Can someone answer question 10-11-12 for me.

Book: Haese mathematics 8
Page: 434

This one:
The length of a rectangle is 4 cm more than its width , and the area of the rectangle is 96 cm ? Find the width of the rectangle .

Width of the rectangle is 12 cm.

Solution:

The length of a rectangle is 4 cm more than its width , and the area of the rectangle is 96 cm². Find the width of the rectangle.

Given data:

Let x be width of the rectangle.

Length of the rectangle = (x + 4) cm

Area of the rectangle = 96 cm²

length × breadth = 96

Subtract 96 from both sides.

Let us factor the polynomial.

Take x common in 1st two terms and -12 common in next two terms.

Now, take (x + 8) common in both terms.

x + 8 = 0 and x - 12 = 0

x = -8 and x = 12

Dimension cannot be in negative terms, so ignore x = -8.

Width = 12 cm

Width of the rectangle is 12 cm.

x=30

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.