The sum of 7 and twice a number, squared

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?

Asequence is a function whose is the set of natural numbers

Astrid spent $36 on new shoes. this was $12 less than twice what she spent on a new skirt. part a: which equation would solve for how much she spent on the skirt? part b: solve the equation in the workspace provided below. how much did astrid spend on her skirt?