Xian and his cousin Kai both collect stamps. Xian has 56 stamps, and Kai has 80 stamps. The boys recently
joined different stamp-collecting clubs. Xian's club
send him 12 new stamps
will send him 16 new stamps per month. Kai's club will
stamps? How
per month. After how many months will Xian and Kai have the same number of
many stamps will each have?
After
months Xian and
his cousin will have
stamps each.

Let the number of months Xian and Kai will have the same number of stamps be x, then

56 + 12x = 80 + 8x

12x - 8x = 80 - 56

4x = 24

x = 24/4 = 6

Therefore, after 6 months Xian and Kai will have the same number of stamps.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0