jason received a $50 gift certificate for his birthday. he wants to buy a dvd and a poster from a media store. (assume that sales tax is included in the prices.) write and solve a linear inequality to show how much he would have left to spend after making these purchases.
all dvd's only $14.95
all cd's only $11.25
all posters only $10.99

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?

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

Solve 13 + w/7= -18 (w/7 is a fraction)