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Vinil7 [7]
3 years ago
6

At a party, everyone shook hands with everybody else. These were 66 handshakes. How many people were at the party?

Mathematics
1 answer:
nignag [31]3 years ago
7 0
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n. Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66. This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
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y-y_1=m\left(x-x_1\right)

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In our case:

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substituting the values m = -5/6 and the point (1, -5) in the point-slope form of the equation of the line

y-y_1=m\left(x-x_1\right)

y-\left(-5\right)=-\frac{5}{6}\left(x-1\right)

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Thus, the point-slope form of the equation of the line is:

y+5=-\frac{5}{6}\left(x-1\right)

Question 4)

Given

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substituting the values m = -7/2 and the point (-1, 5) in the point-slope form of the equation of the line

y-y_1=m\left(x-x_1\right)

y-5=-\frac{7}{2}\left(x-\left(-1\right)\right)

y-5=-\frac{7}{2}\left(x+1\right)

Thus, the point-slope form of the equation of the line is:

y-5=-\frac{7}{2}\left(x+1\right)

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