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3 years ago

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

Mathematics

2 answers:

Gnoma [55]3 years ago

3 0

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!

nataly862011 [7]3 years ago

3 0

Answer:

Uhm. You didnt get this from me, But If there was 66 handshakes, and each person shakes another persons hand, all you gotta do is divide it by 2 and you get 66.

Step-by-step explanation:

Im right ik ty ;)

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Vlada [557]

9 - [42 - (3 + 2)]

Parentheses first:

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Brackets next:

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Now subtract to get -28

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Find the indicated arc and angle measures:

nevsk [136]

Answer:

arc AB = 70°

arc BC = 110°

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Step-by-step explanation:

Since these angles are not inscribed, but are at the center point of the circle, the angles and arcs will be the same measure.

Solve for arc AB:

Angle AFB = 70°, so arc AB = 70°

Solve for arc BC:

Angle AFC is a straight angle so it is 180°. To find angle BFC, subtract angle AFB from 180°.

180 - 70 = 110°

Since angle BFC = 110°, arc BC = 110°

Solve for arc ABC:

Add arc AB and arc BC together.

70° + 110° = 180°

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3 years ago

How do you solve this problem

djyliett [7]

Answer: Undefined

Step-by-step explanation:

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3 years ago

A box holding pennies, nickels and dimes contains thirteen coins with a total value of 83 cents. How many coins of each type are

Art [367]

Answer:

The number of pennies,nickels and dimes are (p,n,d)=(3,4,6).

Further explanation:

Given:

A box holding pennies, nickels and dimes contains thirteen coins in a box.

Total value is 83 cents.

Calculation:

Consider p,n and d be the number of pennies, nickel and dimes.

Now, total is 13 coins so $p+n+d=13$

As we know that these following are US coin.

Penny=1 cent

Nickel=5 cents

Dime=10 cents

Step 1:

The value is already given as 83 cents that is 80+3 cents.

80 cents can be possible in many combinations as follows:

(N,D)=(0,8),(2,7),(4,6),(6,5),(8,4),(10,3),(12,2),(14,1),(16,0)

It is given that the total number of cents is 13 so we choose (4,6) as (n,d) .

So the value of nickel n=4

Dimes d=6

Step 2:

The value of p is calculated as follows:

Substitute 4 for n, 6 for d in equation $p+n+d=13$ as follows:

$p+4+6=13$

$p+10=13$

$p=13-10$

p=3

Thus, the number of pennies,nickels and dimes are (p,n,d)=(3,4,6).

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3 years ago