Prove Propositions 32 and 33 of the Maasei Hoshev: a) 1 + (1 + 2) + (1 + 2 + 3) + ... + (1 + 2 + ... + n) =    1 2 + 32 + ... + n 2 , if n is odd; 2 2 + 42 + ... + n 2 , if n is even.

Look at this system of equations. -3x + 3y = 12 y = x + 4 the solution set of this system is best explained by which of these statements? a) the graphs of the equations are the same line because the equations have the same slope and the same y-intercept. the system has infinitely many solutions. b) the graphs of the equations are parallel lines because they have the same slope but different y-intercepts. the system has no solution. c) the graphs of the equations are lines that intersect at one point because the equations have the same slope but different y-intercepts. the system has exactly one solution. d) the graphs of the equations are lines that intersect at one point because the equations have the same slope and the same y-intercept. the system has exactly one solution.