All Questions ⁺⁰234950 Questions

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+1095

Geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

learnmgcat Oct 5, 2024

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+1095

Geometry

In square ABCD, P is on BC such that BP = 4 and PC = 1, and Q is on line CD such that DQ = 2 and QC = 3. Find sin angle PAQ.

learnmgcat Oct 5, 2024

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+13

Probability Problem

Six teams play a single round-robin tournament, in which each team plays every other team exactly once, there are no ties, and for each team, the probability of winning any given game is 1/2. What is the probability that at least two different teams read more ..

Halplz Oct 5, 2024

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+712

Geometry

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.

magenta Oct 5, 2024

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+712

Geometry

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

magenta Oct 5, 2024

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+712

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 $XY = 15$ and $WY = 10,$ find $WX.$

magenta Oct 5, 2024

Oct 4, 2024

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+675

Number Theory

What is the greatest prime factor of the sum of the arithmetic sequence 1 + 2 + 3?

AnswerscorrectIy Oct 4, 2024

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+675

Number Theory

The product of two positive integers minus their sum is 39. The integers are relatively prime, and each is less than 2. What is the sum of the two integers?

AnswerscorrectIy Oct 4, 2024

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+1724

Geometry

What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+2x-6y+3$?

ABJeIIy Oct 4, 2024

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+1724

Geometry

For what value of $c$ will the circle with equation $x^2 - 10x + y^2 + 10y + c = 0$ have a radius of length 1?

ABJeIIy Oct 4, 2024

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1

+577

Counting

Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have an 8 on them.
a) What is the expected value of the number shown when we draw a single slip of paper?
b) What is read more ..

gnistory Oct 4, 2024

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+577

Counting

In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are 19 skaters, including 2 Americans and 5 Canadians, in how many ways can the medals be awarded to three of the 19 skaters read more ..

gnistory Oct 4, 2024

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+280

Geometry

Let be a regular polygon. A rotation centered at with an angle of takes to . Given that , find in degrees

ABJelly Oct 4, 2024

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+191

Geometry

In triangle $ABC,$ $BC = 32,$ $\tan B = \frac{3}{5},$ and $\tan C = \frac{1}{4}.$ Find the area of the triangle.

MeIdHunter Oct 4, 2024

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+191

Geometry

In triangle $ABC,$ $AB = 3,$ $AC = 5,$ $BC = 7,$ and $D$ lies on $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC.$ Find $\cos \angle BAD.$

MeIdHunter Oct 4, 2024

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+191

Geometry

What are the coordinates of the points where the graphs of f(x)=x^3 + x^2 - 3x + 5 and g(x) = x^3 + 2x^2 intersect?
Give your answer as a list of points separated by commas, with the points ordered such that their -coordinates read more ..

MeIdHunter Oct 4, 2024

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+1375

Geometry

A circle is inscribed in a quarter-circle, as shown below. If the radius of the quarter-circle is $4,$ then find the radius of the circle.

kittykat Oct 4, 2024

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+1375

Geometry

Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length AB.

kittykat Oct 4, 2024

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+1375

Geometry

Chords UV, WX, and YZ of a circle are parallel. The distance between chords UV and WX is 1, and the distance between chords WX and YZ is also 1. If UV =6 and YZ = 4, then find WX.

kittykat Oct 4, 2024

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+1375

Geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

kittykat Oct 4, 2024

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+866

Algebra

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 $a + b$.

Hi6942O Oct 4, 2024

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