Apacking company is doing an inventory of boxes. their most popular box is display below: 2ft,(3x-5)ft,(2x-1)ft you can use the formula v= lwh to find the volume of the box. the volume of the box is 40ft3.what is the value of x ? find the length and width of the box. describe any extraneous solutions.

Length of box is(l)  =2 ft

width of box is (w)  = 3 x - 5 =3(3)-5 = 9-5=4

height of box is (h) = 2 x - 1 =2(3)-1 = 6 -1 =5

Step-by-step explanation:

Step 1:-

Volume of the box is  V= l w h

Given Volume of the box is V = 40 ft^3

                          given 2 × (3 x-5)×(2 x-1) =40..........(1)

Step 2:-

           simplification  

take common 2

 Find factors

         x=

Step 3:-  The value of x is not satisfied

              the value of x =3 is satisfied in equation(1)

             Therefore the length of the box is l = 2

              the width of the box is w = 3 x-5=3(3)-5=9-5=4

              The height of the box is h= 2 x-1 = 2 (3) -1 =5

Verification:-

           V = 2(4)(5)  =40

           In the given problem volume is 40 so both are equal

- The length of the box is l = 2

              The width of the box is w =4

              The height of the box is h= 5

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

step-by-step explanation:

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