As Felicia gets on the freeway to drive to her cousin's house, she notices she is a little low on gas. There is a gas station at the exit she usually takes, and she wonders if she will
have to get gas before then. She sets her cruise control at the speed limit of 60 mph and
the freeway portion of the drive takes about an hour and fifteen minutes. Her car gets
25 miles per gallon on the freeway, and gas costs $1.85 per gallon.

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?

Consider the function f(x)=−2/3x+5 . what is f(1/2) ? enter your answer, as a simplified fraction, in the box. f(1/2)=

Astudent simplified a rational expression as shown.