Subtract 1/6a+3 from 1/3a−5 a. −1/6a+8 b. 1/6a−8 c. −1/6a−2 d. 1/6a−2

The answer is:   [B]:  " ⅙ a − 8 " .

Note:

  (⅓ a  −  5)  −  (⅙ a  +  3) = 
 
       (⅓ a  −  5)  −  1 (⅙ a  +  3)


Note the "distributive property" of multiplication:a(b + c) = ab + ac ;
a(b – c) = ab – ac .So, let us examine the following portion of our expression:

             "  − 1 (⅙ a  +  3)  "  ; 

                    − 1 (⅙ a  +  3) ;

                      =  (-1 * ⅙ a)  +  (-1 * 3)  ;

                      = (-1/1 * ⅙ a)  + (-1 * 3) ;

                      =  -⅙ a + (-3) ;  →  {Note: "Adding a negative" is the same                                                                     thing as "adding a positive".}. 

                      =  -⅙ a – 3 ; 

So, we can rewrite the original equation:

     " (⅓ a  −  5)  −  (⅙ a  +  3) "  ;

as:   →  " ⅓ a  −  5  −  ⅙ a  –  3 " ; 

Change the " (⅓ a)" to "(²/₆ a)" ;  {since "1/3 = (1*2)/ (3*2) = 2/6" } ;

And since we want the TWO (2) "fraction values" in the expression to having "matching denominators" ;

Rewrite as:

           →  " ²/₆ a  −  5  −  ⅙ a  –  3 " ; 

Now, combine the "like terms" ; 

→   ²/₆ a  −  ⅙ a = (2-1)/6  a =  ⅙ a 

→   −5 − 3 = -8 ; 

So we can rewrite the expression as:

→    " ⅙ a − 8 "  ;  which is:  "Answer choice:  [B]:  " ⅙ a − 8 " .

    

The answer is 625in²

Step-by-step explanation:

The area of any quadrilateral can be determined by multiplying the length of its base by its height. Since we know the shape here is square, we know that all sides are of equal length. From this we can work backwards by taking the square root of the area to find the length of one side.