messages listlengths 2 2 |
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"role": "user",
"content": "A linear function $f(x) = ax + b$ is defined on the interval $[-10, 10]$ such that the sum of the absolute values of $f(x)$ at $100$ evenly spaced points in the interval is equal to $1000$. Let $M$ be the maximum possible value of $|f(0)|$ and let $m$ be the minimum possible va... |
[
{
"role": "user",
"content": "In a mathematical competition, six teams are participating, and each team has four members. The teams are arranged in two rows of three teams each, with each team facing another team in the opposite row. The sum of the ages of the members of each team is written on a card, and ... |
[
{
"role": "user",
"content": "All sides of the convex hexagon $ABCDEF$ are of equal length, and $\\angle A = \\angle B = \\angle C = 90^\\circ$. What is the degree measure of $\\angle F$?\nPlease reason step by step, and put your final answer within \\boxed{{}}.\n"
},
{
"role": "assistant",
"con... |
[{"role":"user","content":"The number $x$ can be expressed as a three-place decimal $0.abc,$ where $(...TRUNCATED) |
[{"role":"user","content":"A function $f(x)$ is defined for all positive integers $x$, such that:\n\(...TRUNCATED) |
[{"role":"user","content":"Let $O$ be the origin. There exists a scalar $k$ so that for any points (...TRUNCATED) |
[{"role":"user","content":"Let $\\alpha$ and $\\beta$ be two distinct complex numbers such that $\\a(...TRUNCATED) |
[{"role":"user","content":"Let $f(x) = x^3 + ax^2 + bx + c$ be a cubic polynomial with rational coef(...TRUNCATED) |
[{"role":"user","content":"A prism has a base of a square with a side of 20 cm. Inside the prism, th(...TRUNCATED) |
[{"role":"user","content":"Find the maximum value of \n\\[abc + def\\]\nwhere $a, b, c, d, e, f$ are(...TRUNCATED) |
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