A garden measuring 12 meters by 6 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 160 square meters. What will be the width of the pathway? (The pathway will be the same width around the entire garden).

x=2

Step-by-step explanation:

Original width = 6

New width 6+x+x

Orignal length 12

New length  12+x+x

A = l*w

160 = ( 6+2x) ( 12+2x)

Factor

160 = 2( 3+x) 2(6+x)

Divide each side by 4

40 = (3+x) (6+x)

FOIL

40 = 18+ 6x+3x+ x^2

40 = 18 +9x+x^2

Subtract 40 from each side

0 = x^2 +9x -22

Factor

0 = (x +11) (x-2)

Using the zero product property

x +11 =0   x-2 =0

x= -11   x=2

Since we cannot have a negative  sidewalk

x =2

-1/2 +2

step-by-step explanation:

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.