All Questions ⁺⁰230829 Questions

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Geometry

Let $\overline{AB}$ be a diameter of a circle, and let $C$ be a point on the circle. The angle bisector of $\angle ACB$ intersects the circle at point $M.$ Find $CM.$ read more ..

Stanry 27 mins ago

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+48

Geometry

In triangle $ABC,$ points $P$ and $Q$ are on side $\overline{AB},$ and point $R$ is on side $\overline{AC}.$ If $\frac{AP}{2} = \frac{PQ}{5} = \frac{QB}{11}$ and $\frac{AR}{8} = \frac{RC}{13},$ then find $\frac{[QBC]}{[CRQ]}.$

Stanry 28 mins ago

May 1, 2024

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+48

Geometry

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 $4,$ and $AB = 10$, then find the area of triangle $ABC read more ..

Stanry 3 hours ago

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+48

Geometry

Altitudes AD and BE of acute triangle ABC intersect at point H. If angle ABH = 30 and angle DAC = 45, then what is angle HCA in degrees?

NotThatSmart ●

Stanry 4 hours ago

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+37

Common Sense or Math?

My school algebra teacher gave us this question, and it stumped all of us, even the generational geniuses in our class (not me).
She told us it had something to do with common sense and not variables, but not one person could read more ..

NotThatSmart 4 hours ago

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+48

Geometry

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

Stanry 5 hours ago

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+48

Geometry

Points M, N, and O are the midpoints of sides KL, LJ, and JK, respectively, of triangle JKL. Points P, Q, and R are the midpoints of NO, OM, and MN, respectively. If the area of triangle PQR is 27, then what is the area of triangle OPQ?<read more ..

Stanry 6 hours ago

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+48

Geometry

Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle AMC if [ABC]=180.

Stanry 7 hours ago

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+744

Geometry

Let ABCD be a rectangle. Find PD.

LiIIiam0216 7 hours ago

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+18

due soon please help

In the diagram below, $\angle PQR = \angle PRQ = \angle STR = \angle TSR$, $RQ = 8$, and $SQ = 3$. Find $PQ$. [asy] unitsize(5 cm); pair A,B,C,D,E; A = (0, 0.9); B = (-0.4, 0); C = (0.4, 0); D = (-0.275, 0.16); E = (0.11, 0.65); draw(A--B); draw(A--C);read more ..

rtsdyhfdts 8 hours ago

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+48

Geometry

In triangle ABC, angle B = 90 degrees. Point X is on line AC such that angle BXA = 90 degrees, AX = 15, and AB = 25. What is BX?

Stanry 8 hours ago

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+48

Geometry problem

In triangle ABC, point D lies on side AC such that line segment BD bisects angle ABC. Angle A measures 30 degrees, angle C measures 45 degrees, and the length of side AC is 10 units. Determine the area of triangle ABD.

Stanry 8 hours ago

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+744

need help

The roots of the quadratic equation x^2 + bx + c are 5 + 3i and 1 - i. What is b + c?

LiIIiam0216 9 hours ago

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+744

help me plz

Find all ordered pairs x, y of real numbers such that x + y = 10 and x^2 + y^2 = x^3 + y^3.

For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

LiIIiam0216 9 hours ago

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+1133

System

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a+2b+3c+4d+5e=41
2a+3b+4c+5d = 34
3a+4b+5c =15 read more ..

parmen 9 hours ago

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+1133

Algebra

Let a and b be complex numbers. If a + b = 4 and a^2 + b^2 = 6 + 2ab, then what is a^3 + b^3?

parmen 9 hours ago

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+1133

Algebra

Compute
\frac{1}{1 \times 7} + \frac{1}{4 \times 10}

parmen 9 hours ago

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+1133

Algebra

Let
f(x) = \sqrt{x - \sqrt{x}}
Find the largest three-digit value of x such that f(x) is an integer.

parmen 9 hours ago

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+223

Algebra

Let a be a real number such that a + \frac{1}{a} + a^2 + \frac{1}{a^2} = 0. Compute a^5.

Pythagorearn 9 hours ago

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+223

Algebra

Let a1, a2, a3, \dots be a sequence. If
a_n = a_{n - 1} - a_{n - 2}
for all $n \ge 3,$ and a1 = 11 and a2 = 7, then find a6.

Pythagorearn 9 hours ago

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+223

Algebra

Find the value of
\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{2}}}

Pythagorearn 9 hours ago

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+223

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{42}} + \frac{1}{\sqrt{39} + \sqrt{45}}

Pythagorearn 9 hours ago

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+48

Geometry

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

Stanry 10 hours ago

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+48

Geometry

Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G,$ $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $DEFG$ is $18.$ Find the volume of pyramid $EFGH$

Stanry 10 hours ago

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+48

Geometry

Let $APQRS$ be a pyramid, where the base $PQRS$ is a square. The total surface area of pyramid $APQRS$ (including the base) is $800$. Let $W$, $X$, $Y$, and $Z$ be the midpoints of $\overline{AP}$, $\overline{AQ}$, $\overline{AR}$, and $\overline{AS}$, read more ..

Stanry 10 hours ago

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+11

Very confused on trigonometry problem

Intuitively, this problem makes sense, but I am having a hard time showing it. can someone give me a hint
Show that if

theadfas May 1, 2024, 3:49:38 AM

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+36

Counting

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

RedDragonl May 1, 2024, 3:28:16 AM

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+36

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?

RedDragonl May 1, 2024, 3:28:02 AM

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+36

Counting

Determine the number of ways of choosing three points from the grid below, so that they form an isosceles right triangle.

RedDragonl May 1, 2024, 2:33:34 AM

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