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kakasveta [241]
3 years ago
10

What is the simplest form of 2 square root of 2 over square root of 3 minus square root of 2

Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
7 0
The answer would be A or 2 square root of 6 + 4!! Hope that helped please give me 5 stars and a thanks! Thanks so much ! Do well on your test!
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If a=-2 and b=1, then 3a-2b=
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<span>If a=-2 and b=1, then
3a-2b
= 3(-2) -2(1)
= -6 -2
= -8</span>
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Which equation represents a line that passes through (2, –1/2) and has a slope of 3?
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Hello,

y+1/2=3(x-2)
or y=3x-13/2

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Haylee can run 16 laps in 8 minutes. If she continues at this rate, how many minutes will it take her to run 30 laps?
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3 years ago
Find the sum of the geometric series 512+256+ . . .+4
mario62 [17]

\bf 512~~,~~\stackrel{512\cdot \frac{1}{2}}{256}~~,~~...4

so, as you can see above, the common ratio r = 1/2, now, what term is +4 anyway?

\bf n^{th}\textit{ term of a geometric sequence}\\\\a_n=a_1\cdot r^{n-1}\qquad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\a_n=+4\end{cases}

\bf 4=512\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{4}{512}=\left( \cfrac{1}{2} \right)^{n-1}\\\\\\\cfrac{1}{128}=\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{1}{2^7}=\left( \cfrac{1}{2} \right)^{n-1}\implies 2^{-7}=\left( 2^{-1}\right)^{n-1}\\\\\\(2^{-1})^7=(2^{-1})^{n-1}\implies 7=n-1\implies \boxed{8=n}

so is the 8th term, then, let's find the Sum of the first 8 terms.

\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\n=8\end{cases}

\bf S_8=512\left[ \cfrac{1-\left( \frac{1}{2} \right)^8}{1-\frac{1}{2}} \right]\implies S_8=512\left(\cfrac{1-\frac{1}{256}}{\frac{1}{2}}  \right)\implies S_8=512\left(\cfrac{\frac{255}{256}}{\frac{1}{2}}  \right)\\\\\\S_8=512\cdot \cfrac{255}{128}\implies S_8=1020

7 0
3 years ago
Solve 2x-1/y = w+2/2z for w.
Tanzania [10]

Answer:

Step-by-step explanation:

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