All Questions ⁺⁰232717 Questions

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Geometry

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length AB. read more ..

Hi6942O May 26, 2024

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+591

Algebra

Find all values of c such that 3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18. If you find more than one value of c, then list your values in increasing order, separated by commas.

Hi6942O May 26, 2024

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+591

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{39} + \sqrt{40}} + \frac{1}{\sqrt{40} +\sqrt{45}}

Hi6942O May 26, 2024

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+591

Algebra

Let $x$ and $y$ be complex numbers. If $x + y = 2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

Hi6942O May 26, 2024

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+591

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

Hi6942O May 26, 2024

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+121

Algabra

Hi69420 May 26, 2024

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+121

geometry

How many isosceles triangles with whole-number length sides have a perimeter of 20 units?

Hi69420 May 26, 2024

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+121

Help

Hi69420 May 26, 2024

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+121

geometry

If the volume of a 2-cm-by-2cm-by-2cm cube is increased by 19 cubic centimeters to form a larger cube, what is the length in centimeters of one edge of the new cube?

Hi69420 May 26, 2024

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+121

Geometry

What is the radius of the circle inscribed in triangle ABC if AB = 15, AC = 41, and BC = 52?

Hi69420 May 26, 2024

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+641

Counting

How many solutions are there to the equation
u + v + w + x + y + z = 2,
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $1?$

eramsby1O1O May 26, 2024

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+641

Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly $7$ chocolates?

eramsby1O1O May 26, 2024

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+641

Counting

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends, if every friend gets at least one sticker.

eramsby1O1O May 26, 2024

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+641

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.)

eramsby1O1O May 26, 2024

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+140

Geometry

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

BRAlNBOLT May 26, 2024

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+140

Geometry

In the diagram below, we have $AB = 24$ and $\angle ADB =90^\circ$. If $\sin A = \frac13$ and $\sin C = \frac12$, then what is $BC$?
read more ..

BRAlNBOLT May 26, 2024

May 25, 2024

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+140

Geometry

In triangle $ABC,$ $BC = 32,$ $\tan B = \frac{3}{5},$ and $\tan C = \frac{1}{4}.$ Find the area of the triangle.

BRAlNBOLT May 25, 2024

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+28

Let k be a positive real number. The line and the circle are drawn. Find k so that the line is tangent to the circle.

Let k be a positive real number. The line and the circle are drawn. Find k so that the line is tangent to the circle.

jumbean May 25, 2024

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+624

Geometry

In triangle $ABC,$ $AB = 3,$ $AC = 5,$ $BC = 7,$ and $D$ lies on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC.$ Find $\cos \angle BAD.$

learnmgcat May 25, 2024

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+624

Need help

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates read more ..

learnmgcat May 25, 2024

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+624

Help with math

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has slope $2$. Find $a + b$.

learnmgcat May 25, 2024

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+624

Math problem

Find all points (x,y) that are 5 units away from the point (2,7) and that lie on the line x + y = 13.

learnmgcat May 25, 2024

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+624

Algebra

Assume that f(3) = 4. Name a point that must be on the graph of y= (5 + f(2x/3))/11$.

learnmgcat May 25, 2024

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+385

Geometry

In square ABCD, P is on BC such that BP = 5 and PC = 2, and Q is on CD such that DQ = 4 and QC = 3. Find sin angle PAQ.

Pythagorearn May 25, 2024

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+385

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 ..

Pythagorearn May 25, 2024

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