All Questions ⁺⁰234503 Questions

0

10

0

+1467

Counting

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

parmen Jun 12, 2024

0

6

0

+1015

Algebra

The graphs of x = y^4 and x + y^2 = 1 + x^2 - y^3 intersect at two points. The distance between these points is of the form sqrt(u + v*sqrt(5)), where u and v are integers. Find the ordered pair (u,v).

learnmgcat Jun 12, 2024

0

6

1

+1015

Algebra

A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to five times the number of units in the sum of the lengths of its legs. What is the sum of all the different possible areas of cool right read more ..

learnmgcat Jun 12, 2024

0

9

1

+1015

Algebra

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

learnmgcat Jun 12, 2024

-3

8

1

+161

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.

BRAlNBOLT Jun 12, 2024

-3

6

1

+161

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.

BRAlNBOLT Jun 12, 2024

-3

13

1

+161

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.

BRAlNBOLT Jun 12, 2024

0

5

1

+56

halp pls asap

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/5 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

ghistory Jun 12, 2024

Jun 11, 2024

-3

11

0

+161

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 $BXA$.

BRAlNBOLT Jun 11, 2024

0

9

1

+16

how?

The x intercepts of a circle are -3 and 10. One of the y intercepts is 5. What is the other y intercept? What is
the area of the circle?

Pearsse Jun 11, 2024

-4

9

0

+161

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 ..

BRAlNBOLT Jun 11, 2024

-4

7

1

+161

Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$,
<read more ..

BRAlNBOLT Jun 11, 2024

+1

3

1

+276

Help me!

Find the largest integer k such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.

BRAINBOLT Jun 11, 2024

0

7

0

+1467

Geometry

Altitudes $\overline{AP}$ and $\overline{BQ}$ of an acute triangle $\triangle ABC$ intersect at point $H$. What is the area of triangle $ABC$?

parmen Jun 11, 2024

0

6

1

+1307

Counting

The six faces of a cube are painted black. The cube is then cut into 6^3 smaller cubes, all the same size. One of the small cubes is chosen at random, and rolled. What is the probability that when it lands, the face on the top is black?

blackpanther Jun 11, 2024

0

8

2

+85

Quadratics

PurpleWasp Jun 11, 2024

0

4

2

+1307

Counting

A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is times the probability that a freshman is elected. Everyone on the junior varsity read more ..

blackpanther Jun 11, 2024

0

8

1

+1307

Counting

Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 2 or a 3
- The sum of the digits is 5

blackpanther Jun 11, 2024

0

6

2

+1307

Algebra

Let x \mathbin{\spadesuit} y = \frac{x^2}{y} for all x and y such that y\neq 0. Find all values of $a$ such that $a \mathbin{\spadesuit} (a + 1) = 9$. Write your answer as a list separated by commas.

blackpanther Jun 11, 2024

0

7

1

+85

Quadratics

The two positive integer solutions of the equation x^2-mx+n are k and t, where m and n are both prime numbers and k>t. What is the value of ?

PurpleWasp Jun 11, 2024

0

2

2

+28

NUMERO

Given that is a prime number, evaluate

wassyo Jun 11, 2024

0

8

1

+1307

Algebra

Suppose $a(x) = 2x + 5 - 3x^2 + x^3$ and $b(x) = 4 - x^2 + 4x^4$. Find $(a\circ b)(3) - (b\circ a)(3).$

blackpanther Jun 11, 2024

+1

10

2

+28

Number Theory

How many ways are there to fill in the tens digit and hundreds digit of 1_ _4 so that it is divisible by 11?

wassyo Jun 11, 2024

0

9

1

+2633

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 BC, then find AC + BC + AB.

LiIIiam0216 Jun 11, 2024

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