All Questions ⁺⁰236007 Questions

-1

34

0

+1839

Geometry

Triangle DEF is equilateral. Find AE.

DA = 3, AF = 2

ABJeIIy May 14, 2024

0

9

1

+27

Help!

Six teams play a single round-robin tournament, in which each team plays every other team exactly once, there are no ties, and for each team, the probability of winning any given game is 1/2. What is the probability that at least two different teams finish read more ..

colinqiu May 14, 2024

-1

19

0

+1839

Geometry

Let \alpha and \beta be acute angles whose sum is also acute, such that $\angle BAC = \alpha,$ $\angle DAB = \beta,$ and $AB = 1$. Let $E$ be the foot of the perpendicular from $A$ to $BC$, and $F$ be the foot of the perpendicular from $E$ to $AB$, as shown read more ..

ABJeIIy May 14, 2024

-1

18

0

+1839

Geometry

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

ABJeIIy May 14, 2024

-1

19

0

+1839

Geometry

In triangle ABC, point X is on side BC such that AX=5, BX=5, CX=4, and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.

ABJeIIy May 14, 2024

-1

22

0

+1839

Geometry

Semicircles are constructed on AB, AC, and BC. A circle is tangent to all three semicircles. Find the radius of the circle.

ABJeIIy May 14, 2024

0

23

0

+948

Math problem

If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?

Rangcr897 May 14, 2024

0

31

0

+948

Math problem

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.

Rangcr897 May 14, 2024

0

22

0

+1505

Geometry

In the diagram below, D is a point on segment CE such that segments AD and BE are parellel and point A is not on segment BC. Line segments AD and BC intersect at point P.
If angle CAD = 67 degrees, then what is angle read more ..

blackpanther May 14, 2024

0

21

0

+1505

Geometry

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.

blackpanther May 14, 2024

0

33

0

+1505

Geometry

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

blackpanther May 14, 2024

0

33

0

+1505

Geometry

Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.

blackpanther May 14, 2024

0

15

0

+868

Inequality

Find all $x$ such that both $2x$ and $3x-7$ are in the interval $(-1,12)$.

eramsby1O1O May 14, 2024

0

36

0

+868

Inequality

Find all $x$ such that $1-3x < x + 8 \le 7-x$. Give your answer in interval notation.

eramsby1O1O May 14, 2024

0

18

0

+868

Inequality

Find all $z$ such that neither $2+z-5z$ nor $2-z+8z$ is in the interval $(-7,13]$. Express your answer as an interval or as a union of intervals.

eramsby1O1O May 14, 2024

0

25

0

+868

Inequality

Find all $w$ so that neither $-2(6+2w)\le -16 + 7w$ nor $-3w\ge 18 - 5w + 3$.

eramsby1O1O May 14, 2024

0

34

0

+297

Geometry

Let ABCD be a trapezoid with bases AB and CD. Let P be a point on side CD, and let X, Y be the feet of the altitudes from P to AD, BC respectively. Prove that if AD = 5, BC = 7, AB = 6, CD = 12, and CP/PD = 1, then PX = 12*sqrt(6)/5 and PY = read more ..

rtsdylifdts May 14, 2024

+1

25

1

+86

Minimum value of expression

Find the minimum value of over all real numbers

eramsby1010 May 14, 2024

0

24

0

+297

Algebra

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

rtsdylifdts May 14, 2024

0

23

0

+297

Algebra

Let f(x) = \left \lfloor \frac{2 - 3x}{x + 3} + x^2 \right \rfloor.
Find f(1) + f(2) + f(3) + ... + f(999) + f(1000).

rtsdylifdts May 14, 2024

0

30

0

+297

Algebra

Find all values of t such that floor(t) = 3t + 4 - t^2. If you find more than one value, then list the values you find in increasing order, separated by commas.

rtsdylifdts May 14, 2024

0

28

0

+297

Algebra

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 ..

rtsdylifdts May 14, 2024

0

29

0

+842

Geometry

In quadrilateral $PQRS$, $PQ = QR = RS = SP$, $PR = 8$, and $QS = 8$. Find the perimeter of $PQRS$.

RedDragonl May 14, 2024

0

32

0

+842

Geometry

Let $X$, $Y$, and $Z$ be points on a circle. Let line $XY$ and the tangent to the circle at $Z$ intersect at $W$. If $\overline{WY} \perp \overline{WZ}$, then find $YZ$.

RedDragonl May 14, 2024

0

25

0

+842

Geometry

Chords $\overline{PR}$ and $\overline{QS}$ of a circle are perpendicular. Find $RS$.

RedDragonl May 14, 2024

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