A bus traveled 205 1/5} miles in 3 3/5 hours. How many miles per hour did the bus travel? How far would the bus travel in 1 3/4 hours at the same speed? Explain your reasoning.

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?

Lines b and c are parallel. what is the measure of 2? m2 = 31° m2 = 50° m2 = 120° m2 = 130°

Find the area of the region that is inside r=3cos(theta) and outside r=2-cos(theta). sketch the curves.