The length of a rectangle is 3mm less than four times the width. If the area of the rectangle is 1,387 mm2, what are the dimensions of the rectangle?

The dimension of the rectangle is 19mm by 73mm

Step-by-step explanation:

In this question, we are tasked with calculating the dimensions of the rectangle given the information in the question.

Let the width of the rectangle be x, we are told that length is 3mm less than four times width

Mathematically this means l = 4x - 3

Now we are given the area, what this means is that when we multiply the width and the length, we get the area value

Thus, mathematically

x(4x - 3) = 1,387

4x^2 - 3x = 1387

4x^2 - 3x - 1387 = 0

Solving the quadratic equation, we have;

x = 19 or -73/4

since length cannot be negative, we ignore -73/4

Now the length = 4x - 3 = 4(19) - 3 = 73mm

Thus the dimension of the rectangle is 19mm by 73mm

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.