There would be 12 people at the party!
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.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Hope this helps!
Answer:
let the no.s be : x, x+1, x+2
then,
=> x + x+1 + x+2 = 183
=> 3x + 3 = 183
=> 3x = 183 - 3
=> x = 180/3
=> x = 60
therefore, the whole no.s are 60, 61, and 62
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<h3>Answer : y = ⅚x - 3</h3>
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<h3>Known</h3>
x1 = 6
y1 = 2
x2 = (-6)
y2 = (-8)
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<h3>Question</h3>
Equation of the line (y = mx + c)
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<h3>Way to do</h3>
#First, you find the gradient (m)

#Now use the formula of equation of the line
y - y1 = m(x - x1)
y - 2 = ⅚(x - 6)
y - 2 = ⅚x - 5
y = ⅚x - 5+2
y = ⅚x - 3
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