

+73

HELP!!!

Circle O has radius 5. Segment $\overline{AS}$ has length $5$ and is tangent to circle $O$ at $A$. If $P$ is the projection of A onto OS, find length PS.

Clnsbstnkng Jul 28, 2025

Jul 27, 2025

-1

+295

Plz help

Two points, A and B, are on the pavement 6 inches apart. Cassidy the caterpillar traces out a path walking along all the points that are equidistant to as from . Cassidy has red paint on her feet, so she literally traces out the whole path! read more ..

CInsbstnkng Jul 27, 2025

-1

+295

Help me

Let f(x) be a polynomial. Find the remainder when f(x) is divided by x(x - 1)(x - 2), if f(0) = 0, f(1) = 1, and f(2) = 4.

CInsbstnkng Jul 27, 2025

-1

+295

Plz help

In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

CInsbstnkng Jul 27, 2025

-1

+295

Help help help

Recall that a partition of a positive integer n means a way of writing n as the sum of some positive integers, where the order of the parts does not matter. For example, there are five partitions of 4:
4
3 + 1
2 + 2 read more ..

CInsbstnkng Jul 27, 2025

-1

+295

Help me

Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of triangle ABC?
A is at (0,0), B is at (1,0), and C is at (1,1).

CInsbstnkng Jul 27, 2025

-1

+295

Need help

In the complex plane, z, z2, z3, form, in some order, three of the vertices of a non-degenerate square. Enter all possible areas of the square, separated by commas.

CInsbstnkng Jul 27, 2025

Jul 26, 2025

+73

HELP!!!

In the diagram below, \overline{AD} and \overline{BE} are angle bisectors of \angle BAC and \angle ABC, respectively, and they intersect at T. We know that BD=12, AE=8, and BF=3+AE. Find AB.

Clnsbstnkng Jul 26, 2025

-1

+295

Help CPHILL!!!

Compute the smallest positive integer n such that n+i, (n+i)2, and (n+i)3 are the vertices of a triangle in the complex plane whose area is greater than 2015.

CInsbstnkng Jul 26, 2025

Jul 25, 2025

+73

HELP!!!

In the diagram, \overline{AD} is an altitude, \overline{BE} is a median, and \overline{AD}, \overline{BE}, and \overline{CF} are concurrent. If AE = 11, BE = 9, and AD = 6\sqrt{2}, what is AF?

Clnsbstnkng Jul 25, 2025

-1

+295

Help!

How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, and the sum of the digits is 6?

CInsbstnkng Jul 25, 2025

-1

+295

Help

How many positive integers are there whose digits strictly decrease from left to right, and the sum of the digits is 6?

CInsbstnkng Jul 25, 2025

+295

Help

Karlanna places 600 marbles into m total boxes such that each box contains an equal number of marbles. There is more than one box, and each box contains more than one marble. For how many values of m can this be done?

CInsbstnkng Jul 25, 2025

+68

Number Theory

Right triangles ABC, ADE, EFG, and GHC are all similar. Also, $[ADE] = 1,$ $[EFG] = 1,$ and $[GHC] = 1.$ Find the area of the red region.

bqimath Jul 25, 2025

-1

+295

Help help

CInsbstnkng Jul 25, 2025

Jul 24, 2025

-1

+295

Help me

Let f(x) be a polynomial such that f(0) = 4, f(1) = 8, and f(2) = -6. Find the remainder when f(x) is divided by x.

CInsbstnkng Jul 24, 2025

-1

+295

Help!

The polynomial
g(x) = x^3 - x^2 - (m^2 + m + 18) x + 2m^2 - 14m - 6
is divisible by x - 5 and all of its zeroes are integers. Find all possible values of m.

CInsbstnkng Jul 24, 2025

+73

HELP!!!

Let z be a complex number such that |z|=1.
Find the maximum value of |1+z|+|1-z+z2|.

Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, no two Cs are next to each other, and no two Ds are next to each other.

Clnsbstnkng Jul 24, 2025

-1

+295

Help help

CInsbstnkng Jul 24, 2025

-1

+295

Help me plz

A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3) is a permutation of (1,2,3,4,5).
Find the number of permutations (x_1, x_2, \dots, x_8) read more ..

Find the number of sequences (a_1, a_2, a_3, \dots, a_8) such that:
* a_i \in \{1, 2, 3, 4, 5, 6, 7, 8\} for all 1 \le i \le 8.
* Every number1, 2, 3, 4, 5, 6, 7, 8 appears at least once in the sequence.

CInsbstnkng Jul 24, 2025

-1

+295

Help help

A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit.
You are dealt a hand of read more ..

CInsbstnkng Jul 24, 2025

-1

+295

Plz help

CInsbstnkng Jul 24, 2025

-1

+295

Help

If an ant crawls from one corner to the other corner of a 3 \times 5 rectangle, then it will cross through seven squares.
If the ant crawls from one corner to the other corner of a 4 \times 4 rectangle, then how many squares will it read more ..

CInsbstnkng Jul 24, 2025

-1

+295

Help

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 1, and the line is y = x.

CInsbstnkng Jul 24, 2025

-1

+295

Help plz

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $11,$ and the slope of line segment $\overline{OQ}$ is $13.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

CInsbstnkng Jul 24, 2025

-1

+295

Help help

CInsbstnkng Jul 24, 2025

-1

+295

Help meee

How many 7-digit sequences have a digit that appears at least 6 times?
(For example, 3339333 and 0200000 are two such sequences. A sequence is allowed to begin with 0.)

CInsbstnkng Jul 24, 2025

-1

+295

Need help

Triangle ABC has side lengths AB = 8, BC = 10, and AC = 12. Find \dfrac{\cos A}{\cos B}.

Find the number of paths from A to B in the grid below, so that
* Each step is down or to the right.
* The path cannot pass through any point more than once.

An example path is shown.
The grid is 3 by 3, with read more ..

CInsbstnkng Jul 24, 2025

-1

+295

Help me

Let z be a complex number such that |z|=1.
Find the maximum value of |1+z|+|1-z+z2|.

CInsbstnkng Jul 24, 2025

Jul 23, 2025

+73

HELP!!!

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{12}.

Clnsbstnkng Jul 23, 2025

Jul 22, 2025

+850

Help math

The roots of Ax^2+Bx+1 are the same as the roots of x^2- 3x + 5 + x^2 - 2x + 1. What is A+B?

cooIcooIcooI17 Jul 22, 2025

+1761

Help algebra

Let $G$ be the center of equilateral triangle $XYZ.$ A dilation centered at $G$ with scale factor $-1$ is applied to triangle $XYZ,$ to obtain triangle $X'Y'Z'.$ Let $A$ be the area of the region that is contained in both triangles $XYZ$ and $X'Y'Z'.$ Find read more ..

parmen Jul 22, 2025

+1004

help me

Hi6942O Jul 22, 2025

+1524

Need help

Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{3}, \\
N &\equiv 2 \pmod{7}, \\
N &\equiv 2 \pmod{10}.

Find the number of ways of filling in the squares of a 3 \times 3 grid so that:
* Each square contains a 0 or a 1.
* The sum of the numbers in each row and each column is at most 1.
An example is shown below.

learnmgcat Jul 22, 2025

+190

help math

HumanBemg Jul 22, 2025

+73

HELP!!!

If z is a complex number such that z+z-1=√3,
what is the value of z2010+z-2010?

Let \omega be a nonreal root of x^3 = 1. Compute
(1 - \omega + \omega^2)^6 + (1 + \omega - \omega^2)^6.

Clnsbstnkng Jul 22, 2025

Jul 21, 2025

+190

help me

A permutation of the numbers (1,2,3,\dots,n) is a rearrangement of the numbers in which each number appears exactly once. For example, (2,5,1,4,3)$ is a permutation of (1,2,3,4,5).
Let \pi = (x_1,x_2,x_3,\dots,x_n) be a permutation read more ..

HumanBemg Jul 21, 2025

+1301

Math

AnswerscorrectIy Jul 21, 2025

+1301

Math

Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

Let z1 and z2 be two complex numbers such that |z1| = 5 and (z1/z2)+(z2/z1)=1.
Find |z1-z2|2.
Note: The answer is not 75.

AnswerscorrectIy Jul 21, 2025

+73

HELP!!!

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?

Clnsbstnkng Jul 21, 2025

Jul 20, 2025

+483

Math

Let x, y, and z be real numbers. If x^2 + y^2 + z^2 = 1, then find the maximum value of
3x + 4y + 5z + x^3 + \frac{4x^2 y}{z} + \frac{z^5}{xy^2}

bIueb3rry Jul 20, 2025

Jul 12, 2025

+483

Algebra

Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1 + 2x_2 + \dots + 100x_{100} = 1,
then find the minimum value of x_1/1 + x_2/2 + \dots + x_{100}/100.

bIueb3rry Jul 12, 2025

Jul 11, 2025

+483

Algebra

In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$. If $AX = 15$, $BY = 20$, $\angle ACB= 60^\circ$, and $CY = 3 \cdot CX$, then find $AB$.

bIueb3rry Jul 11, 2025

Jul 8, 2025

Jul 7, 2025

+1301

Math

In my derivation for the tangential normal expression for an acceleration vector, I got that acceleration equals:
However, I also learned it can be expressed as:
How are these two expressions read more ..

AnswerscorrectIy Jul 7, 2025

Jul 6, 2025

+12

help with simple multi-variable calc/physics concept

In the diagram below, ABCD is a square, DE = EF = FG = 2, GH = 1, HB = 5, and \angle DEF = \angle EFG = \angle FGH = \angle GHB = 60^\circ. Find the area of the shaded region.

albertthesav Jul 6, 2025

Jul 3, 2025

+1301

Math

In triangle ABO, M is the midpoint of \overline{AB}. Points C, D, and N lie on line segments $\overline{AO},$ $\overline{BO},$ and $\overline{MO}$ extended, respectively, so that $DO = BO,$ $NO = MO,$ and $CO = AO.$ If $K$ is the area of triangle read more ..

AnswerscorrectIy Jul 3, 2025

+1301

Math

Franklin the Fly lives at one corner of a cube of side length 1. He doesn't like to wander too far from home; in fact, Franklin is only willing to travel to a point on the cube if he can reach it by crawling a distance of at most \sqrt{5} along the read more ..

AnswerscorrectIy Jul 3, 2025

+1301

Math

Five positive integers are written around a circle so that no two or three adjacent number have a sum
divisible by 3. In this collection the number of numbers divisible by 3 is .
(A) 0 (B) 1 (C) 2 (D) 3

AnswerscorrectIy Jul 3, 2025

+10

Pls help with this question

The equation
holds for exactly two real values of and their sum is . Find

Brilliance Jul 3, 2025

Jul 2, 2025

+215

Hard Math Question!

Find all values of the real number $a$ so that the four complex roots of \[z^4 - 6z^3 + 11az^2 - 3(2a^2 + 3a - 3) z + 1 = 0\]
form the vertices of a parallelogram in the complex plane. Enter all the values, separated by commas.
I read more ..

xud33 Jul 2, 2025

Jun 24, 2025

In how many ways can I choose 2 cooks on a backpacking trip with 8 people if any of the 8 people may be cooks?

mercurym999 ●

ansonh138 Jun 24, 2025

Jun 21, 2025

+24

complex number roots

What is the distance between the points (\cos 37^{\circ}, \sin 37^{\circ}) and (\cos 127^{\circ}, \sin 127^{\circ})?

mercurym999 Jun 21, 2025

Jun 20, 2025

+963

Geometry

Find an acute angle A such that \sin 4A = \sin A + \sin 2A. Express your answer in degrees.

booboo44 Jun 20, 2025

+963

Geometry

In the complex plane, let $S$ be the set of complex numbers $z$ such that \[\left| z + \frac{1}{z} \right| \le 2.\]
Find the area of $S.$
Thanks

booboo44 Jun 20, 2025

Jun 19, 2025

+24

complex number geometry help

Find the number of arithmetic sequences such that:
* The arithmetic sequence contains three terms
* All the terms are integers in \{0, 1, 2, \dots, 10\}
* The sum of the terms is 9.

mercurym999 Jun 19, 2025

+1301

Counting

Bosco ●●●

AnswerscorrectIy Jun 19, 2025

+15

Geometery

A cube has side length . Its vertices are alternately colored black and purple, as shown below. What is the volume of the tetrahedron whose corners are the purple vertices of the cube? (A tetrahedron is a pyramid with a triangular base.) read more ..

Let x_1, x_2, \dots, x_{100} be real numbers. If
x_1 + 2x_2 + \dots + 100x_{100} = 1,
then find the minimum value of x_1/1 + x_2/2 + \dots + x_{100}/100.

Ibrahim097YT Jun 19, 2025

Jun 17, 2025

Jun 12, 2025

+120

Algebra

Given the function y = f(x) = x2.
a) From the graph of the function y = f(x) (Figure 4), indicate the increasing and decreasing intervals of the given function.
b) Calculate the derivative of f'(x) and examine the sign of f'(x).
c) read more ..

coIinqiu Jun 12, 2025

Given the function y = f(x) = x2.

What is the area, in square units, of a regular hexagon inscribed in a circle whose area is square units? Express your answer in simplest radical form.

molisa Jun 12, 2025

Help plz enter explaination

Arrange the following numbers in increasing order (smallest first, biggest last):
1.
2.
3. read more ..

ilrelyt Jun 12, 2025

Jun 11, 2025

+20

Algebra

Consider the set
S = {1, 2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 15, 16, 17, 18, 23, 24, ..., 12345678},
which consists of all positive integers whose digits strictly increase from left to right, and the digits are from 1 to 8. This set is read more ..

Chiccen Jun 11, 2025

+1301

Counting

Find the number of ways filling in a 4 \times 4 grid, such that
* Each cell contains a 0 or a 1.
* The sum of the numbers in each row and each column is at least 2.

An example is shown below.
0110 read more ..

AnswerscorrectIy Jun 11, 2025

+1301

Counting

AnswerscorrectIy Jun 11, 2025

Jun 10, 2025

How many 6-digit sequences have a digit that appears at least 5 times?

In pentagon ABCDE, \overline{AC} bisects \angle BCE and $\overline{AD}$ bisects $\angle BDE.$ If $\angle CBD = 30^\circ$ and $\angle CED = 60^\circ,$ then find $\angle CAD,$ in degrees.

Beecomen1983 Jun 10, 2025

Jun 9, 2025

Jun 8, 2025

Jun 6, 2025

Jun 5, 2025

Jun 2, 2025

May 29, 2025

+850

Geometry

Not sure if anyone remembers me anymore; I randomly remembered about this app and the good times I had on it asking for help and helping others with their math, so just wanted to say hi :D hope everyone is doing well! and if you are reaeding this, have read more ..

cooIcooIcooI17 May 29, 2025

May 28, 2025

+707

Hello Guys!

Circle O has radius 5. Segment $\overline{AS}$ has length $5$ and is tangent to circle $O$ at $A$. If $P$ is the projection of A onto OS, find length PS.

Nirvana May 28, 2025

+190

Geometry

Two runners start at vertices A and B simultaneously and run clockwise around the perimeter of square ABCD at the same speed. A drone flies so that it is always at the midpoint of the two runners. What is the minimum distance between the two runners? read more ..

HumanBemg May 28, 2025

May 27, 2025

+483

Geometry

Let x and y be real numbers such that x^2 + y^2 = 2x + 4y. Find the largest possible value of x + y.

bIueb3rry May 27, 2025

+343

Geometry

CPhill ●●

jaekg May 27, 2025

+810

Geometry

Two black lines pass through the origin, as shown below. If their slopes are 2 and 8, then find the slope of the red line that bisects the acute angle between these lines.

CPhill ●●

crimefightingvigiI May 27, 2025

+1301

Geometry

What is the sine of an acute angle whose cosine is \frac{5}{7}?

NotThatSmart ●●

AnswerscorrectIy May 27, 2025

May 26, 2025

In the diagram below, we have angle ABC= angle CAB= angle DEB= angle BD. Find CA.

If x and y are integers such that 12^2 \cdot 18^3 = xy, find x+y.

greenflag May 26, 2025

May 25, 2025

-1

+1301

Algebra

In the figure, point is the center of the circle, the measure of angle RTB is 28 degrees, and the measure of angle ROB is three times the measure of angle SOT. What is the measure of minor arc RS , in degrees?
I read more ..

AnswerscorrectIy May 25, 2025

May 24, 2025

+23

In the figure, point is the center of the circle, the measure of angle RTB is 28 degrees, and the measure of angle ROB is three times the

CPhill ●

Dragononweb2.0calc May 24, 2025

May 23, 2025

-1

Probability

You have a standard deck of 52 cards.
(a) What is the probability that when you draw 5 cards at random, you draw a straight (any 5 cards in order)? Order doesn't matter (e.g. A-2-3-4-5 is the same as 3-5-A-4-2.)
(b) read more ..

How many subsets of \{0, 1, \dots, 9\} have the property that there are at least two elements and the sum of the two largest elements is 4?

serenitypie May 23, 2025

+190

Counting

A teacher was using a random group generator to split 24 different students, including A, B, and C, in 8 groups of 3. What is the probability that the 3 students, A, B, and C, are in the same group?

HumanBemg May 23, 2025

May 22, 2025

Probability

We choose a positive divisor of 20^{20} at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of 5?

serenitypie May 22, 2025

+190

Counting

Which of these is the general solution for ? Is it or is it ? I'm so confused, is it because it is less?

HumanBemg May 22, 2025

May 19, 2025

Which of these is the general solution for -sqrt3sectheta = 2?

Find the number of ways of arranging one A, two Bs, three Cs, and four Ds, so that no two Bs are next to each other, no two Cs are next to each other, and no two Ds are next to each other.

panickedferret May 19, 2025

+483

Counting

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 ..

bIueb3rry May 19, 2025

May 15, 2025

+53

Geometry

A rectangle in the coordinate plane is shown below. A line with slope 2 splits this rectangle into two regions with equal area. What is the y-intercept of this line?
The rectangle has coordinates (-1,-1), (-1,1), (1,1), read more ..

Ibrahin097YT May 15, 2025

What is the focus of the parabola? y=14x2−x−1

CPhill ●●

smithale May 15, 2025

May 13, 2025

-1

+53

Geometry

Ibrahin097YT May 13, 2025

-1

+53

Geometry

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 1, and the line is y = x.

Ibrahin097YT May 13, 2025

-1

+53

Geometry

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.

Ibrahin097YT May 13, 2025

+53

Geometry

How many positive integers are there whose digits strictly decrease from left to right, and have at most one even digit, and the sum of the digits is 6?

Ibrahin097YT May 13, 2025

-1

+53

Geometry

Ibrahin097YT May 13, 2025

+53

Geometry

Ibrahin097YT May 13, 2025

May 12, 2025

May 10, 2025

+456

Counting

The following cards are split into four piles at random, so that every pile contains the same number of cards. What is the probability that every pile contains an Ace?
The cards are:
Ace of clubs
Ace of diamonds read more ..

Jasmo May 10, 2025

+483

Counting

A bag contains red and blue tiles. Each tile has a number from the set \{-1, 0, 1\} written on it. I want to arrange 7 of these tiles in a row, so that the numbers on any three consecutive tiles sum to 3. In how many ways can this be done, assuming that read more ..

bIueb3rry May 10, 2025

+483

Counting

bIueb3rry May 10, 2025

-1

+53

i need answer now

Ibrahin097YT May 10, 2025

-1

+53

plz help now

If an ant crawls from one corner to the other corner of a 3 \times 5 rectangle, then it will cross through seven squares.
If the ant crawls from one corner to the other corner of a 15 \times 16 rectangle, then how many squares will read more ..

Ibrahin097YT May 10, 2025

-1

+53

help me help help

A survey conducted among 150 high school students revealed that

* 68 students like Math
* 85 students like English
* 55 students like History
* 20 students like both Math and English
* 15 students like both Math and read more ..

Ibrahin097YT May 10, 2025

+53

help really need help

What is the value of the expression. Express your asnwer as a common fraction.

Ibrahin097YT May 10, 2025

+15

HELP PLEASE ASAP!!!!