( x-5 ) (x + 6 )
multiply
X times X + 6x - 5x - 5 times 6
connect like terms
x squared + 6x - 5x - 30
Answer is
x squared + x - 30
Answer:
14 feet and 5 inches
Step-by-step explanation:
11 feet + 2 feet= 13 feet
9 inches + 8 inches = 17 inches
17 inches = 1 foot and 5 inches
13 + 1 = 14 feet
5 inches + 0 inches = 5 inches
Answer:
Equilibrium quantity = 26.92
Equilibrium price is $31.13
Step-by-step explanation:
Given :Demand function : ![p^2 + 16q = 1400](https://tex.z-dn.net/?f=p%5E2%20%2B%2016q%20%3D%201400)
Supply function : ![700 -p^2 + 10q = 0](https://tex.z-dn.net/?f=700%20-p%5E2%20%2B%2010q%20%3D%200)
To Find : find the equilibrium quantity and equilibrium price.
Solution:
Demand function :
--A
Supply function :
---B
Now to find the equilibrium quantity and equilibrium price.
Solve A and B
Subtract B from A
So, equilibrium quantity = 26.92
Substitute the value of q in A
So, equilibrium price is $31.13
First Find slope by using
![\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=%20%5Cfrac%7By2-y1%7D%7Bx2-x1%7D%20)
![\frac{4-6}{-2-2} = \frac{-2}{-4} = \frac{1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4-6%7D%7B-2-2%7D%20%3D%20%5Cfrac%7B-2%7D%7B-4%7D%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20)
Now use point Slope form to find the equation of the line (y-y₁)=m(x-x₁)
(y-6)=
![\frac{1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20)
(x-2)
y-6=
![\frac{1}{2} x-1](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20x-1)
y=
![\frac{1}{2} x+5](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20x%2B5)
is your equation
Answer:
![10C1 *9C1*8C1 = 10*9*8=720](https://tex.z-dn.net/?f=%2010C1%20%2A9C1%2A8C1%20%3D%2010%2A9%2A8%3D720)
Step-by-step explanation:
For this case in order to select the one admiral, captain and commander, all different. We are assuming that the order in the selection no matter, so we can begin selecting an admiral then a captain and then a commander.
So we have 10C1 ways to select one admiral since we want just one
Now we have remaining 9 people and we have 9C1 ways to select a captain since we want a captain different from the admiral selected first
Now we have remaining 8 people and we have 8C1 ways to select a commander since we want a commander different from the captain selected secondly.
The term nCx (combinatory) is defined as:
![nCx = \frac{n!}{x! (n-x)!}](https://tex.z-dn.net/?f=%20nCx%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%20%28n-x%29%21%7D)
And by properties ![nC1= n](https://tex.z-dn.net/?f=nC1%3D%20n)
So then the number of possible way are:
![10C1 *9C1*8C1 = 10*9*8=720](https://tex.z-dn.net/?f=%2010C1%20%2A9C1%2A8C1%20%3D%2010%2A9%2A8%3D720)
If we select first the captain then the commander and finally the admiral we have tha same way of select ![10*9*8=720](https://tex.z-dn.net/?f=%2010%2A9%2A8%3D720)
For all the possible selection orders always we will see that we have 720 to select.