A group of 8 friends shared all the sports cards in 3 packages. Each package contained 1,400 sports cards. Each friend received the same number of sports cards. How many sports cards did each friend receive?

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?

Which graph corresponds to the function f(x) = x2 + 4x – 1?

Non-euclidean geometry was discovered when, in seeking cleaner alternatives to the fifth postulate, it was found that the negation could also be true a. true b. false