All Questions ⁺⁰235690 Questions

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Geometry

In triangle $ABC$, $M$ is the midpoint of $\overline{BC}$, and $N$ is the midpoint of $\overline{AC}$. The perpendicular bisectors of $BC$ and $AC$ intersect at a point $O$ inside the triangle. If $\angle AOB = 90^\circ$, then find the measure read more ..

AnswerscorrectIy Nov 6, 2024

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+536

Algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $214$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

cooIcooIcooI17 Nov 6, 2024

Nov 5, 2024

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+552

Counting

At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if each scientist must sit next to a mathematician? (Two seatings are considered equivalent read more ..

Pythagorearn Nov 5, 2024

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Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

Pythagorearn Nov 5, 2024

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Counting

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

Pythagorearn Nov 5, 2024

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+263

Algebra

If I give my brother $5$ dollars, then we will have the same amount of money. If instead he gives me $10$ dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

bIueb3rry Nov 5, 2024

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+263

Algebra

Five times a number is divided by $2$ more than that number. If the result is $6,$ then what was the original number?

bIueb3rry Nov 5, 2024

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Algebra

Find all values of $a$ that satisfy the equation
\frac{a}{3} + 1 = \frac{a + 3}{a} - \frac{a^2 + 2}{a}.

bIueb3rry Nov 5, 2024

Nov 4, 2024

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Algebra

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

Pythagorearn Nov 4, 2024

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+552

Algebra

Find all values of t such that floor(t) = 3t + 4 - t^2. If you find more than one value, then list the values you find in increasing order, separated by commas.

Pythagorearn Nov 4, 2024

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Algebra

Let
f(x) = \left\lfloor\frac{2 - 3x}{3x + 1}\right\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.)

Pythagorearn Nov 4, 2024

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+263

Algebra

A line passes through the points A, B, and C. Find y.
A = (-7,2), B = (8,-14), C = (10,y)

bIueb3rry Nov 4, 2024

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+263

Algebra

Find the equation whose graph is shown below. Write your answer in standard form.
(Standard form is $Ax+By = C$, where $A$ is positive, and $A$, $B$, and $C$ are integers with greatest common divisor $1$.)

bIueb3rry Nov 4, 2024

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+263

Geometry

Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find read more ..

bIueb3rry Nov 4, 2024

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+250

Counting

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends, if every friend gets at least one sticker.

MEMEG0D Nov 4, 2024

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Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly $7$ chocolates?

MEMEG0D Nov 4, 2024

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Counting

How many solutions are there to the equation
u + v + w + x + y + z = 2,
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $1?$

MEMEG0D Nov 4, 2024

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