Standard form is just putting (in this case) variables in alphabetical order. First we simplify- 2x+4=4y would become 1/2x+1=y. This is already in standard form, as numbers w/o variables come at the end. simplifying the next one is more tricky. first you get a variable/number alone-
9-2x-2y=4x+3
9-2y=6x+3
6-2y=6x
1-1/3y=x
1=x+1/3y
3=x+y
x+y=3
sorry if I was wrong and not of any help, But I do believe this is correct.
X = 4
-26 = -8x + 6
-32 = -8x
4 = x
Answer:
<em>27 feet for the south wall and 18 feet for the east/west walls</em>
Maximum area= 
Step-by-step explanation:
<u>Optimization</u>
This is a simple case where an objective function must be minimized or maximized, given some restrictions coming in the form of equations.
The first derivative method will be used to find the values of the parameters that control the objective function and the maximum value of that function.
The office space for Billy-Sean will have the form of a rectangle of dimensions x and y, being x the number of feet for the south wall and y the number of feet for the west wall. The total cost of the space is
C=8x+12y
The budget to build the office space is $432, thus

Solving for y

The area of the office space is

Replacing the value found above

Operating

This is the objective function and must be maximized. Taking its first derivative and equating to 0:

Operating

Solving


Calculating y


Compute the second derivative to ensure it's a maximum

Since it's negative for x positive, the values found are a maximum for the area of the office space, which area is

Answer:
792 ounces
Step-by-step explanation:
The equations below model the ounces of water, y, in each container after x minutes.
Container A: y = 62x + 48
Container B: y = -2x² + 80x + 120
Now, at a time when both the containers hold the same amount of water, is given by
62x + 48 = -2x² + 80x + 120
⇒ 2x² - 18x - 72 = 0
⇒ x² - 9x - 36 = 0
⇒ x² - 12x + 3x - 36 = 0
⇒ (x - 12)(x + 3) = 0
Hence, x = 12 or - 3.
But x can not be negative.
So, x = 12 minutes.
Therefore, after 12 minutes both the container will have the same amount of water and the quantity is = 62 × 12 + 48 = 792 ounces. (Answer)