<h3>
Answer: D) 18</h3>
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Work Shown:
Here are the variables we're working with
- a = first term
- b = last term (aka nth term)
- n = number of terms
- S = sum of the first n terms
In this case, we know that
- a = unknown (what we want to solve for)
- b = -12
- n = 14
- S = 42
We can use this formula to help find the answer
S = (n/2)*(a+b)
This formula only works for arithmetic sequences
So,
S = (n/2)*(a+b)
42 = (14/2)*(a+(-12))
42 = 7(a-12)
42/7 = a-12
6 = a-12
6+12 = a
18 = a
a = 18 is the first term of this arithmetic sequence
That's why the answer is choice D.
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Side note: your book or your teacher may use the notation but I figured it would be easier to use 'a' and b in place of and respectively.
<h3>
Answer: C) 3</h3>
The rule we'll use is a^b*a^c = a^(b+c). So we add the exponents.
That means 5^n*5^3 = 5^(n+3)
So 5^n*5^3 = 5^6 turns into 5^(n+3) = 5^6
The bases are equal to 5, so the exponents be equal to one another.
n+3 = 6
n+3-3 = 6-3
n = 3
So 5^3*5^3 = 5^(3+3) = 5^6.
lets set up our problem.
We need to multiply our recipe by 2. soo..
×
But we have to change our 2 and 1/2 fraction into an improper fraction.
So you multiply the denominator and add the numerator to get the new numerator. So 2 x 2 +1 = 5 and the old denominator stays the same. 5/2
Now we can multiply.
× =
10 ÷ 2 = 5
So this means that you will need 5 pounds of cream cheese in order to make 2 cheese cakes. - Yum
Good Luck! :)
Answer:
A- sss
Step-by-step explanation: