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- What is the largest number $c$ such that $2x^2+5x+c=0$ has at least one real solution? Express your answer as a common fraction.
- Square $ABCD$ has side lengths of 13 units. Point $E$ lies in the interior of the square such that $AE = 5$ units and $BE = 12$ units. What is the distance from $E$ to side $AD$?
- Compute the sum of all possible values for $x,$ where $(x, y)$ is a solution to the system of equations \\\\[\\\\begin{aligned} x &= y^2 - 6y + 5, \\\\\\\\ y &= |x|. \\\\end{aligned}\\\\]
- In this problem, $a$ and $b$ are positive integers.\\n\\nWhen $a$ is written in base $9$, its last digit is $5$.\\n\\nWhen $b$ is written in base $6$, its last two digits are $53$.\\n\\nWhen $a-b$ is written in base $3$, what are its last two digits? Assume $a-b$ is positive.
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