Show step by step and solve will mark 7h/12 - 4h/12=18/12

h=6

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides:

                    7*h/12-4*h/12-(18/12)=0

                 3

Simplify   —

                 2

      h      h   3

 ((7•——)-(4•——))-—  = 0

     12     12   2

            h

Simplify   ——

           12

        h           h      3

 ((7 • ——) -  (4 • ——)) -  —  = 0

       12          12      2

                  h

Simplify   ——

                  12

        h     h     3

 ((7 • ——) -  —) -  —  = 0

       12     3     2

     Least Common Multiple:  12

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      7h

  ——————————————————  =   ——

        L.C.M             12

  R. Mult. • R. Num.      h • 4

  ——————————————————  =   —————

        L.C.M              12  

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

7h - (h • 4)     3h

————————————  =  ——

     12          12

 3h    3

 —— -  —  = 0

 12    2

 Find the Least Common Multiple

     The left denominator is :       4

     The right denominator is :       2

     Least Common Multiple:  4

Making Equivalent Fractions :

Rewrite the two fractions into equivalent fractions

  L. Mult. • L. Num.      h

  ——————————————————  =   —

        L.C.M             4

  R. Mult. • R. Num.      3 • 2

  ——————————————————  =   —————

        L.C.M               4  

Adding fractions that have a common denominator :

h - (3 • 2)     h - 6

———————————  =  —————

     4            4  

 h - 6

 —————  = 0

   4  

Now,to get rid of the denominator, multiply both sides of the equation by the denominator.

 h-6

 ——— • 4 = 0 • 4

  4

Now, on the left hand side, the  4  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

  h-6  = 0

Solve  :    h-6 = 0

 h = 6

1.3

step-by-step explanation:

3x2=6   9x+6

bring down the 6 on both sides

6+6=12

12= 9x

divide by 9

12/9 =

1.3 =x

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt