Let g be a group of order 9, and let x be a set of cardinality 8. suppose g admits a left group action on x. prove that this group must have a fixed point; that is, prove that there exists x ∈ x such that for all g ∈ g, we have g · x = x. equivalently, prove that there exists x ∈ x such that ox = {x}.

1-for what value of x is line a parallel to line b 2-for what value of x is line a parallel to line b

Which situation can be modeled by the inequality 5 + 10w ≥ 45? a. you start with $5 and save $10 a week until you have at least $45. b.you start with 5 baseball cards and purchase 10 cards every week until you have at most 45 cards. c.you start with 5 water bottles and purchases cases of 10 water bottles each until you have a total of 45 water bottles. d.you spend $5 plus $10 per week until you have less than $45.

Given: klmn is a parallelogram m? n=3m? k, lf ? kn , ld ? nm kf=2 cm, fn=4 cm find: lf, ld