Answer:
19° I'm not completely sure but I think this is it
Answer:
0.00187393
Hope this helps! :)
Please mark me the Brainliest!
Part A
Answer: The common ratio is -2
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Explanation:
To get the common ratio r, we divide any term by the previous one
One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2
Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time
Side Note: each term is multiplied by -2 to get the next term
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Part B
Answer:
The rule for the sequence is
a(n) = (-2)^(n-1)
where n starts at n = 1
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Explanation:
Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio
The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)
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Part C
Answer: The next three terms are 16, -32, 64
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Explanation:
We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms
-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64
showing that the next three terms are 16, -32, and 64
An alternative is to use the formula found in part B
Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier
Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier
Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier
while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
c = cost per pound of chocolate chips
w = cost per pound of walnuts.
![\bf \stackrel{\textit{3 lbs of "c"}}{3c}+\stackrel{\textit{5 lbs of "w"}}{5w}~~=~~\stackrel{\textit{costs}}{15} \\\\\\ \stackrel{\textit{12 lbs of "c"}}{12c}+\stackrel{\textit{2 lbs of "w"}}{2w}~~=~~\stackrel{\textit{costs}}{33} \end{cases}\qquad \impliedby \textit{let's use elimination} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llccccccl} 3c+5w=15&\times (-4)\implies &-12c&+&-20w&=&-60\\ 12c+2w=33&&12c&+&2w&=&33\\ \cline{3-7}\\ &&0&&-18w&=&-27 \end{array}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7B3%20lbs%20of%20%22c%22%7D%7D%7B3c%7D%2B%5Cstackrel%7B%5Ctextit%7B5%20lbs%20of%20%22w%22%7D%7D%7B5w%7D~~%3D~~%5Cstackrel%7B%5Ctextit%7Bcosts%7D%7D%7B15%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7B12%20lbs%20of%20%22c%22%7D%7D%7B12c%7D%2B%5Cstackrel%7B%5Ctextit%7B2%20lbs%20of%20%22w%22%7D%7D%7B2w%7D~~%3D~~%5Cstackrel%7B%5Ctextit%7Bcosts%7D%7D%7B33%7D%20%5Cend%7Bcases%7D%5Cqquad%20%5Cimpliedby%20%5Ctextit%7Blet%27s%20use%20elimination%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllccccccl%7D%203c%2B5w%3D15%26%5Ctimes%20%28-4%29%5Cimplies%20%26-12c%26%2B%26-20w%26%3D%26-60%5C%5C%2012c%2B2w%3D33%26%2612c%26%2B%262w%26%3D%2633%5C%5C%20%5Ccline%7B3-7%7D%5C%5C%20%26%260%26%26-18w%26%3D%26-27%20%5Cend%7Barray%7D)
You will want to round to 977.259
look at the number to the right of 9, it is 8, and 8 > 5. IF the number is 5 or greater, round up.
so your answer is 977.260
hope this helps
