Determine the length of the chord that is 8 inches from the center of a circle with a radius of 17 inches?

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?

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Which steps could be part of the process in algebraically solving the system of equations, y+5x=x^2+10 and y=4x-10