maximum

260 Questions
128 Answers

-3

157

1

+835

asymptotes

How many vertical asymptotes does the graph of $y = \frac{1}{x^3-3x^2+7x-15}$ have?

maximum 28.08.2023

-3

157

2

+835

triangles

Find the radius of the incircle of triangle $ABC$.

maximum 28.08.2023

-1

93

2

+835

discriminant question

I choose a random integer $n$ between $1$ and $10$ inclusive. What is the probability that for the $n$ I chose, there exist no real solutions to the equation $x^2 - 8x + n = 0$? Express your answer as a common fraction.

maximum 27.08.2023

-1

114

1

+835

help quadratic

The roots of the quadratic equation $3x^2+5x+k = 0$ are $\frac{-5\pm i\sqrt{131}}{6}$. What is $k$?

maximum 27.08.2023

-1

82

1

+835

quadratic equations

The roots of the quadratic equation $x(x-3)=1+8x-5$ may be expressed in the form $\frac{a+\sqrt{b}}{c}$ and $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are prime numbers. Find $abc$.

maximum 27.08.2023

-2

1

84

1

+835

coordinates

The point $(x,y)$ in the coordinate has a distance of $6$ units from the $x$-axis, a distance of $15$ units from the point $(5,7)$, and a distance of $\sqrt{n}$ from the origin. If both $x$ and $y$ are negative, what is $n$?

maximum 26.08.2023

-2

93

1

+835

help quadratic

There is exactly one value of $x$ for which the distance from $(5,6)$ to $(3x-1,ax+5)$ is $4$. If $a \neq 0,$ what is $a$?

maximum 26.08.2023

-2

115

1

+835

quadratic

Find the non-zero value of $c$ for which there is exactly one positive value of $b$ for which there is one solution to the equation $x^2 + (b + 4c)x + c^2 = 0$.

maximum 26.08.2023

-1

63

1

+835

worker question

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $8$ days earlier. If the job needs to completed $28$ days earlier, how many additional workers should be hired?

maximum 25.08.2023

-2

101

1

+835

rate question

I have tried to solve this problem. Can anyone help?
Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $5$ km mehr ..

maximum 25.08.2023

+835

-1

Do not post AoPS homework.

maximum20.01.2025