This exercise concerns subgroups of Z x Z. a. Let C1 = {(a, b) ∈ Zx Z | a = b} Show that C1 is asubgroup of Z x Z.
b. For each positive integer n >= 2, let Cn = {(Cn ={(a, b) ∈ Z x Z|a b (mod n)}.Show that Cn is a subgroup of Z x Z.
c. Show that every subgroup of Z xZ that contains C1 has the formCn, for some positive integer n.

As part of an annual fundraiser to raise money for diabetes research, diane joined a bikeathon. the track she biked on was 1,920 yards long. diane biked 38.5 laps. her sponsors agreed to donate an amount of money for each mile she biked. how many miles did she bike? first fill in the blanks on the left side using the ratios shown. then write your answer. given ratios: 5280ft / 1 mi , 1 mi /5280 ft , 1,920 yards / 1 lap , 1 lap / 1,920 yards , 3 ft / 1 yard , 1 yard / 3 ft. blanks: 38.5 laps / 1 yard x (blank) x (blank) x (blank) = (blank) miles i'm really confused on how to do this, and the explanations aren't exactly . if you could walk me through how to do this, it would be greatly appreciated.

In the given triangle, ∠aed ∼ ∠ abc, ad = 6.9, ae = 7.2, de = 5.2, and bc = 10.2. find the measure of bd and ce. round your answer to the nearest tenth.

What are the solutions of the following system? y=-2x^2 y=x-2