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bogdanovich [222]
4 years ago
7

Simplify. x² − x − 30÷x² − 12 x + 36

Mathematics
1 answer:
madreJ [45]4 years ago
7 0
(x² - x - 30)/(x² - 12x + 36)
Factor: [(x-6)(x+5)]/[(x-6)(x-6)]
Simplify: (x + 5)/(x - 6)

Reminder that x ≠ 6 (because it would make the expression undefined)

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117. Sami opens an account and deposits $100 into it at the end of each month. The account earns 2% per year compounded monthly.
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Answer:

The explicit function is:

S_{n} =Pz^{n-1} +C(\frac{z^{n-1}-1}{z-1} )

where

z=(1+\frac{0.02}{12})

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Step-by-step explanation:

Expanding a few steps of the compound interest:

S_{1}=100\\S_{2}=S_{1}(1+\frac{0.02}{12})+100\\S_{3}=S_{2}(1+\frac{0.02}{12})+100\\...\\S_{n}=S_{n-1}(1+\frac{0.02}{12})+100

We can write:

(1+\frac{0.02}{12})=z

100=C for deposits

Then, expanding the previous equations would yield:

S_{1}=C\\S_{2}=Cz + C\\S_{3}=Cz^{2}+Cz + C\\S_{n}=Cz^{n-1} +...+Cz+C

This is a geometric series form, which can be simplified to:

S_{n}=C(\frac{z^{n}-1}{z-1} )

plugin in the values for the 12 month gives:

S_{12}=100(\frac{(1+\frac{0.02}{12})^{12} -1}{\frac{0.02}{12}})=1211.0613

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Answer:

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Answer:

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