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:
Step-by-step explanation:
81
=
3
4
and
27
=
3
3
, so this equation can also be written as
3
4
x
=
3
3
(
x
+
2
)
=
3
3
x
+
6
.
Since the bases are now the same, we can equate exponents to get
4
x
=
3
x
+
6
so that
x
=
6
(technically this equating of exponents requires the fact that exponential functions (with base not equal to 1) are one-to-one functions).
(do u understand?)
Answer:
2x^{4}
Step-by-step explanation:
You would subtract 7 and 5 and you would leave the exponent so it would be 2x^{4}
Answer:
0.012
Step-by-step explanation:
0.004 * 3 = 0.012
Answer: the domain of f(x)=2x+2 is all real numbers and the domain of g(x)=x^2 is (0, infinity)
Step-by-step explanation:
there is no horizontal asymptote given