bIueb3rry

24 Questions
0 Answers

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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 6 from one wall, and a distance of 6 from the other wall. Find the radius of the read more ..

bIueb3rry Sep 10, 2024

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Geometry

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$ read more ..

bIueb3rry Sep 10, 2024

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Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

bIueb3rry Sep 7, 2024

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Number Theory

A school orders $99$ textbooks, all for the same price. When the bill for the total order comes, the first and last digits are obscured. What are the missing digits?
$_5801.3_

bIueb3rry Sep 4, 2024

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Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $30$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}45$ p.m. read more ..

bIueb3rry Aug 30, 2024

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Geometry

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 $a + b$.

bIueb3rry Aug 25, 2024

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Geometry

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

bIueb3rry Aug 25, 2024

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Geometry

The perimeter of a rectangle is $40,$ and the length of one of its diagonals is $10 \sqrt{2}.$ Find the area of the rectangle.

bIueb3rry Aug 22, 2024

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Geometry

Find the area of parallelogram ABCD.

bIueb3rry Aug 22, 2024

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Geometry

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$ Find the area of the rhombus.

bIueb3rry Aug 22, 2024

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Algebra

Find the domain of the function $$f(x) = \frac{\sqrt{x}}{\sqrt{x^2}}.$$ Express your answer as an interval or as a union of intervals.

bIueb3rry Aug 18, 2024

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Algebra

Let
$$f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.$$
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

bIueb3rry Aug 18, 2024

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+96

Geometry

In the diagram, $ABCD$ is a square. Find $PR.$
The side length of the square is 10. L, M, N, O are midpoints.

bIueb3rry Aug 18, 2024

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Geometry

Find the coordinates of the center of the circle.
The points on the circle are (22,15), (-25,0), (22,-29).

bIueb3rry Aug 18, 2024