Answer:
3 7/8
Step-by-step explanation:
6 1/4 = 25/4 and 2 5/8 = 19/8
25/4 - 19/8 = 3 7/8
The formula for the sum of n terms in an arithmetic progression is:
S = n/2 * (2a + (n-1)d)
Here, the common difference, d, is 8 and the first term, a, is 1. Substituting these into the formula, we get:
S = n/2 * (2*1 + 8(n - 1))
S = n + 4n² - 4n
S = 4n² - 3n
The answer is A.
There isn't enough info to prove the triangles to be congruent or not. So we can't say for sure either way.
We have angle CAD = angle ACB given by the arc markings, and we know that AC = AC due to the reflexive theorem. However we are missing one third piece of information.
That third piece of info could be....
- AD = BC which allows us to use SAS
- angle ACD = angle CAB which allows us to use ASA
- angle ABC = angle CDA which allows us to use AAS (slight variation of ASA)
Since we don't know any of those three facts, we simply don't have enough information.
side note: If AB = CD, then this leads to SSA which is not a valid congruence theorem. If we had two congruent sides, the angle must be between the two sides, which is what AD = BC allows.
