Plz help me 1.) The Zero Divisor Theorem. If {\displaystyle M\neq 0}{\displaystyle M\neq 0} has finite projective dimension and {\displaystyle r\in R}r\in R is not a zero divisor on {\displaystyle M}M, then {\displaystyle r}r is not a zero divisor on {\displaystyle R}R.

2.)Bass's Question. If {\displaystyle M\neq 0}{\displaystyle M\neq 0} has a finite injective resolution then {\displaystyle R}R is a Cohen–Macaulay ring.

I can't
figure this out!!!?

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?

Aline has a slope of and a y-intercept of –2. what is the x-intercept of the line?

The measure of an angle is 117°. what is the measure of a supplementary angle?