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!!!?

In the following diagram it is given that dec,ab || dc, ad || eb, and ad is congruent to bc. a)why isn't abc a parallelogram even though it has a pair of parallel sides and a pair of congruent sides b)explain why be must be congruent to bc. further explain what type of triangle this makes triangle abc and what it tells you about angle 1 and angle 2c) finally why must angle 3 be congruent to angle 1? further, explain why we know that angle 3 is congruent to angle 2

The ph level of a blueberry is 3.1 what is the hydrogen-ion concentration [h+] for the blueberry

Given that the images represent 4 steps in the construction of a line segment congruent to a given line segment, which is step 3 in the construction?