Answer:
red line is 4x+y=3 and blue line is 2x-3y=3
Step-by-step explanation:
We let x and y be the measures of the sides of the rectangular garden. The perimeter subtracted with the other side should be equal to
2x + y = 92
The value of y in terms of x is equal to,
y = 92 – 2x
The area is the product of the two sides,
A = xy
Substituting,
A = x (92 – 2x) = 92x – 2x2
Solving for the derivative and equating to zero,
0 = 92 – 4x ; x = 23
Therefore, the area of the garden is,
<span> A = 23(92 – 2(23)) = 1058 yard<span>2</span></span>
Answer: The required constant of proportionality is 10.
Step-by-step explanation: Given that y is directly proportional to x, and y = 150 when x = 15.
We are to find the constant of proportionality.
According to the given information, we can write
![y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~~~~~~~[\textup{where k is the constsnt of propotionality}].](https://tex.z-dn.net/?f=y%5Cpropto%20x%5C%5C%5C%5C%5CRightarrow%20y%3Dkx~~~~~~~~~~~~~~~~%5B%5Ctextup%7Bwhere%20k%20is%20the%20constsnt%20of%20propotionality%7D%5D.)
When y = 150 and x = 15, we get from the above equation that

Thus, the required constant of proportionality is 10.