An investment of 8000 in a certain certificate of deposit doubles in value every several year. The function that models the growth of this investment fx)=8000x2 to the x power, where x is the number of doubling periods. If the Investor does not withdraw any money form his CD, how much money will be available for withdraw after 28 years.

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?

Np4=12np2 with clear explanation.

Will give are given that xy is parallel to zw. if xz is a transversal that intercepts xy and zw, angle angle alternate interior angles. since xy is parallel to zw, we know that these angles are we also know that angle xvy and angle zvw are , and thus congruent. we can conclude that △xyv ~ △zwv using the similarity theorem.