Respuesta :

mixter17

Hello!

The answer is:

[tex]r^{2}-8r-33=(r+3)(r-11)[/tex]

With:

[tex]r=-3\\r=11[/tex]

Why?

Factoring the quadratic expression we have:

We are looking for two possible values that multiplied gives as result -33 and its algebraic sum gives as result -8, so:

[tex]r^{2}-8r-33=(r+3)(r-11)[/tex]

Also,

There are two possible values that make the equation equal to zero: -3 and 11

Let's prove by substituting each value:

Substituting -3

[tex](-3+3)(-3-11)=(0)(-14)=0[/tex]

Substituting 11

[tex](11+3)(11-11)=(14)(0)=0[/tex]

So, there are two possible values for r (area):

[tex]r=-3\\r=11[/tex]

Have a nice day!

zainebamir540

Answer:

r²-8r-33 = (r-11)(r+3)  where r = 11  , r = -3

Step-by-step explanation:

We have given the area a rectangular rug.

Area = r²-8r -33

We have to find the value of r.We have to use  factorization method.

r²-8r-33

We have to find two numbers whose product is -33r² and sum is -8r

r²-8r-33 = r²-11r+3r-33

r²-8r-33 =r(r-11)+3(x - 11)

r²-8r-33 = (r-11)(r+3)

To find the value of r put  (r-11)  = 0         or     (r+3) = 0

r = 11    or    r = -3

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