ANSWER ASAP CORRECT ANSWER GETS BRAIN THINGY!!!
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Answer:
Step-by-step explanation:
The formula for this is
∠G = 1/2(arcEH - arcHF)
We have angle G (5x - 10) and we have arcEH (195) so we have to solve for x to find the measure of arcEHF so we can add arcEH + arcHF = arcEHF
Filling in the formula with what we have:
which simplifies down a bit to
which simplifies down a bit more to
Multiply both sides by 2 to get rid of the fraction and get:
2(5x - 10) = 178 - 8x which of course simplifies to
10x - 20 = 178 - 8x. Now add 8x to both sides and at the same time add 20 to both sides to get:
18x = 198 so
x = 11. Now we can find the measure of arcHF:
arcHF is 8x + 17, so arcHF is 8(11) + 17 which is 105°.
arcEH + arcHF = arcEHF so
195 + 105 = arcEHF so
arcEHF = 300°
In an arithmetic sequence, consecutive terms have a fixed distance d between them. If a₁ is the first term, then
2nd term = a₂ = a₁ + d
3rd term = a₃ = a₂ + d = a₁ + 2d
4th term = a₄ = a₃ + d = a₁ + 3d
and so on, up to
nth term =
so that every term in the sequence can be expressed in terms of a₁ and d.
6. It's kind of hard to tell, but it looks like you're given a₁₃ = -53 and a₃₅ = -163.
We have
a₁₃ = a₁ + 12d = -53
a₃₅ = a₁ + 34d = -163
Solve for a₁ and d. Eliminating a₁ and solving for d gives
(a₁ + 12d) - (a₁ + 34d) = -53 - (-163)
-22d = 110
d = -5
and solving for a₁, we get
a₁ + 12•(-5) = -53
a₁ - 60 = -53
a₁ = 7
Then the nth term is recursively given by
and explicitly by
7. We do the same thing here. Use the known terms to find a₁ and d :
a₁₉ = a₁ + 18d = 15
a₃₈ = a₁ + 37d = 72
⇒ (a₁ + 18d) - (a₁ + 37d) = 15 - 72
⇒ -19d = -57
⇒ d = 3
⇒ a₁ + 18•3 = 15
⇒ a₁ = -39
Then the nth term is recursively obtained by
and explicitly by
8. I won't both reproducing the info I included in my answer to your other question about geometric sequences.
We're given that the 1st term is 3 and the 2nd term is 12, so the ratio is r = 12/3 = 4.
Then the next three terms in the sequence are
192 • 4 = 768
768 • 4 = 3072
3072 • 4 = 12,288
The recursive rule with a₁ = 3 and r = 4 is
and the explicit rule would be