If we let x and y represent length and width, respectively, then we can write equations according to the problem statement.
.. x = y +2
.. xy = 3(2(x +y)) -1
This can be solved a variety of ways. I find a graphing calculator provides an easy solution: (x, y) = (13, 11).
The length of the rectangle is 13 inches.
The width of the rectangle is 11 inches.
______
Just so you're aware, the problem statement is nonsensical. You cannot compare perimeter (inches) to area (square inches). You can compare their numerical values, but the units are different, so there is no direct comparison.
Answer: Raymond is correct
The DJ charges $75 an hour.
=================================================
Explanation:
x = number of hours
y = total cost
The DJ does a 3-hour event for $275. This means one point is (x,y) = (3,275)
Another point is (5,425) because a 5-hour event costs $425.
Let's find the slope of the line through these two points.

The slope is 75, meaning that each time y goes up by 75, x goes up by 1.
Flipped around it means each time x goes up by 1, y goes up by 75.
This means each time we add on an extra hour, the cost goes up by $75.
The DJ charges $75 an hour. Raymond is correct.
Answer with explanation:
→→→Function 1
f(x)= - x²+ 8 x -15
Differentiating once , to obtain Maximum or minimum of the function
f'(x)= - 2 x + 8
Put,f'(x)=0
-2 x+ 8=0
2 x=8
Dividing both sides by , 2, we get
x=4
Double differentiating the function
f"(x)= -2, which is negative.
Showing that function attains maximum at ,x=4.
Now,f(4)=-4²+ 8× 4-15
= -16 +32 -15
= -31 +32
=1
→→→Function 2:
f(x) = −x² + 2 x − 3
Differentiating once , to obtain Maximum or minimum of the function
f'(x)= -2 x +2
Put,f'(x)=0
-2 x +2=0
2 x=2
Dividing both sides by , 2, we get
x=1
Double differentiating the function,gives
f"(x)= -2 ,which is negative.
Showing that function attains maximum at ,x=1.
f(1)= -1²+2 ×1 -3
= -1 +2 -3
= -4 +2
= -2
⇒⇒⇒Function 1 has the larger maximum.