maximum

256 Questions
128 Answers

0

89

1

+818

counting

I run a book club with $n$ people, not including myself. Every day, for $100$ days, I invite $14$ members in the club to review a book. What is the smallest positive integer $n$ so that I can avoid ever having the exact same group of $14$ members lire plus ..

maximum 29 oct. 2023

0

87

1

+818

need help

Solve the inequality -4(x + 4) > x + 7 + 8x + 21.

maximum 25 oct. 2023

0

106

2

+818

help plz

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ of the total load her four trucks combined can carry. lire plus ..

maximum 25 oct. 2023

0

88

1

+818

Inequality

Solve the inequality 2x - 5 <= -x + 12 - 7x + 18.

maximum 25 oct. 2023

0

46

1

+818

perpendicular bisector

Write the equation for the perpendicular bisector of the line segment connecting the points $(3,2)$ and $(-1,7)$ in the form $y = mx + b$.
Note: The perpendicular bisector of the line segment $\overline{AB}$ is the line that passes through the midpoint lire plus ..

maximum 25 oct. 2023

0

104

1

+818

line

Fill in the blanks with integers, and select the correct operator ($+$ or $-$), to give an equation whose graph is the line that passes through the point $(-1,8)$ and is parallel to the graph of $4x + 3y = -8 - x - 15y.$

maximum 24 oct. 2023

0

55

1

+818

equation of line

Line $\ell_1$ represents the graph of $3x + 2y = -14 - 8x + 5y$. Line $\ell_2$ passes through the point $(5,-6)$, and is perpendicular to line $\ell_1$. Write the equation of line $\ell_2$ in the form $y=mx +b$.

maximum 24 oct. 2023

0

59

1

+818

Inequality

I need help with this
Here is a summary of some inequality rules.
Fill in the blanks to complete the rules. (The first rule is already complete.)

You can add or subtract the same quantity from both sides. lire plus ..

maximum 24 oct. 2023

0

103

0

+818

polynomial problem

A polynomial with integer coefficients is of the form
\[12x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 24 = 0.\]
If $r$ is a rational root of this polynomial, then find the number of different possible values of $r.$

maximum 23 oct. 2023

0

119

0

+818

help needed

The entries in a certain row of Pascal's triangle are
\[1, n, \dots, n, 1.\]
The average of the entries in this row is 2. Find $n$.

maximum 23 oct. 2023

+818

-1

Do not post AoPS homework.

maximum20 janv. 2025