The area of a rectangular rug is given by the trinomial r^2-4r-21. What are the possible dimensions of the rug?

There are two possible values for r (area):  r =-7 or r=3

Step-by-step explanation:

Given the rectangular rug area is:

We have to convert the above equation into factored form.

So two numbers whose product is -21r² and sum is -4r

<=>  

=

= r (r -7) + 3(r -7)

= (r-7)(r+3)

We set     = 0

<=> (r-7)(r+3) = 0

<=> (r-7) = 0 or (r+3)  = 0

<=> r =-7 or r=3

So, there are two possible values for r (area):  r =-7 or r=3

a) justify

step-by-step explanation:

justifying is just part of everyday life. justify kind of means proof so i think the answer is a) justify.

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)