Last year Kareem had $ 20 , 000 to invest. He invested some of it in an account that paid 8 % simple interest per year, and he invested the rest of it in an account that paid 7 % simple interest per year. After one year, he received a total of $ 1610 in interest. How much did he invest in each account?

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?

A20? -foot ladder is placed against a vertical wall of a? building, with the bottom of the ladder standing on level ground 19 feet from the base of the building. how high up the wall does the ladder? reach?

What is f(3) for the quadratic functionf(x)=2x2 + x – 12? f -3g 3h 6i. 9