WILL MARK BRAINLIEST FOR THE BEST ANSWER. PLEASE SHOW ALL WORK NECESSARY PLEASE AND THANK YOU. Jasmine is fencing in a new garden along the side of her house as shown below. She has 12 m of fencing for the 3 sides of the garden. What is the length of the garden, in metres, with the maximum area? THANKS>.

9514 1404 393

  6 m

Step-by-step explanation:

Let p represent the length of the perimeter fence. Let x represent the length parallel to the house. Then the width perpendicular to the house is ...

  w = (p -x)/2

and the area of the garden is ...

  area = length · width

  area = x(p -x)/2

For a fixed perimeter length p, this equation describes a parabola that opens downward. Its vertex is on the line of symmetry, halfway between the zeros. The area will be zero when x=0 and when x=p, so the vertex (maximum area) is located at ...

  x = (0 +p)/2 . . . . . average of zero values

  x = p/2

Here, we have p=12 m, so p/2 = 6 m, and the width is (12 -6)/2 = 3 m.

The length of the maximum-area garden is 6 meters.

_____

Its area is 18 square meters.

Step-by-step explanation:

Let the width be w and the length be l

We have the measure of 3 sides:

Area of the garden is:

Substitute w with l using the first equation:

The final expression for the area can have maximum value when l - 6 = 0 because the first part of expression gets negative value for any l ≠ 6

And the maximum possible area is 18 m²

So l = 6 m is the answer for maximum area

1760 kilometers

step-by-step explanation:

multiply the amount of time the plane took to travel by it's speed

in the math equation 8 x 7 = 56, the 8 and the 7 are both factors of 56, since in this lesson we will use square tiles to figure out the factors of a whole find as many different arrays as you can, but follow one important rule: all the rows must have the i can make two rows of nine, so 2 and 9 are both factors of 18.

step-by-step explanation: