Your uncle is planting an 8-foot tall tree. he ties support wires to the tree, 1 foot from the top, and ties them to posts on the ground, 4 feet from the trunk of the tree. how long is each wire to the nearest tenth of a foot?

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?

Abus ride for a senior citizen cost $1.25. a monthly pass costs $35. write and inequality that represents the number of times a senior citizen must ride the bus for the monthly pass to be a better deal.

Which of the following is the result of expanding the series