Two tailors, danielle and tammy, sit down to do some embroidery. danielle can embroider 6 shirts
per hour, and tammy can get through 4 shirts per hour. in addition, the tailors had previously
finished some shirts. danielle has already completed 9 shirts, and tammy has completed 11
shirts. danielle and tammy decide to take a break when they have finished the same total number
of shirts. how many shirts, in total, will each tailor have finished? how long will that take?

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?

If f(x)= 3x+6 which of the following is the inverse of f(x)

What is x and y intercepts for y=x+7