All Questions ⁺⁰235549 Questions

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+1234

Geometry

Quadrilateral $ABCD$ is a parallelogram. Let $E$ be a point on $\overline{AB},$ and let $F$ be the intersection of lines $DE$ and $BC.$ The area of triangle $EAD$ is $9.$ If $AE:EB = 3:4$ and the height of parallelogram $ABCD$ is $10$, read more ..

Akhain1 Apr 13, 2024

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27

0

+35

3D Geometry

Problem 1.
A tetrahedron is considered trirectangular if one of the vertices forms 3 90-angles. What is the volume of a trirectangular tetrahedron ABCD if one its faces is a 8,10,12 triangle?
Problem 2.
Let ABCD read more ..

Mather459 Apr 13, 2024

+1

27

1

+1234

Geometry

In triangle ABC, point X is on side BC such that AX=13,BX=10,CX=10, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

Akhain1 Apr 13, 2024

+1

16

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+302

Please Help, Thank you if you help or try :)

What is the sum of the series ? (Note: The number is in Fibonacci Sequence)

aboslutelydestroying Apr 13, 2024

Apr 12, 2024

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21

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+1234

Geometry

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 $DE$?

Akhain1 Apr 12, 2024

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16

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+1234

Geometry

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 $BD$?

Akhain1 Apr 12, 2024

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40

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+1234

Geometry

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

Akhain1 Apr 12, 2024

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20

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+1234

Geometry

In right triangle $ABC,$ $\angle C = 90^\circ$. Median $\overline{AM}$ has a length of 1, and median $\overline{BN}$ has a length of 1. What is the length of the hypotenuse of the triangle?

Akhain1 Apr 12, 2024

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24

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+1234

Geometry

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 $AB$.

Akhain1 Apr 12, 2024

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19

1

+85

Hard Geometry

Very few people have solved these problems
1.

2.
<#> read more ..

Akhaim1 Apr 12, 2024

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21

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+1234

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{36} + \sqrt{45}} + \frac{1}{\sqrt{39} +\sqrt{96}}

Akhain1 Apr 12, 2024

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20

1

+1234

Algebra

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

Akhain1 Apr 12, 2024

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22

0

+1234

Algebra

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

Akhain1 Apr 12, 2024

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18

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+1234

System

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a & + & 2b & + & 3c & + & 4d & + & 5e & = & 47, \\
2a & + & 3b & + & 4c & + & 5d & + & e read more ..

Akhain1 Apr 12, 2024

0

16

1

+830

Geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

magenta Apr 12, 2024

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24

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+830

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

magenta Apr 12, 2024

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14

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+1427

Algebra

Find t if the expansion of the product of 2x^3 + x^2 - 3x + 5 and x^4 - 7x^3 + tx^2 - 11x + 15 has no x^2 term.

blackpanther Apr 12, 2024

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26

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+1427

Algebra

In class, we derived that
\frac{1}{n(n + 1)} = \frac{1}{n} - \frac{1}{n + 1}.
Fill in the blanks to make a true equation:
\frac{5x}{(x - 1)(x^2 + 2)(x + 7)^3)} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + 2} + \frac{D}{x + 7} read more ..

blackpanther Apr 12, 2024

Apr 11, 2024

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15

1

+1427

Algebra

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

blackpanther Apr 11, 2024

+1

25

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+35

Tricky problems

Problem 1.
Find the number of positive integer pairs (x,y) that satisfy xy ≤ 35.
Problem 2.
Find the number of positive integer pairs (x,y) that satisfy 20x ≥ 24y and x < 360. read more ..

Mather459 Apr 11, 2024

0

12

1

+1427

Algebra

Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is $4.$ The sum of the cubes of all the terms is $10.$ Find the common ratio.

blackpanther Apr 11, 2024

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23

2

+81

Geometry problem, need help fast!

A circle is inscribed into a right triangle. From the center of the circle a perpendicular is dropped on the hypotenuse, dividing the hypotenuse into two segments of length 12 and 5. What is the sum of the legs of the triangle?
I did read more ..

moneydude242 Apr 11, 2024

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16

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+1525

Algebra

Let a and b be the roots of the quadratic 2x^2 - 8x + 7 = x^2 + 15x + 23. Compute a^4 + b^4.

parmen Apr 11, 2024

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13

1

+1525

Algebra

Let a and b be the roots of the quadratic x^2 - 5x + 3 = 2x^2 + 15x - 10. Find the quadratic whose roots are a^2 + a + 1 and b^2 + b + 1.

parmen Apr 11, 2024

0

23

1

+817

Algebra

Let a and b be the solutions to 7x^2 + x - 5 = 6x^2 - 11x - 2. Compute (a - 4) + (b - 4).

maximum Apr 11, 2024

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