All Questions ⁺⁰235569 Questions

+1

11

1

+1906

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 May 1, 2024

0

22

1

+330

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 May 1, 2024

0

23

0

+330

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 May 1, 2024

0

21

1

+330

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 May 1, 2024

-1

31

0

+2653

Geometry

Let ABCD be a rectangle. Find PD.

LiIIiam0216 May 1, 2024

0

16

2

+45

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 May 1, 2024

0

20

1

+330

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 May 1, 2024

0

19

3

+330

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 May 1, 2024

0

18

1

+2653

need help

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

LiIIiam0216 May 1, 2024

0

14

1

+2653

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 May 1, 2024

0

15

1

+1537

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 May 1, 2024

0

10

1

+1537

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 May 1, 2024

0

15

1

+1537

Algebra

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

parmen May 1, 2024

0

16

1

+1537

Algebra

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

parmen May 1, 2024

0

14

1

+527

Algebra

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

Pythagorearn May 1, 2024

0

18

1

+527

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 May 1, 2024

0

20

1

+527

Algebra

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

Pythagorearn May 1, 2024

0

14

1

+527

Algebra

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

Pythagorearn May 1, 2024

0

11

1

+330

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 May 1, 2024

0

26

0

+330

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 May 1, 2024

0

22

0

+330

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 May 1, 2024

0

13

1

+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

0

32

1

+826

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

0

19

1

+826

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

0

21

1

+826

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

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