All Questions ⁺⁰236009 Questions

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Algebra

In a store window, there was a box of berries having a total weight of 200 kg. The berries were 99% water, by weight. After two days in the sun, the water content of the berries was only 90%, by weight. What was the total weight of read more ..

Hi6942O May 13, 2024

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mathematician solving problems with coffee

A mathematician works for t hours per day and solves p problems per hour, where and are positive integers. One day, the mathematician drinks some coffee and discovers that he can now solve 4p+5 problems per hour. In fact, he only works read more ..

eramsby1010 May 13, 2024

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Hard Trigonometry Problem

Given constants a, b, and c, let and be solutions to the equations which do not differ by a multiple of . Express in terms of a, b, and c.

eramsby1010 May 13, 2024

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Hard Conic Sections Problem

The ellipse and the hyperbola are tangent. Compute

eramsby1010 May 13, 2024

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Hard Intermediate Algebra Problem

Let and be positive real numbers such that Find the set of all possible values of

eramsby1010 May 13, 2024

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Cool Triangles

A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to twice 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 ..

eramsby1010 May 13, 2024

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Hard Algebra Problem

The graphs of and intersect at two points. The distance between these points is of the form , where and are integers. Find the ordered pair .

eramsby1010 May 13, 2024

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Algebra

All members of our painting team paint at the same rate. If 20 members can paint a 2000 square foot wall in 40 minutes, then how long would it take the 20 members to paint a 6000 square foot wall, in minutes?

Hi6942O May 13, 2024

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Algebra

All members of our painting team paint at the same rate. If 20 members can paint a 2000 square foot wall in 40 minutes, then how long would it take the 20 members to paint a 6000 square foot wall, in minutes?

Hi6942O May 13, 2024

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25

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Algebra

I have to paint one side of a wall. The wall is 12 meters tall and 120 meters long. Each gallon of paint covers 150 square feet. If a foot is approximately 0.3048 meters, then what is the smallest whole number of gallons read more ..

Hi6942O May 13, 2024

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15

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Algebra

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How many cents does read more ..

Hi6942O May 13, 2024

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Algebra

I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 50 miles per hour instead, then I would have arrived 45 minutes later. How many miles did I drive?

Hi6942O May 13, 2024

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Algebra

Find the ordered triple (p,q,r) that satisfies the following system:
p - 2q = 3
q - 2r = -2 + q
p + r = 9 + p read more ..

Hi6942O May 13, 2024

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Hard Algebra Problem

A mathematician works for t hours per day and solves p problems per hour, where t and p are positive integers. One day, the mathematician drinks some coffee and discovers that he can now solve 4p + 2 problems per hour. In fact, read more ..

eramsby1010 May 13, 2024

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29

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Algebra

The quadratic equation $x^2-mx+24 = 10$ has roots $x_1$ and $x_2$. If $x_1$ and $x_2$ are integers, how many different values of $m$ are possible?

Hi6942O May 13, 2024

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Algebra

I drove to the beach at a rate of $40$ miles per hour. If I had driven at a rate of $55$ miles per hour instead, then I would have arrived $25$ minutes earlier. How many miles did I drive?

Hi6942O May 13, 2024

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36

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+976

Algebra

Find all real values of x such that
\frac{x^2 + 2x + 5}{3x^2 - x - 4} + \frac{x^2 + 4x + 8}{x^2 - 4x - 5} \ge 0.
Note: Your solution should be thorough, and explain why all your values are the only values that satisfy the inequality. read more ..

Hi6942O May 13, 2024

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Algebra

Solve the inequality $x^3 + 4x > 5x^2 + 2x - x^3 + 7x^2 - 36$. Write your answer in interval notation.

Hi6942O May 13, 2024

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Algebra

Solve the inequality x^3 + 4x > 5x^2 - 17x - x^4 + 3. Write your answer in interval notation.

Hi6942O May 13, 2024

May 12, 2024

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Geometry

A semicircle is inscribed in triangle $XYZ$ so that its diameter lies on $\overline{YZ}$, and is tangent to the other two sides. If $XY = 10,$ $XZ = 10,$ and $YZ = 10 \sqrt{2},$ then find the area of the semicircle. read more ..

Hi6942O May 12, 2024

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Geometry

Chords $\overline{AB}$ and $\overline{CD}$ of a circle meet at $P$. If $AP = 3 \cdot PB$, then what is $AB$?

Hi6942O May 12, 2024

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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 $YZ$.

Hi6942O May 12, 2024

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Geometry

Let $\overline{AB}$ and $\overline{CD}$ be chords of a circle, that meet at point $Q$ inside the circle. If $CD = 34$, then find the minimum length of $CQ$.

Hi6942O May 12, 2024

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Geometry

Let $\overline{TU}$ and $\overline{VW}$ be chords of a circle, which intersect at $S$, as shown. Find $SW$.

Hi6942O May 12, 2024

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Geometry

A circle is centered at $O.$ The tangent to the circle at $P$ is extended to $Q.$ Line segment $\overline{QS}$ intersects the circle at $R.$ Find the area of the circle.

Hi6942O May 12, 2024

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