The answer is B, because it all goes in order so no need for parentheses
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Let the area be y .
Area = (base) × (height)
Base = 2x
Height = h
Let the area of the rectangular pens be y .
∴ y = 2xh
Perimeter of all the fencing = 4x+3h
∴ 4x+3h = 120
now we solve for h
3h = 120-4x
h = 40 - 4/3 x
Now we will substitute this value in the above first equation:
y = 2xh
or, y = 2x (40 - 4/3 x)
or, y = 80x - 8/3 x²
Now for the maximum area we have to find the first order differentiation of y
now,
dy /dx = 80 - 16/3 x
At dy/dx = 0 we get the value of x for which y is maximum.
80 - 16/3 x = 0
or, - 16/3 x = -80
or, x = 15 feet
Hence height = 40 - 4/3 x = 40 - 20 = 20feet
Maximum area = 2xh = 2×15×40 = 1200 square feet
The dimensions of the rectangular pen should be 15 by 20 feet and the maximum area is 1200 square feet.
Disclaimer : The missing figure for the question is attached below.
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in plain and short, to graph an inequality, we first graph its EQUALITY graph, and then we do the shading.
so to graph y > x + 3, we first graph y = x + 3, which is just a line, and then do a true/false check on a point to see which side we shade.
let's hmmm check the point say (0,2), x = 0, y = 2.
y > x + 3
2 > 0 + 3
2 > 3 <--- is that true? is 2 really larger than 3? nope, so is false.
that simply means that the point (0, 2) is on the false area, so that's the area we do NOT shade, so <u>we shade the other side</u>.
y > x + 3, means "y" is greater than or larger than that line, but not equals, larger not equal, meaning the values on the borderline are not included, so the line is a dashed line.
check the picture below.
Hello and Good Morning/Afternoon
<u>Let's take this problem step by step</u>:
<u>To find the rate of change is essentially like finding a line's slope</u>:
⇒ the <em>x-values</em> are the <em>number of sodas</em>
⇒ the<em> y-values </em>are the <em>total costs</em>
<em> ⇒ choose</em> two sets of coordinates and find the slope
<u>Let's put that into action</u>
⇒ (24, 18)
⇒ (28, 21)

<u>Since the rate of change is total cost over number of sodas</u>
⇒ <em>unit is '</em>total cost/number of sodas'
<u>Answer: 3/4 total cost/number of sodas</u>
<u></u>
Hope that helps!
#LearnwithBrainly
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