maximum

260 Questions
128 Answers

-2

113

1

+834

help quadratic

The graph of the line $y = 3x + a$ intersects the graph of the parabola $y = x^{2} + x$ in two points. If the distance between these points is $\sqrt{13}$, what is the value of $a$? Express your answer as a common fraction. lire plus ..

maximum 9 sept. 2023

-2

134

1

+834

divisors

How many integers from 1 to 9 are divisors of the five-digit number 24,519?

maximum 8 sept. 2023

-2

106

1

+834

coordinates

Can you help with this?
What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+2x-6y+3$?

maximum 8 sept. 2023

-2

143

1

+834

help with circles

I have this question on circles
For what value of $c$ will the circle with equation $x^2 - 10x + y^2 + 10y + c = 0$ have a radius of length 1?

maximum 8 sept. 2023

-2

123

1

+834

help with circles

Let $A$, $B$, $C$, and $D$ be points on a circle such that $AB = 11$ and $CD = 19.$ Point $P$ is on segment $AB$ with $AP = 7$, and $Q$ is on segment $CD$ with $CQ = 8$. The line through $P$ and $Q$ intersects the circle at $X$ and $Y$. If $PQ = 25$, find lire plus ..

maximum 6 sept. 2023

-2

95

5

+834

help plz

help I need to find lengths
$A$, $B$, $C$, and $D$ are points on a circle, and segments $\overline{AC}$ and $\overline{BD}$ intersect at $P$, such that $AP=8$, $PC=2$, and $BD=5$. Find $BP$, given that $BP < DP.$ lire plus ..

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maximum 6 sept. 2023

-2

136

1

+834

digits

All of the digits of a three-digit integer are distinct and non-zero. Furthermore, the three-digit integer is divisible by 13. Find the largest three-digit integer that has these properties.

maximum 5 sept. 2023

-2

153

0

+834

logarithms

If $\log_{b/a} a^2 b = 2$, where $a$ and $b$ are positive real numbers, then find $\log_{ab} b$.

maximum 5 sept. 2023

-2

147

0

+834

trig question

In right triangle $ABC$, we have $\angle BAC = 90^\circ$ and $D$ is the midpoint of $\overline{AC}$. If $AB = 7$ and $BC = 7 \sqrt{3}$, then what is $\tan \angle BDC$?

maximum 5 sept. 2023

-2

122

0

+834

help inverse

Let $f(x) = ax + b$ for $0 \le x \le 1$, where $a$ and $b$ are constants such that $a < 0$. What is the inverse of $f(x)$ in terms of $a$ and $b$?

maximum 3 sept. 2023

+834

-1

Do not post AoPS homework.

maximum20 janv. 2025