A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. With m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?

since the total amount of wire is not given, I looked for a similar question:

since we need to only calculate 3 sides of the land plot, our perimeter will be:

L + 2W = 800

area = L x W

L = 800 - 2W

now we replace:

area = (800 - 2W) x W = 800W - W²

we can write a quadratic equation:

area = -W² + 800W

the vertix of W = -b/2a

the coefficients of our quadratic equation are: -2 and 8

the vertix of W = -800 / (2 x -2) = -800 / -4 = 200 yards

width = 200 yards

length = 800 - (200 x 2) = 400 yards

maximum area enclosed = 200 x 400 = 80,000 sq yards

{3 + i, 3 - i, 3, -1}

step-by-step explanation:

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct