All Questions ⁺⁰235001 Questions

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+8

Number System

For distinct positive integers a, b, and c, N = 5a + 3b + 5c = 4a + 5b + 4c. If 131 < N < 150, then
what is the maximum possible value of a + 2b + 3c?

drax567 Oct 9, 2024

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+165

Algebra

Simplify \dfrac{1}{\sqrt2+sqrt3}+\dfrac{1}{\sqrt2-sqrt3}.

MEMEG0D Oct 9, 2024

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+165

Algebra

Find all ordered pairs x, y of real numbers such that x+y=10 and x^2+y^2=64.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

MEMEG0D Oct 9, 2024

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1

+137

Number Theory

How many numbers between $1000$ and $2000$ leave a remainder of $3$ when divided by $21?$

bIueb3rry Oct 9, 2024

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+260

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $3$ hours and $20$ minutes, but when there is a wind blowing from Penthaven to Jackson at $70$ miles per hour, the trip takes $3$ hours read more ..

nathanl6656 Oct 9, 2024

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1

+260

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

nathanl6656 Oct 9, 2024

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+260

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

nathanl6656 Oct 9, 2024

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1

+21

Simplify

Dysoncloud Oct 9, 2024

Oct 8, 2024

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+732

Algebra

What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?

magenta Oct 8, 2024

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+732

Algebra

There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$

magenta Oct 8, 2024

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+732

Algebra

Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.

magenta Oct 8, 2024

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+904

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 ..

Rangcr897 Oct 8, 2024

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+260

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $100$ square foot wall in $10$ minutes, then how long would it take the $15$ members to paint a $100$ square foot wall, in minutes?

nathanl6656 Oct 8, 2024

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+260

Algebra

Find the largest integer $k$ such that the equation
5x^2 - kx + 8 - 20x^2 + 45 = 0
has no real solutions.

nathanl6656 Oct 8, 2024

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1

+260

Algebra

Find the discriminant of the quadratic 5x^2 - 2x + 8 - 2x^2 + 6x + 2 - 2x^2 + 4x - 1.

nathanl6656 Oct 8, 2024

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+904

Number Theory

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 Oct 8, 2024

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1

+904

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 Oct 8, 2024

Oct 7, 2024

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+1489

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 $ABCD$?

parmen Oct 7, 2024

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+1489

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 $(a,b)$.

parmen Oct 7, 2024

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