The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. what is the 23rd term?

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?

Joanie wrote a letter that was 1 1/4 pages long. katie wrote a letter that was 3/4 page shorter then joagies letter. how long was katies letter

Use this graph to find the cost of 6 show tickets