All Questions ⁺⁰237262 Questions

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Geometry

Points $T$ and $U$ lie on a circle centered at $O$, and point $P$ is outside the circle such that $\overline{PT}$ and $\overline{PU}$ are tangent to the circle. If $\angle TOP = 45^{\circ}$, then what is the measure of minor arc $TU$, in deg read more ..

Vxrtate Feb 11, 2024

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Math question

A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 24500 kilograms. Other shipments weighing 13100 kilograms have read more ..

Jimpix Feb 11, 2024

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Geometry question

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

Vxrtate Feb 11, 2024

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Triangle

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 ..

Vxrtate Feb 11, 2024

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Triangle

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$

Vxrtate Feb 11, 2024

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Triangles

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

Vxrtate Feb 11, 2024

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Trapezoid

Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square. read more ..

Vxrtate Feb 11, 2024

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Circles

Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find read more ..

Vxrtate Feb 11, 2024

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Angles in circles

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

Vxrtate Feb 11, 2024

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HELP ASAP

Find the number of ordered pairs (a, b) of integers such that read more ..

iuuhfeusedhu Feb 11, 2024

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Polygons

The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square.

Vxrtate Feb 11, 2024

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Circular Sector

A sector of a circle is shown below. The sector has an area of $60 \pi.$ What is the radius of the circle? read more ..

Vxrtate Feb 11, 2024

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Triangle

Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle PBA$, and $\angle ABC - \angle ACB = 24^\circ$. Find $\angle PBC$ in degrees.

Vxrtate Feb 11, 2024

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GCD/LCM

How many ordered triples of positive integers $(a, b, c)$ have $\text{GCF}(a, b, c) = 2020$ and $\text{LCM}(a, b, c) = 4020?$

omgitsrne Feb 11, 2024

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Square

Square $ABCD,$ shown here, has side length $6$ units. Points $P$ and $Q$ are located on sides $AD$ and $BC,$ respectively, with $AP = BQ = 1$ unit. Triangles $ACP$ and $BDQ$ overlap in the square to form the shaded quadrilateral. What is the area of the read more ..

omgitsrne Feb 11, 2024

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Circle

In the figure, two circles of radius $1$ inch are internally tangent to a circle of radius $5$ inches so that the centers of all three circles are collinear. The shaded fourth circle is tangent to each of the other three circles as shown. What is the radius read more ..

omgitsrne Feb 11, 2024

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Divisible

Suppose that $n$ is a positive integer for which the product $35n$ is divisible by $10.$ What is the least possible value of $n\, ?$

omgitsrne Feb 11, 2024

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Min/max

If $y = \frac{x}{x^2 + 1},$ and $x$ is any real number, then what is the sum of the maximum and minimum possible values of $y \, ?$

omgitsrne Feb 11, 2024

Feb 10, 2024

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List of Numbers

If the mean of a list of $1000$ consecutive odd integers is 0, what is the least number in the list?

omgitsrne Feb 10, 2024

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Help! Probability

Hans is staying at a hotel that has five floors, numbered $1$ through $5,$ and $10$ rooms per floor, numbered $1$ through $10.$ Hans forgets where his room is, but knows that it is on floor 3, 5, or 7, and the room number is divisible by $3.$ If Hans randomly read more ..

omgitsrne Feb 10, 2024

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Area problem

The rectangle below has been divided into unit squares. Find the total area of the blue shaded region, in square units.
read more ..

Vxrtate Feb 10, 2024

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help geometry

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

Vxrtate Feb 10, 2024

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PLEASE HELP VERY URGENT

Let's try this out with a particular triangle. Consider the triangle ABC with A = (5, 4), B = (-9, 6), and C = (1, -4).
(a) Let D, E, F be the midpoints of , , respectively. Find the equations of medians , , read more ..

Starry Feb 10, 2024

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