Mike drank more than half the juice in his glass. what fraction of the juice could mike have drunk?

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Phillip had some bricks. he stacked them in 6 equal piles. which expression shows the number of bricks phillip put in each pile? let the variable m stand for the unknown number of bricks. m + 6 m÷6    m−6    6m

The graph shows the charges for a health club in a month. make a function table for the input-output values. writes an equation that can be used to find the total charge y for the number of x classes