exam Maths Puzzle Numerical Ability

Please help! Verify that the points (0, 0) and (a, 0) and (a/2,a/2) form the vertices of a right triangle. Work in terms of a.

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After an 8% increase in your wages, you receive $.94 more per hour. About how much did you recive per hour before the increase in your wages? a,b,c are three distinct real numbers and there are real numbers x,y such that a^3+ax+y=0,b^3+bx=y=0 and c^3+cx+y=0 Show that a+b+c=0