All Questions ⁺⁰236302 Questions

0

24

0

+837

Geometry

In triangle $ABC,$ the angle bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ If $\angle BAC = 60^\circ,$ $\angle CAD = 45^\circ,$ and $AD = 24,$ then find the area of triangle $ABC.$

gnistory Jun 21, 2024

0

17

1

+837

Number Theory

A positive integer is called terrific if it has exactly $3$ positive divisors. What is the smallest terrific positive integer?

NotThatSmart ●

gnistory Jun 21, 2024

0

17

1

+2653

Number Theory

A positive integer is called terrific if it has exactly $3$ positive divisors. What is the largest number of primes that could divide a terrific positive integer?

EnormousBighead ●

LiIIiam0216 Jun 21, 2024

0

24

2

+19

Coordinate geo

Let O be the origin. Points P and Q lie in the first quadrant. The slope of line segment OP is 1 and the slope of line OQ segment is 3. If OP=OQ then compute the slope of line segment PQ.

dreadnought Jun 21, 2024

0

16

1

+2653

Number Theory

A positive integer is called terrific if it has exactly $3$ positive divisors. What is the smallest number of primes that could divide a terrific positive integer?

LiIIiam0216 Jun 21, 2024

0

23

1

+2653

Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $52$ pieces of candy per scoop to the vat, and another machine that can remove exactly $39$ pieces of candy with a different scoop from read more ..

LiIIiam0216 Jun 21, 2024

0

17

0

+837

Geometry

Two circles intersect at two points, $P$ and $Q$. The equations of the two circles are $x^2 + (y - 1)^2 = 1$ and $(x - 1)^2 + y^2 = 1$. Find the length PQ.

gnistory Jun 21, 2024

0

28

0

+837

Geometry

Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

gnistory Jun 21, 2024

0

15

1

+837

geometry

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The line is x = 4, and the equation of the circle is x^2 + y^2 = 25.

gnistory Jun 21, 2024

0

27

1

+19

Coordinate geometry

Let be the origin. Points and lie in the first quadrant. The slope of line segment is 1 and the slope of line segment is 3. If then compute the slope of line segment .

dreadnought Jun 21, 2024

0

26

1

+2653

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.

LiIIiam0216 Jun 21, 2024

0

10

10

+19

Angle bisector from two lines of graph

We have the lines y=3x and y=2x. Let y=mx be the angle bisector of these two lines. How can I find "m"?

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dreadnought Jun 21, 2024

0

26

0

+2653

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 $AB = 20$, $AC = 20$, and $BC read more ..

LiIIiam0216 Jun 21, 2024

0

13

1

+2653

Geometry

Point $A$ is reflected over the line shown below to point $B$. Find the coordinates of $B$.
Write your answer as an ordered pair $(x,y)$.
Point A is (5,7), and the line is y = x.

LiIIiam0216 Jun 21, 2024

0

26

1

+33

Geometry

Quadrilateral PRQS is a trapezoid with bases PQ and RS. The MN median meets the diagonals PR and QS at X and Y, respectively. Find PQ .

Tottenham10 ●

jumbean Jun 21, 2024

0

17

1

+837

Algebra

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

Tottenham10 ●

gnistory Jun 21, 2024

0

17

1

+837

Algebra

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

Tottenham10 ●

gnistory Jun 21, 2024

0

15

1

+837

Algebra

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.

gnistory Jun 21, 2024

0

19

1

+837

Algebra

Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

Tottenham10 ●

gnistory Jun 21, 2024

0

12

1

+2653

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.

LiIIiam0216 Jun 21, 2024

0

25

1

+2653

Geometry

A regular hexagon has a perimeter of p (in length units) and an area of A (in square units). If A=3/2 then find the side length of the hexagon.

LiIIiam0216 Jun 21, 2024

0

25

1

+2653

Geometry

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $10$ from one wall, and a distance of $13$ from the other wall. Find the radius read more ..

LiIIiam0216 Jun 21, 2024

0

20

1

+911

Counting

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends. (Not everyone has to get a sticker.)

magenta Jun 21, 2024

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