On your paper, construct a rectangle on a coordinate plane that satisfies these criteria. • The sides of the rectangle are either vertical or horizontal.

• The perimeter of the rectangle is 42 units.

• Each of the vertices lies in a different quadrant.

What are the coordinates of the vertices of your rectangle? Explain how you know the perimeter of your rectangle is

42 units

Step-by-step explanation:

Required

Construct a rectangle whose perimeter is 42 units and satisfies the given conditions.

First, name the rectangle ABCD.

Such that:

For the rectangle to be either horizontal or vertical, then:

and

We have that:

Replace perimeter with its formula

Divide both sides by 2

This implies that, the distance between adjacent sides (through the edges) must be equal to 21

Having said that: a set of coordinates that satisfy the given conditions are:

-- First quadrant

-- Second quadrant

-- Third quadrant

-- Fourth quadrant

The above quadrants satisfy the condition:

and

HOW TO KNOW THE PERIMETER IS 42

To do this, we simply calculate the distance between the edges and add them up

Distance is calculated as:

For AB

For BC

For CD

For DA

So, the perimeter is:

See attachment for rectangle

f is the midpoint of

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb