Find the length and width of a rectangle that has perimeter 24 meters and a maximum area.

Let the length of the rectangle = x

since the perimeter is 24m then the width of rectangle is (12-x)m.

the area of rectangle is:
 A=x*(12-x)

A=-x^2+12x

x=-12/-2 =6:

Since the length is 6m the width will be: 12-6=6m

We conclude that this rectangle has the maximum area when its shape is square of side 6m.
We find the value of area for x=6m :

Area = 6^2 =36M^2

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

income. 10x+1300

expenses 3x+(1800+1500)

expenses 3x+3300

to break even:

income = expense,

10x + 1300 = 3x + 3300,

solve for x.

step-by-step explanation:

mark brainliest