Factor the following expression using the GCF: 42pr

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

Gnoma [55]

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!

3 0

2 years ago

Read 2 more answers

Write a linear function f with the values f(2)=4 and f(−7)=9. A function is f(x)=

ale4655 [162]

Answer:

f(x) = -5/9 x + 5 1/9

Step-by-step explanation:

f(2)=4 and f(−7)=9 means the line pass through (2,4) and (- 7,9)

f(x) = mx + b

m = (y-y') / (x-x') = (9 - 4) / (- 7 - 2) = - 5/9

for (2,4) : b = f(x) - mx = y - mx = 4 - (- 5/9) x 2 = 4 + 10/9 = 46/9 = 5 1/9

f(x) = -5/9 x + 5 1/9

check for (-7, 9) f(-7) = (-5/9) * (-7) + 5 1/9 = 35/9 + 46/9 = 81/9 = 9

5 0

3 years ago

The perimeter of a rectangular store receipt is ten and five-sixths inches. If three of the sides total eight and one-half inche

serg [7]

Answer:

The measure of the fourth side is $\frac{7}{3}$ .

Step-by-step explanation:

Given as :

The Perimeter of rectangular store = ( 10 + $\frac{5}{6}$ ) inches

The measure of three sides of rectangle = ( 8 + $\frac{1}{2}$ ) inches

So, The measure of three sides = length + breadth + length

I,.e 2 L + B = ( 8 + $\frac{1}{2}$ ) inches .....1

∵ perimeter = ( 10 + $\frac{5}{6}$ ) inches

So , 2 L + 2 B = ( 10 + $\frac{5}{6}$ ) inches

Or, 2 L + B + B = ( 10 + $\frac{5}{6}$ ) inches

Or, ( 8 + $\frac{1}{2}$ ) + B = ( 10 + $\frac{5}{6}$ )

or, B = ( 10 + $\frac{5}{6}$ ) - ( 8 + $\frac{1}{2}$ )

Or, B = 10 - 8 + ( $\frac{5}{6}$ ) - $\frac{1}{2}$

or, B = 2 + $\frac{5-3}{6}$

or, B = 2 + $\frac{1}{3}$

∴ B = $\frac{6 + 1}{3}$ = $\frac{7}{3}$

Hence The measure of the fourth side is $\frac{7}{3}$ . Answer

7 0

3 years ago

You work for a pharmacy and monthly sales of asthma inhalers in your pharmacy follows a normal distribution with a mean of 191 i

grin007 [14]

Answer: -1.33 .

Step-by-step explanation:

Formula to find the Z-score :

$Z=\dfrac{\text{Expected value - Mean}}{\text{Standard deviation}}$

Given: Mean = 191 and Standard deviation = 21

Then , the z-score corresponding to the expected value of 163 will be :

$Z=\dfrac{163-191}{21}\\\\=\dfrac{-28}{21}\approx-1.33$

Hence, the z score corresponding to selling 163 inhalers is -1.33 .

3 0

3 years ago

Write an equation of the line in slope-intercept form that passes through the point (3, 8) with slope 4?

iren [92.7K]

Slope intercept form:
Y = mx + b
m = slope, b = y intercept
Given the slope of 4
Y = 4x + b
Plug in the point (3,8)
8 = 4(3) + b
8 = 12 + b, b = -4
Y intercept = -4

Solution: y = 4x - 4

8 0

2 years ago

Factor the following expression using the GCF: 42pr – 3p.