Homer is giving some cookies to each of his three brothers. to the oldest, he gives half of the cookies and half a cookie. he then gives half of what is left and half a cookie to his second brother. finally, he gives half of what is now left and half a cookie to his youngest brother. at no time is a cookie broken or cut. how many cookies did homer have to begin with?

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?

Name the most appropriate metric unit for each measurement

Deshawn uses 3/4 of a box of rice to cook dinner the portion he uses weighs 12 ounces right and solve an equation to find the weight of the full box of rice