All Questions ⁺⁰235702 Questions

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Geometry

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

gnistory Nov 11, 2024

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+834

Geometry

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

gnistory Nov 11, 2024

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+834

Geometry

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.

gnistory Nov 11, 2024

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+263

Counting

Catherine rolls a standard 6-sided die six times. If the product of her rolls is 200, then how many different sequences of rolls could there have been? (The order of the rolls matters.)

bIueb3rry Nov 11, 2024

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+263

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

bIueb3rry Nov 11, 2024

Nov 10, 2024

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+1222

Geometry

Points A, B, and c are given in the coordinate plane. There exists a point Q and a constant k such that for any point P,
PA^2 + PB^2+PC^2=3PQ^2 + k
If A = (4, -1), B = (8, 2), and C = (-7, 4), then find the constant k.

learnmgcat Nov 10, 2024

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+263

Counting

Annville Junior High School has a math club and a science club. There are $3$ students in the math club and $3$ students who are members of both clubs. There are twice as many students in the science club as in the math club. Find read more ..

bIueb3rry Nov 10, 2024

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+544

Geometry

A line and a circle intersect at A and B as shown below. Find the distance between A and B.
The circle is x^2 + y^2 = 1, and the line is y = x.

cooIcooIcooI17 Nov 10, 2024

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+544

Geometry

A rectangle in the coordinate plane is shown below. A line with slope 1/3 splits this rectangle into two regions with equal area. What is the y-intercept of this line?
The rectangle is at (2,1), (2,-1), (-2,1), (-2,-1). read more ..

cooIcooIcooI17 Nov 10, 2024

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+544

Geometry

Let O be the origin. Points P and Q lie in the first quadrant. The slope of line segment OP is 7 and the slope of line segment is 10. If then compute the slope of line segment
Note: The point read more ..

cooIcooIcooI17 Nov 10, 2024

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+834

Algebra

In a store window, there was a box of berries having a total weight of 200 kg. The berries were 95% 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 the read more ..

gnistory Nov 10, 2024

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+834

Algebra

The distance between the points $A$ and $B$ is $\sqrt{5}.$ If $A = (a,-1)$ and $B = (2,2a-7),$ then find the sum of all possible values of $a.$

gnistory Nov 10, 2024

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+834

Algebra

Arrange the following numbers in increasing order (smallest first, biggest last):
A = 2*1/2*4*1/6
B = 12*128
C = 1*8*1/5^2 read more ..

gnistory Nov 10, 2024

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+8

Help pls

In the diagram below, each side of convex quadrilateral is trisected. (For example, ) The area of convex quadrilateral is 180. Find the area of the shaded region.
[asy] unitsize(1 cm); pair read more ..

CeeisDee Nov 10, 2024

Nov 9, 2024

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+1364

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 $\overline{PA}$ is $5,$ and $AB$ has a length of 6. Find the radius of the circle.</ read more ..

sandwich Nov 9, 2024

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+1364

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 $3$ from one wall, and a distance of $3$ from the other wall. Find the radius read more ..

sandwich Nov 9, 2024

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+1364

Geometry

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $AB = 2$, then find $AC.$

sandwich Nov 9, 2024

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+1364

Geometry

The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XZ = 5$ and $YZ = 2,$ find $WX.$

sandwich Nov 9, 2024

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