Answer: it will take 125 additional minutes for both costs to be equal.
Step-by-step explanation:
Let a represent the number of additional minutes that it will it take for the two to be the same.
Company A charges a flat fee of 59.99 a month and .43 additional minutes. This means that the total cost of a additional units would be
0.43x + 59.99
Company B charges 69.99 a month and .35 for additional minutes. This means that the total cost of a additional units would be
0.35x + 69.99
For the cost of the two plans to be the same, it means that
0.43x + 59.99 = 0.35x + 69.99
0.43x - 0.35x = 69.99 - 59.99
0.08x = 10
x = 125
Answer:
8 days
Step-by-step explanation:
On day 8, Isabella will save 256 nickels, bringing her total to 510.
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The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.
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The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.
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The number of nickels saved on day n is a geometric sequence with first term 2 and common ratio 2. The n-th term of the sequence is ...
an = a1·r^(n-1) = 2·2^(n-1) = 2^n
The sum of n terms of the sequence is ...
S = a1(r^n -1)/(r -1) = 2(2^n -1)/(2-1)
S = 2^(n+1) -2
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We want S > 500, so ...
500 < 2^(n+1) -2
502 < 2^(n+1)
251 < 2^n
log(251) < n·log(2)
n > log(251)/log(2)
n > 7.97 . . . . . . . . 8 days or more to save more than 500 nickels
5c^5 + 60c^4 + 180c^3
find the GCF, 5c³
5c³(5c^5 + 60c^4 + 180c^3/ 5c^3)
5c³(c² + 12c + 36)
5c³(c² + 2(c)(6) + 6²)
5c³(c + 6)² <<< the answer.
hope this helps, God bless!
Answer:
81, 64, 47, 30, <u>13, -4</u>
The plot and slot formula
