2x + 3 /12 = 2x/8
⇒ 48x/24 + 6/24 = 6x/24
⇒ (48x+ 6)/24= 6x/24
⇒ 48x+ 6 = 6x
⇒ 48x- 6x= -6
⇒ 42x= -6
⇒ x= -6/42
⇒ x= -1/7
<span>
x=-1/7~</span>
Answer:
![\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3](https://tex.z-dn.net/?f=%5Cfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%20%20%3D%5Cfrac%7Bf%28x_2%29-f%28x_1%29%7D%7Bx_2-x_1%7D%20%3D%5Cfrac%7B6-%28-12%29%7D%7B3-%28-3%29%7D%20%3D%5Cfrac%7B18%7D%7B6%7D%3D%203)
Step-by-step explanation:
To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:
![Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1} =\frac{f(x_2)-f(x_1)}{x_2-x_1}](https://tex.z-dn.net/?f=Average%5Chspace%7B3%7Drate%5Chspace%7B3%7Dof%5Chspace%7B3%7Dchange%3DSlope%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%20%20%3D%5Cfrac%7Bf%28x_2%29-f%28x_1%29%7D%7Bx_2-x_1%7D)
So, the average rate of change of:
![f(x)=-x^2+3x+6](https://tex.z-dn.net/?f=f%28x%29%3D-x%5E2%2B3x%2B6)
Over the interval ![-3](https://tex.z-dn.net/?f=-3%3Cx%3C3)
Is:
![f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12](https://tex.z-dn.net/?f=f%28x_2%29%3Df%283%29%3D-%283%29%5E2%2B3%283%29%2B6%3D-9%2B9%2B6%3D6%5C%5C%5C%5Cf%28x_1%29%3Df%28-3%29%3D-%28-3%29%5E2%2B3%28-3%29%2B6%3D-9-9%2B6%3D-12)
![\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3](https://tex.z-dn.net/?f=%5Cfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%20%20%3D%5Cfrac%7Bf%28x_2%29-f%28x_1%29%7D%7Bx_2-x_1%7D%20%3D%5Cfrac%7B6-%28-12%29%7D%7B3-%28-3%29%7D%20%3D%5Cfrac%7B18%7D%7B6%7D%3D%203)
Therefore, the average rate of change of this function over that interval is 3.
Answer:
A. y = 3x/4
Step-by-step explanation:
a proportional relationship between x and y is a straight line passing through the origin (0, 0).
The equation must be in the form y = kx.
y = 3x/4
y = 3/4x
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.