A bakery sells mocha cupcakes and vanilla cupcakes. It sold 200 cupcakes in a day, and 44% of them were vanilla. How many of the cupcakes sold that day were mocha?

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?

What is the distance between the points 4,10 and -3,-14 on the coordinate plane

Solve each equation using the quadratic formula. find the exact solutions. 6n^2 + 4n - 11