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omeli [17]
3 years ago
6

A rectangular kitchen is 4 meters longer than it is wide. If the area of the kitchen is 192 square feet meters, how many meters

long is it.

Mathematics
1 answer:
Lunna [17]3 years ago
3 0
Lets x = width
length = x + 4 (4 meters longer than wide)

A = L * W
192 = x ( x +4)
192 = x^2 + 4x
x^2 + 4x - 192 = 0
(x +16)(x-12) = 0
 x - 12 = 0, x = 12
 x + 16 = 0, x = -16
so width x = 12
length = 12 + 4 = 16 (4 meters longer than wide)

answer. J
16
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Simplify (4x^2+2)÷(2x^2-9x-5)​
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Answer:

4.1     Pull out like factors :

   4x2 + 2  =   2 • (2x2 + 1) 

Polynomial Roots Calculator :

 4.2    Find roots (zeroes) of :       F(x) = 2x2 + 1

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  2  and the Trailing Constant is  1.

 The factor(s) are:

of the Leading Coefficient :  1,2

 of the Trailing Constant :  1

 Let us test ....

  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      3.00        -1     2      -0.50      1.50        1     1      1.00      3.00        1     2      0.50      1.50   

Polynomial Roots Calculator found no rational roots

Trying to factor by splitting the middle term

 4.3     Factoring  2x2 - 9x - 5 

The first term is,  2x2  its coefficient is  2 .

The middle term is,  -9x  its coefficient is  -9 .

The last term, "the constant", is  -5 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -5 = -10 

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   -9 .

     -10   +   1   =   -9   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  1 

                     2x2 - 10x + 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

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              Add up the last 2 terms, pulling out common factors :

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Step-5 : Add up the four terms of step 4 :

                    (2x+1)  •  (x-5)

             Which is the desired factorization

Final result :

2 • (2x2 + 1) —————————————————— (x - 5) • (2x + 1)

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