I have two questions. Please try to answer both! How many non-similar triangles have angles whose degree measures are distinct positive integers in an arithmetic progression?

In an arithmetic sequence a7 −2a4 = 1, a3 = 0. Find the common difference.

Thank you!

(a)59

(b)

Step-by-step explanation:

Part A

The nth term of an arithmetic sequence,

Let the first angle of the triangle =a

Let the common difference = d.

Since the measures of the angles are in an arithmetic progression

We have:

a + (a + d) + (a + 2d) = 180

3a+3d=180

a+d=60

Since a or d cannot be equal to zero, the minimum possible values of a and d is 1 and the maximum possible values of a and d is 59.

Therefore, there are 59 non-similar triangles.

Part B

In an arithmetic sequence

Common difference,

Therefore:

gaddgad

step-by-step explanation:

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?