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Gemiola [76]
3 years ago
9

How do you solve this equation ​

Mathematics
1 answer:
lesantik [10]3 years ago
6 0

\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ e^{x-6}=\left( \cfrac{1}{e^4} \right)^{x+2}\implies e^{x-6}=\left( e^{-4} \right)^{x+2}\implies \stackrel{\textit{same bases, same exponents}}{e^{x-6}=e^{-4x-8}} \\\\\\ x-6=-4x-8\implies 5x=-2\implies x=-\cfrac{2}{5}

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First we gather all the information we have about the amount of miles that Carolyn runs:
Monday, Wednesday, Friday: 4 1/2 miles
Tuesday, Saturday: 2 3/4 miles
And the question is the amount of miles that she runs in 4 weeks.
So lets begin by calculating the amount of miles she runs in one week, then we just multiply by 4 and we'll have the final answer.
So, we have to add 4 1/2 three times (Monday, Wed, Friday), and 2 3/4 two times (Tuesday, Sat):
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lets add the whole parts and the fraction parts apart:
1 week Miles = (4 + 4 + 4 + 2 + 2) + (1/2 + 1/2 + 1/2 + 3/4 + 3/4)
1 week <span>Miles = (16) + (3/2 + 6/4)
</span>we can reduce the last fraction:
1 week <span>Miles = (16) + (3/2 + 3/2)
</span>1 week <span>Miles = (16) + (6/2)
</span>1 week <span>Miles = (16) + (3)
</span>1 week <span>Miles = 19
</span>therefore Carolyn runs 19 miles each week, so for 4 weeks we have to add 19 four times or multiply it by 4, is the same:
4 weeks <span>Miles = 4*19
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hence Carolyn runs 76 miles in 4 weeks.</span>
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