Lucy bought 9 yards of ribbon on a spool. She cut the ribbon into 1_2-yard pieces. Which equation represents the number of pieces of ribbon, n, Lucy has now?

Given that abcd is a parallelogram solve for m

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?

Place the following steps in order to complete the square and solve the quadratic equation,