All Questions ⁺⁰232565 Questions

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+44

Geometry! Help!

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

BRAINBOLT Jun 15, 2024

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+4

Let ABCD be a square. Let E and F be points lying on the sides BC and CD, respectively. Help very appreciated, thanks!

Let ABCD be a square. Let E and F be points lying on the sides and , respectively. If and , find the angle in degrees.
It is a square with a triangle in the middle, triangle has angles 45, 65, 70, read more ..

jagss8 Jun 15, 2024

Jun 14, 2024

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+1170

Algebra

Let x and y be nonnegative real numbers. if x^2+5y^2=30, what is the max value of x + y?

kittykat Jun 14, 2024

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+1170

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 $3$, and $AB = 1$, then find $\frac{AC}{BC}.$

kittykat Jun 14, 2024

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+1170

Algebra

Let
f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.
Find the inverse $f^{-1}(x)$.

kittykat Jun 14, 2024

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+1170

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 $WX.$

kittykat Jun 14, 2024

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+195

Algebra

Let a1, a2, a3, ... be an arithmetic sequence. Let Sn denote the sum of the first n terms. If S_5 = 1/5 and S_10 = 1/10, then find S_15.

NotThatSmart ●

BRAlNBOLT Jun 14, 2024

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+195

Algebra

Let a1, a2, a3, ..., a10 be an arithmetic series. If a1 + a3 = -2 and a2 + a4 + a6 = 1, then find a1.

BRAlNBOLT Jun 14, 2024

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+195

Algebra

Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 100, Shirley runs screaming from the room. What number does Laverne say that sends read more ..

BRAlNBOLT Jun 14, 2024

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+1161

Geometry

Determine the coordinates of the point $P$ on the line $y=-x+6$ such that $P$ is equidistant from the points $A(10,-12)$ and $O(2,8)$ (that is, so that $PA=PO$). Express your answer as an ordered pair $(a,b)$.

ABJeIIy Jun 14, 2024

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+1161

Geometry

In the diagram, the four points have coordinates $A(0,1)$, $B(1,3)$, $C(5,2)$, and $D(4.5,0)$. What is the area of quadrilateral $ABCD$?

ABJeIIy Jun 14, 2024

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+1170

Factor

Find the sum of the distinct prime factors of 5005 + 6192 + 11823.

kittykat Jun 14, 2024

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1

+1170

Factor

Find the sum of the distinct prime factors of 781 + 691 + 3858.

kittykat Jun 14, 2024

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1

+1170

Factor

Find the sum of the distinct prime factors of 728 + 118 + 2024.

kittykat Jun 14, 2024

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1

+1170

Factor

Find the sum of the distinct prime factors of 248 + 113 + 2870.

kittykat Jun 14, 2024

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1

+1170

Factor

Find the sum of the distinct prime factors of 333 + 183 + 401.

kittykat Jun 14, 2024

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+1170

Factor

Find the sum of the distinct prime factors of 123 + 456 + 789.

kittykat Jun 14, 2024

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+372

Primes

Some of the following integers are prime. Select all the prime integers in the list.
1 2 3 4 5 6 7 8 9 10

NotThatSmart ●

Rangcr897 Jun 14, 2024

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+372

Number Theory

What is the fifth smallest prime number greater than 100?

NotThatSmart ●

Rangcr897 Jun 14, 2024

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+372

Number Theory

Jon teaches a fourth grade class at an elementary school where class sizes are always at least 10 students and at most 15. One day Jon decides that he wants to arrange the students in their desks in a rectangular grid with no gaps. Unfortunately read more ..

Rangcr897 Jun 14, 2024

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+372

Decimals

What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{7}$ is written in base $16$?

Rangcr897 Jun 14, 2024

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+372

Decimals

Express 2.\overline{57} as a base 10 fraction in reduced form.

NotThatSmart ●

Rangcr897 Jun 14, 2024

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+579

Number Theory

Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim read more ..

Hi6942O Jun 14, 2024

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+579

Number Theory

What is 100000_{16} * E21A8_{16} in base 16?

Hi6942O Jun 14, 2024

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+579

Decimals

Express 0.11012 as a base 10 fraction in reduced form.

Hi6942O Jun 14, 2024

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