If  m ≠ 0  has finite projective dimension (i. e.,  m  has a finite projective (=free when  r  is local) resolution: the projective dimension is the length of the shortest such) and  r ∈ r  is not a zerodivisor on  m, then  r  is not a zerodivisor on  r.

State whether weight is a function of height for the six students and explain. a. yes, height is a function of weight because two students weigh 165 pounds but have different heights. b. no, height is not a function of weight because two students weigh 165 pounds but have different heights. c. yes, weight is a function of height because for each value of height there is one corresponding value of weight. d. no, weight is not a function of height because there is not enough data to determine a function.

Draw a tape diagram to represent each situation.for some of the situations,you need to decide what to represent with a variable andre bakes 9 pans of brownies.he donates 7 pans to the school bake sale and keeps the rest to divide equally among his class of 30 students

Axel follows these steps to divide 40 by 9: start with 40. 1. divide by 9 and write down the remainder. 2. write a zero after the remainder. 3. repeat steps 1 and 2 until you have a remainder of zero. examine his work, and then complete the statements below.