Max walked 1 3/4 miles east and then he walked 2 7/10 miles west. which describes max's location from his original starting point?
a. 4 9/20 miles east
b. 4 9/10 miles west
c. 19/20 miles east
d. 19/20 miles west

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?

In the figure below, segment ac is congruent to segment ab: triangle abc with a segment joining vertex a to point d on side bc. side ab is congruent to side ac which statement is used to prove that angle abd is congruent to angle acd? segment ad bisects angle cab. triangle acd is similar to triangle abd. segment ad is congruent to segment ac. angle cab is congruent to angle cba.

Asurvey of 2,000 doctors showed that an average of 3 out of 5 doctors use brand x aspirin. how many doctors use brand x aspirin