The length of a rectangle is 1 unit more than the width. The area of the rectangle is 56 units. What is the width in units of the rectangle

Width = 7units

Step-by-step explanation:

The area of a rectangle

A = h * w

A - area of a rectangle

h - height of a rectangle

w - width of a rectangle

Or

A = length * breadth

It's all the same

Given :

h = 1 + w

w = w

A = 56

56 = ( 1 + w) * w

56 = ( 1 + w)w

56 = w + w^2

56 = w^2 + w

w^2 + w - 56 = 0

Find a factor that can be multiplied to give -56

and added to give + 1

The factor is 8 and -7

Substitute 8w - 7w for w

w^2 + 8w - 7w - 56 = 0

( w^2 + 8w) - (7w - 56) = 0

w( w + 8) - 7( w + 8) = 0

( w - 7) = 0

( w + 8) =0

w - 7 = 0

w = 7

w + 8 = 0

w = -8

Since a side of any rectangle can not be negative

w = 7

The width of the rectangle is 7units

The length of the rectangle is 1 + w = 1 + 7 = 8units

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

m∠5 + m∠3 = m∠1   is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6   is true

m∠2 +m∠3 +m∠5 = 180   is true