[["Problem: Solve for $x$: $$\\left(\\frac{1}{25}\\right)^{x + 2} = 125^{-x}.$$\nAnswer:",["\n"]],["Problem: Find the constant $c$ such that $$(x^2-4x+3)(x+5) - (x^2+4x-5)(x-c)=0$$ for all $x.$\nAnswer:",["\n"]],["Problem: Let $x$ be a value such that $9x^2 - 18x - 16 = 0$ and $15x^2 + 28x + 12 = 0.$ What is the value of $x$? Express your answer as a simplified common fraction.\nAnswer:",["\n"]],["Problem: The parabola $y=ax^2+bx+c$ has vertex $(p,p)$ and $y$-intercept $(0,-p)$, where $p\\neq\n0$. What is $b$?\nAnswer:",["\n"]],["Problem: Given that $f(x)$ is a function such that $f(1)=2$, $f(4)=3$, $f(7)=4$, and $f^{-1}(x)$ is the inverse of $f(x)$, what is $f^{-1}(f^{-1}(3))$?\nAnswer:",["\n"]],["Problem: Rationalize the denominator: $\\frac{5}{\\sqrt{3}}$ .\nAnswer:",["\n"]],["Problem: If the roots of the quadratic equation $\\frac12x^2+99x+c=0$ are $x=-99+\\sqrt{8001}$ and $x=-99-\\sqrt{8001}$, then what is the value of $c$?\nAnswer:",["\n"]],["Problem: Find the sum of the slope and $y$-intercept of the line through the points $(7,8)$ and $(9,0)$.\nAnswer:",["\n"]],["Problem: The sum of the two $5$-digit numbers $AMC10$ and $AMC12$ is $123422.$ What is $A + M + C?$\nAnswer:",["\n"]],["Problem: Let $0 \\le a, b, c \\le 5$ be integers. For how many ordered triples $(a,b,c)$ is $a^2b+b^2c+c^2a-ab^2-bc^2-ca^2 = 0$?\nAnswer:",["\n"]]]
