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-BARSIC- [3]
3 years ago
11

My roommate and I are having a house party. We invite 15 couples. At the party, everyone must shake hands with everyone whom the

y do not already know. At the end of the party, I can't remember the number of people I have met, so I go ask all other people at the party how many hands they have shaken, and they each tell me a different number. You do not shake hands with yourself or your 'partner' (the person with whom you came). How many hands did my roommate shake?
Mathematics
1 answer:
Elanso [62]3 years ago
7 0

Answer: There are 105 handshakes that his roommate shake.

Step-by-step explanation:

Since we have given that

Number of couples = 15

As we know the "Handshaking lemma"

Here, n = 15

So, the number of handshakes would be

\dfrac{n(n-1)}{2}\\\\=\dfrac{15(15-1)}{2}\\\\=\dfrac{15\times 14}{2}\\\\=15\times 7\\\\=105

Hence, there are 105 handshakes that his roommate shake.

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the solutions to the related equation are 0,2,3 .

<u>Step-by-step explanation:</u>

Here we have , function  f(x) = x3 – 5x2 + 6x . Graph of this function is given below  . We need to find What are the solutions to the related equation . Let's find out:

Solution of graph means the  value of x at which the value of f(x) or function is zero . We can determine this by seeing the graph as at what value of x does the graph intersect or cut x-axis !

At x = 0 .

From the graph , at x=0 we have f(x) = 0 i.e.

⇒ f(x) = x^3- 5x^2 + 6x

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At x = 2 .

From the graph , at x=2 we have f(x) = 0 i.e.

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