Answer:
Equation: 
Solve for n: n = 112
Step-by-step explanation:
To first set up the equation, you need to look at the verbal description and translate into numbers and operations:
'three fourths a number' = 
'plus 8' = + 8
'is' =
'20 less' = - 20
'the number' = n
Put the expressions together:
'three fourths a number plus 8': 
'20 less than the number': n - 20
Set them equal to each other and solve:
Add 20 to both sides: 
Subtract 
from both sides: 
Multiply both sides by 
: 
Solve for n: n = 112
Answer:
y=(x+3)^2 +5
Step-by-step explanation:
Answer:
Step-by-step explanation:
Consider the revenue function given by 
. We want to find the values of each of the variables such that the gradient( i.e the first partial derivatives of the function) is 0. Then, we have the following (the explicit calculations of both derivatives are omitted).
From the first equation, we get, 
.If we replace that in the second equation, we get
From where we get that 
. If we replace that in the first equation, we get
So, the critical point is 
. We must check that it is a maximum. To do so, we will use the Hessian criteria. To do so, we must calculate the second derivatives and the crossed derivatives and check if the criteria is fulfilled in order for it to be a maximum. We get that
We have the following matrix,
![\left[\begin{matrix} -10 & -2 \\ -2 & -16\end{matrix}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Bmatrix%7D%20-10%20%26%20-2%20%5C%5C%20-2%20%26%20-16%5Cend%7Bmatrix%7D%5Cright%5D)
.
Recall that the Hessian criteria says that, for the point to be a maximum, the determinant of the whole matrix should be positive and the element of the matrix that is in the upper left corner should be negative. Note that the determinant of the matrix is 
and that -10<0. Hence, the criteria is fulfilled and the critical point is a maximum
Answer:
For question 2 (Triangle):
The triangle hThe entire triangle area = 2 * 13.125 =
26.25
Triangle perimeter both legs = 16.6 + base (7) = 23.6
For question 1 (Parallelogram):
longer congruent sides = 6-0 OR 4-(-2) = 6units
area= 3×6 = 18units^2
