All Questions ⁺⁰235702 Questions

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+829

Geometry

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 ..

AnswerscorrectIy Sep 4, 2024

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2

2

+829

Geometry

Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 120^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle YXZ$, in degrees.

AnswerscorrectIy Sep 4, 2024

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5

2

+19

Need help again :)

Mr. Earl E. Bird leaves his house for work at exactly 8:00 A.M. every morning. When he averages 40 miles per hour, he arrives at his workplace three minutes late. When he averages 60 miles per hour, he arrives three minutes early. At what average speed, read more ..

catttttttttt Sep 4, 2024

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7

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+448

Algebra

All members of our painting team paint at the same rate. If $15$ members can paint a specific wall in $45$ minutes, then how long would it take $20$ members to paint the same wall, in minutes?

onyuIee Sep 4, 2024

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3

1

+448

Algebra

A geometric sequence has $400$ terms. The first term is $500$ and the common ratio is $-\frac{1}{20}.$ How many terms of this sequence are greater than $1?$

onyuIee Sep 4, 2024

0

5

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+337

Geometry

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 $PQ = 36$, $PM read more ..

MeIdHunter Sep 4, 2024

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9

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+838

Counting

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row?

magenta Sep 4, 2024

+1

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5

+19

A Hard Question For Me :( neeeeed helppppp plzzzzz :)

Kwan must read a book that is 400 pages long. He reads at a rate of one page per minute. If he begins reading on a Saturday and he reads one-half hour every day until he finishes the book, on what day of the week will he finish the book?

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catttttttttt Sep 4, 2024

0

7

2

+544

Counting

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, if there must be at least three yellow squares?

cooIcooIcooI17 Sep 4, 2024

Sep 3, 2024

0

13

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+838

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.

magenta Sep 3, 2024

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11

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+479

Algebra

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

ChiIIBill Sep 3, 2024

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6

1

+544

Counting

Find the coefficient of u^2*v^9 in (2u - 3*v^3)*5*(3u^3 - 2v^5)^3.

cooIcooIcooI17 Sep 3, 2024

0

10

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+544

Counting

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

cooIcooIcooI17 Sep 3, 2024

0

14

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+279

Geometry

Let A1 A2 A3 ... A15 be a regular polygon. A rotation centered at $A_4$ with an angle of $\alpha$ takes $A_3$ to $A_5$. Given that $\alpha < 180^\circ$, find $\alpha,$ in degrees.

fjeihqoO Sep 3, 2024

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6

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+145

Pls help me

Nicky had some 50-cent and 20-cent coins. He had 4 more 50-cent coins than 20-cent coins at first. He exchanged 1/3 of his 50-cent coins for some 20-cent coins such that the total value of the coins remained the same. In the end, the total value of read more ..

sugabreaddoughman Sep 3, 2024

Sep 2, 2024

0

8

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+448

Algebra

Let f(x) = lfloor (2 - 3x)/(3x + 8) \rfloor
Evaluate $f(1)+f(2) + f(3) + \dots + f(999)+f(1000).$ (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

onyuIee Sep 2, 2024

0

8

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+448

Algebra

Find constants A and B such that
(2x + 11)/(x^2 - 6x + 5) = A/(x - 3) + B/(x + 4)
for all x such that x neq 7 and x neq 8

onyuIee Sep 2, 2024

0

3

1

+552

Geometry

A sphere is inscribed in a cone with height $3$ and base radius $3$. What is the ratio of the volume of the sphere to the volume of the cone?

Pythagorearn Sep 2, 2024

0

5

1

+552

Geometry

Rose has a spherical plum of radius $2$ and a spherical watermelon of radius $8$. She builds a glass sphere around the two fruits to contain them, making the sphere as small as possible. When she has done this, she places a golf ball inside read more ..

Pythagorearn Sep 2, 2024

0

10

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+250

Geometry

A sphere of radius $4$ inches is inscribed in a cone with a base of radius $8$ inches. In inches, what is the height of the cone? Express your answer as a decimal to the nearest tenth.

MEMEG0D Sep 2, 2024

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