All Questions ⁺⁰236027 Questions

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+1521

Geometry

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.

blackpanther Oct 21, 2024

0

7

0

+1521

Geometry

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.

blackpanther Oct 21, 2024

0

5

0

+1521

Geometry

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

blackpanther Oct 21, 2024

0

3

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+1310

Geometry

Let $ABCDEFGH$ be right rectangular prism. The total surface area of the prism $15.$ Also, the sum of all the edges of the prism is $17.$ Find the length of the diagonal joining one corner of the prism to the opposite corner.

learnmgcat Oct 21, 2024

0

4

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+1310

Geometry

Let $x$ and $y$ be real numbers. If $x$ and $y$ satisfy
x^2 + y^2 = 4x - 8y + 17x - 5y + 25,
then find the largest possible value of $x.$ Give your answer in exact form using radicals, simplified as far as possible.

learnmgcat Oct 21, 2024

0

5

0

+1310

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 $A = (7,-11),$ $B = (10,13),$ and $C = (18,-22)$, then find the constant read more ..

learnmgcat Oct 21, 2024

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1

+862

Number Theory

A positive integer is called terrific if it has exactly $12$ positive divisors. A positive integer is called fine if it has exactly 2 positive divisors. Which numbers are fine?

magenta Oct 21, 2024

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+862

Number Theory

A positive integer is called terrific if it has exactly $12$ positive divisors. A positive integer is called good if it has exactly 4 positive divisors. Which numbers are good?

magenta Oct 21, 2024

+1

4

1

+5

Finding last digit using mod

I understand the first part (2^4 is 1 mod 5), but how can you extend this to 2^2^2022?

, so

mkumar22 Oct 21, 2024

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5

1

+785

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?

gnistory Oct 21, 2024

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3

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+785

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 $1?$

gnistory Oct 21, 2024

Oct 20, 2024

+1

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3

+135

Cool problem I made

What is the only solution to 1/x + 1/y = 1/123 where x < y?

Maxematics Oct 20, 2024

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4

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+281

Algebra

Compute
1 + \frac{3}{6} + \frac{5}{6^2} + \frac{7}{6^3} + 2 + \frac{2}{5} + \frac{2}{5^3} + \frac{2}{5^4}

jaekg Oct 20, 2024

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6

0

+281

Algebra

Let $x$ and $y$ be complex numbers. If $x + y = 2$ and $x^3 + y^3 = 5$, then what is $x^2 + y^2$?

jaekg Oct 20, 2024

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3

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+281

Algebra

Compute the sum
\frac{1}{\sqrt{36} + \sqrt{39}} + \frac{1}{\sqrt{39} + \sqrt{40}} + \frac{1}{\sqrt{40} +\sqrt{45}}

jaekg Oct 20, 2024

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3

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+281

Algebra

Find all values of c such that 3(2c + 1) = 28*(3c) - 9 + 45(3c) - 18. If you find more than one value of c, then list your values in increasing order, separated by commas.

jaekg Oct 20, 2024

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3

1

+606

Counting

Fill in the blanks with integers to get an identity.
(n - k + 2)^2 = __ n^2 + ___ k^2 + ___ n + ___k + ___ nk + ___

cooIcooIcooI17 Oct 20, 2024

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3

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+606

Counting

In a series of coin flips, a run is a series of one or more consecutive coin flips that all have the same result. For example, in the sequence
TTHHHTTHHHTH

the red letters form a run of length $3$. (A run of length $1$ is still read more ..

cooIcooIcooI17 Oct 20, 2024

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7

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+606

Counting

Joanna has several beads that she wants to assemble into a bracelet. There are seven beads: five of the beads have the same color, and the other two all have different colors. Using all seven beads, in how many different ways can Joanna assemble read more ..

cooIcooIcooI17 Oct 20, 2024

0

8

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+606

Counting

A standard six-sided die is rolled $8$ times. You are told that among the rolls, there was two $1$'s, two $2$'s, two $3$'s, and two $4$s. How many possible sequences of rolls could there have been? (For example, $2,$ $1,$ $3,$ $4,$ $2,$ read more ..

cooIcooIcooI17 Oct 20, 2024

+1

4

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+18

Help!

A school orders textbooks, all for the same price. When the bill for the total order comes, the first and last digits are obscured. What are the missing digits?
a482.7b

●●●●●●●●

NewMathsAlways Oct 20, 2024

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+4

Which options use the correct LaTeX delimiters and are formatted properly? Select all that apply

Which options use the correct LaTeX delimiters and are formatted properly? Select all that apply
option 1 \\[x = 10\\]
option 2 $x = 10$
option 3 \\[ read more ..

goldengineer14 Oct 20, 2024

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