What property is this?
(10b+12b)+7b=(12b+10b)+7b

Commutative Property

a + b = b + a

Because:

(10b+12b)+7b=(12b+10b)+7b

(10b + 12b) in the first bracket is the same as (12b + 10b) 

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.