maximum

256 Questions
128 Answers

-2

108

1

+818

solving an equation

How do you solve this?
Find all values of $a$ such that $\frac{a-3}{\sqrt{a}} = -a \sqrt{a}$.

maximum 25 août 2023

-2

87

1

+818

help stuck

Help I'm really stuck here
Ruth has a beaker containing a solution of 800 mL of acid and 200 mL of water. She thinks the solution is a little strong, so she drains 150 mL from the beaker, adds 150 mL of water, and stirs the solution. lire plus ..

maximum 25 août 2023

-2

88

1

+818

domain

Find the domain of the function $$f(x)=\sqrt{-10x^2-11x+6+9x^2-5x}.$$

maximum 22 août 2023

-2

101

2

+818

gcd

Find the greatest common divisor of $2^{1001}-1$ and $2^2-1$.

maximum 22 août 2023

-1

85

1

+818

domain

Find the domain of the function $$f(x)=\sqrt{3+5-\sqrt{x}}.$$

maximum 22 août 2023

-1

84

1

+818

domain

Find the smallest integer $c$ such that the domain of the function $f(x)=\frac{x^2+1}{x^2-x+c+3x^2-7x}$ is all real numbers.

maximum 22 août 2023

-1

104

0

+818

domain

Find the values of $x$ that are not in the domain of
\[f(x)=\frac{1}{(x^2+3x-4)+(x^2-9x+20)}.\]

maximum 22 août 2023

-2

104

1

+818

quadratic

The roots of the equation $2x^2 - 5x - 4 = -x^2 - 7x + 6$ can be written in the form $x = \frac{m \pm \sqrt{n}}{p}$, where $m$, $n$, and $p$ are positive integers with a greatest common divisor of $1$. What is the value of $n$?

maximum 21 août 2023

-2

107

0

+818

gcd

Find the greatest common divisor of $2^{1001}-1$ and $2^2-1$.

maximum 21 août 2023

-2

87

1

+818

bisectors

Let $I$ be the incenter of triangle $ABC$. If $AB = BC = 4$ and $\angle B = 60^\circ$, then find the length $BI$.
Express your answer in the form $a + b\sqrt{c},$ where $a,$ $b,$ and $c$ are integers, and $c$ is not divisible by any perfect lire plus ..

maximum 21 août 2023

+818

-1

Do not post AoPS homework.

maximum20 janv. 2025