All Questions ⁺⁰237734 Questions

-1

110

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 Aug 22, 2023

0

127

0

help me plz

The function $f(x),$ defined for $x > 0,$ is positive, differentiable, and decreasing. The function $f(x)$ has the following property: Let $P$ be a point on the graph, and draw the tangent to the graph at $P.$ Let the tangent meet the $x$-axis read more ..

Guest Aug 22, 2023

0

106

6

Difficult problems.

1. In triangle PQR let X be the intersection of the angle bisector of angle P with side QR, and let Y be the foot of the perpendicular from X to side PR. If PQ = 9, QR = 10 ,and PR = 17 then compute the length of XY.
2. The read more ..

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Guest Aug 22, 2023

0

111

2

expected value

A standard deck of cards contains $52$ cards. These $52$ cards are arranged in a row, at random. Find the expected number of pairs of adjacent cards that are both Aces.

Guest Aug 22, 2023

Aug 21, 2023

0

114

3

+8

counting basics

How many positive five digit numbers have a 1, 3, 7 or 5 in them?

emotionaldamage Aug 21, 2023

0

126

2

+8

counting 'basics'

At a wedding, the bride and groom want to take a picture in a line with their 5 other friends.
However, the bride and groom have requested that they be placed next to each other. How
many ways can they line up for the picture?

emotionaldamage Aug 21, 2023

-2

109

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 Aug 21, 2023

-2

111

0

+818

gcd

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

maximum Aug 21, 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 read more ..

maximum Aug 21, 2023

-1

120

2

+82

HELPPP!!!!!

What is the $x$-coordinate of the point on the $x$-axis that is equidistant from points $A( -2, 0)$ and $B(0,4)$?

xxyoohoo Aug 21, 2023

-1

141

3

Help with simplifying

How do I simplify this?
Thank you!

Guest Aug 21, 2023

0

134

0

help with geometry

Let $I$ be the incenter of triangle $ABC$. If $AB = AC$, $BC = 30,$ and $IC = 20$, then find the inradius of the triangle.

Guest Aug 21, 2023

0

119

2

In triangle ABC, point X is on side BC such that AX = 13, BX = 10, CX = 4

In triangle ABC, point X is on side BC such that AX = 13, BX = 10, CX = 4 ,and the circumcircles of triangles ABX and ACX have the same radius. Find the area of triangle ABC.
I have had a look at similar questions to this, read more ..

Guest Aug 21, 2023

-2

130

1

+818

quadratic

Find the value of $c$ so that the quadratic equation $4x^2 + 2x + c = 3x^2 - 8x$ has exactly one solution in $x$.

maximum Aug 21, 2023

-2

92

1

+818

quadratic

Find the value of $h$ such that the quadratic equation $7x^2 + 5x = h + 6x^2 + 3x$ has exactly one real solution in $x$.

maximum Aug 21, 2023

0

138

0

polynomial

Let $f(x)$ be a polynomial with integer coefficients. There exist distinct integers $p,$ $q,$ $r,$ $s,$ $t$ such that
\[f(p) = f(q) = f(r) = f(s) = 1\]
and $f(t) > 1.$ What is the smallest possible value of $f(t)?$

Guest Aug 21, 2023

0

140

0

inequality

Triangle ABC has sides a, b, and c, and circumradius R. Prove that a^2 + b^2 + c^2 <= 9R^2. When does equality occur?

Guest Aug 21, 2023

-2

101

0

+818

terminating decimals

Find the number of integers $n$ in the interval $1 \le n \le 120$ such that the decimal representation of $\frac{n}{123}$ terminates.

maximum Aug 21, 2023

-2

123

0

+818

help with parabola

Points $A$ and $B$ lie on the graph of $y=3x^2-5x-3+2x-11$, and the origin is the midpoint of $\overline{AB}$. Find the square of the length of $\overline{AB}$.

maximum Aug 21, 2023

0

126

0

coordinates

The circles $x^2 + y^2 = 4$ and $(x - 5)^2 + (y - 8)^2 = 60$ intersect in two points $A$ and $B.$ Find the distance $AB$.

Guest Aug 21, 2023

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