All Questions ⁺⁰237360 Questions

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36

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+864

Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

RedDragonl May 1, 2024

0

53

0

+305

geometry

Let $PQRSTUVW$ be a rectangular prism, as shown. The area of face $TUVW$ is $10,$ the area of face $TUQP$ is $10,$ and the area of face $TPSW$ is $10.$ Find the volume of the rectangular prism.

rtsdylifdts May 1, 2024

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48

1

+305

Geometry

Jessica has one cube with a side length of $1,$ and another cube with a side length of $1.$ She then glues the two cubes together, to form one single solid. What is the smallest possible surface area of the single solid?

rtsdylifdts May 1, 2024

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29

1

+305

Geometry

A rectangular prism has a length of $3$, a width of $5$, and a height of $11$. What is the distance between two opposite corners of the prism?

rtsdylifdts May 1, 2024

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43

1

+8

Please Help, Geometric Probability

The numbers are chosen at random in the interval Let be the interval between and and let be the interval between and . Find the probability that intervals and read more ..

Noctuous May 1, 2024

Apr 30, 2024

0

40

1

+305

Geometry

A plane and a sphere intersect in a circle. The circle has an area of $25 \pi$. The distance between the plane and the center of the sphere is $5$ units. Find the surface area of the sphere.

rtsdylifdts Apr 30, 2024

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51

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+305

Geometry

Triangle $ABC$ below is rotated completely around side $\overline{BC}$, sweeping out a solid in space. Find the volume of the solid. read more ..

rtsdylifdts Apr 30, 2024

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52

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+305

Geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

rtsdylifdts Apr 30, 2024

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31

1

+305

Coordinates

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 ..

rtsdylifdts Apr 30, 2024

0

30

1

+305

Coordinates

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 $a + b$.

rtsdylifdts Apr 30, 2024

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42

1

+1266

Similar Triangles

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

Akhain1 Apr 30, 2024

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13

2

+1266

help with 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 ..

Akhain1 Apr 30, 2024

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37

1

+1266

Geometry

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 ..

Akhain1 Apr 30, 2024

+1

21

4

+1950

Polynomial Factorization

This problem was in my math textbook, and I found it really interesting. It took me a while to do, but the solution is kind of simple. If you want a fun little problem, here you go I geuss!
Good Luck!
The polynomial is read more ..

NotThatSmart Apr 30, 2024

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31

1

+1266

Trapezoid

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.

Akhain1 Apr 30, 2024

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39

2

+972

plz help

Plz help! I'm really confused!
The diagram below consists of a small square, four equilateral triangles, and a large square. Find the area of the large square. read more ..

Rangcr897 Apr 30, 2024

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38

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+789

Circle

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 ..

bingboy Apr 30, 2024

+6

36

2

+71

Geometry - pls help i don't understand how to do it

In triangle PQR, M is the midpoint of \overline{PQ}. Let X be the point on \overline{QR} such that \overline{PX} bisects \angle{QPR} and let the perpendicular bisector of \overline{PQ} intersect \overline{PX} at Y. If PQ = read more ..

Starry Apr 30, 2024

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64

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+305

help with geometry

The area of a trapezoid is $80$. The length of one base is $4$ units greater than the other base, and the height of the trapezoid is $12$. Find the perimeter of the trapezoid.

rtsdylifdts Apr 30, 2024

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20

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+305

Parallelogram

In parallelogram EFGH, let M be the point on \overline{EF} such that FM:ME = 3:5, and let N be the point on \overline{EH} such that HN:NE = 2:5. Line segments \overline{FH} and GN intersect at Q. Find PQ/FH.

rtsdylifdts Apr 30, 2024

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31

1

+4

Help pls!!!

a⃗ =⟨(−1,−4)⟩ and b⃗ =⟨(3,2)⟩.
Represent a⃗ −b⃗ using the head-to-tail method.
Use the Vector tool to draw the vectors, complete the subtraction by the head-to-tail method, and draw a⃗ −b⃗ .
To read more ..

Zagreus732 Apr 30, 2024

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46

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+305

need help fast

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid read more ..

rtsdylifdts Apr 30, 2024

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42

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+305

Hard geo

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 5 from one wall, and a distance of 5 from the other wall. Find the radius of the table.</ read more ..

rtsdylifdts Apr 30, 2024

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47

1

+305

help me

We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

rtsdylifdts Apr 30, 2024

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31

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+305

Geometry question

Points $A$ and $B$ are on side $\overline{YZ}$ of rectangle $WXYZ$ such that $\overline{WA}$ and $\overline{WB}$ trisect $\angle ZWX$. If $WX = 2$ and $XY = 3$, then what is the area of rectangle $WXYZ$?

rtsdylifdts Apr 30, 2024

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