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zhannawk [14.2K]
2 years ago
11

N/8 = 11/5 what is n?

Mathematics
1 answer:
Reika [66]2 years ago
3 0

Answer:

n = 88/5

Step-by-step explanation:

Clear out the fractions by multiplying both sides by 8:

n = 88/5

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In triangle ABC, medians AD, BF, and CE intersect at G. What is the length of GE is CH=12?
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You do not have any point labeled "H" in your diagram.

What I can tell you is that point "G" (where all 3 medians meet) is called a centroid.
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the distance from EACH vertex to the centroid (point G) is TWICE the distance from the centroid to the side.
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Find a and b such that gcd(a, b) = 14, a &gt; 2000, b &gt; 2000, and the only prime divisors of a and b are 2 and 7.
choli [55]

Answer:

a = 2^\alpha.14 \ ,\alpha\geq 8\\b = 7^\delta.14 \ , \delta\geq 3

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As 2  and 7 are the only prime divisors of both a and b we know that both can be written as:

a = 2^\alpha . 7^\beta \ , \alpha ,\beta\ \in \mathbb{N}_{0}\\b = 2^\gamma . 7^\delta \ , \gamma ,\delta\ \in \mathbb{N}_{0}\\

Where \mathbb{N}_{0} is the set of all natural numbers adding the zero (careful because this part is important as I'll explain next).

We also know that 14 divides both numbers and that is actually the greatest common divisor between them. So we can rewrite a and b as follows:

a = 2^\alpha . 7^\beta.14 \ , \alpha ,\beta\ \in \mathbb{N}_{0}\\b = 2^\gamma . 7^\delta.14 \ , \gamma ,\delta\ \in \mathbb{N}_{0}\\

Why do I write them like this? Because this way is easier to observe that if \alpha and \gamma were both greater than zero, then 28 would divide both hence 14 wouldn't be their g.c.d.. Likewise, if \beta and \delta were both greater than zero, then 98 would divide both and once again, 14 wouldn't be their g.c.d.

So either of them has to be equal to zero. And then we have that

a = 2^\alpha.14 \\b = 7^\delta.14

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