All Questions ⁺⁰234620 Questions

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Number Theory

You have a total supply of $1000$ pieces of candy, and an empty vat. You also have a machine that can add exactly $52$ pieces of candy per scoop to the vat, and another machine that can remove exactly $39$ pieces of candy with a different scoop from read more ..

gnistory Sep 6, 2024

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+820

Geometry

Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle BEC if [ABC] = 14.

Hi6942O Sep 6, 2024

+1

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1

+820

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

Hi6942O Sep 6, 2024

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+617

Algebra

Find the area of the region enclosed by the graph of x^2+y^2=2x-6y+6+4x-4y+12

AnswerscorrectIy Sep 6, 2024

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+617

Algebra

The graph of $y = ax^2 + bx + c$ has an axis of symmetry of $x = 2.$ If $(4,7)$ lies on the graph, find another point on the graph.

AnswerscorrectIy Sep 6, 2024

Sep 5, 2024

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+617

Algebra

The parabola y = ax^2 + bx + c is graphed below. Find a \cdot b \cdot c. (The grid lines are one unit apart.)

AnswerscorrectIy Sep 5, 2024

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3

+1212

Algebra

Find the coordinates of the center of the circle.

Akhain1 Sep 5, 2024

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+1212

Algebra

For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.

Akhain1 Sep 5, 2024

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+820

Algebra

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be a sequence. If
\[a_n = a_{n - 1} + a_{n - 2}\]
for all $n \ge 3,$ and $a_{11} = 1$ and $a_{10} = 4,$ then find $a_6.$

Hi6942O Sep 5, 2024

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1

+820

Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 1$ and $a^2 + b^2 = 2,$ then what is $a^3 + b^3?$

Hi6942O Sep 5, 2024

Sep 4, 2024

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+864

Algebra

Find the constant k such that the quadratic 2x^2 + 3x + 8x - x^2 + 4x + k has a double root.

Rangcr897 Sep 4, 2024

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+864

Algebra

Find all values of $x$ such that $x^2 - 5x + 4 = -x^2 - 25x - 14$. If you find more than one value, then list your solutions, separated by commas.

Rangcr897 Sep 4, 2024

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+4

Factorize

Can anyone please explain how to arrive there? I don't understand it...

Aaronmath Sep 4, 2024

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+864

Algebra

One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 48$ and $ab^3 = 24$. What is the value of b in this ordered pair?

Rangcr897 Sep 4, 2024

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+96

Number Theory

A school orders $99$ 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?
$_5801.3_

bIueb3rry Sep 4, 2024

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+1039

Number Theory

The number $N$ is a multiple of $7$. The base $2$ representation of $N$ is
111100111010001ABC01_2.
Compute $A,$ $B,$ and $C$.

learnmgcat Sep 4, 2024

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+1039

Number Theory

Find a six-digit multiple of $64$ that consists only of the digits $2$ and $4$.

learnmgcat Sep 4, 2024

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