Answer:
The final amount is $1109.81
Step-by-step explanation:
In order to find the total amount, start with the know amount, which is Ms. Moore's class. Her class raised $249. Now we can use that to find the amount from Ms. Aguilar's class.
$249 + $396.62 = $645.62
Now we can use the amount from Ms. Aguilar's class to find the amount from Ms. Barry's class
$645.62 - $430.43 = $215.19
Now we can add the three amounts together to find the total amount.
$249 + $645.62 + $215.19 = $1109.81
Answer: The value of
is
.
Step-by-step explanation:
Given: 
To find: 
As we know it is composition function which means that g(x) function is in f(x) function.
So we have
![(f_\circ g) (x) = f[g(x)]](https://tex.z-dn.net/?f=%28f_%5Ccirc%20g%29%20%28x%29%20%3D%20%20f%5Bg%28x%29%5D)

Now substitute the value of g(x) we get

Hence, the value of
is
.
The product of one term of a multiplicand and one term of its multiplier
To obtain the total surface we have to calculate the surface of the 4 triangles and add up the areas (remember that the area of a triangle is (b*h)/2 , b is the base, h is the height ).
We will caculate first the area of the base triangle for that we considerer the fact that it is an equilateral triangle with sides of lenght 6 cm, now we calculate the height, I am going to draw please wait a moment
using the pythagorean theorem we have that
![\begin{gathered} h^2=6^2cm^2-3^2\operatorname{cm}=27cm^2 \\ h=\text{ }\sqrt[]{27\text{ }}cm \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20h%5E2%3D6%5E2cm%5E2-3%5E2%5Coperatorname%7Bcm%7D%3D27cm%5E2%20%5C%5C%20h%3D%5Ctext%7B%20%7D%5Csqrt%5B%5D%7B27%5Ctext%7B%20%7D%7Dcm%20%5Cend%7Bgathered%7D)
Then, the area of the triangle is 6*h/2 = 3h = 15.59 cm^2.
Now we calculate the area of the other 3 triangles, notice that those triangles have the same base and height so we will calculate for one of them and multiply by 3. From the image we know that the height is 15cm and the base is 6 cm so the area is 45cm^2, and 45*3 cm^2 = 135cm^2.
Finally we add up all the areas:
(A)






(B)




But we assume
is a function of
alone, so there is not potential function here.
(C)






For (A) and (C), we have
, which makes
for both.