Why is the sum of two rational numbers always rational?
select from the drop-down menus to correctly complete the proof.

let a/b and c/d
represent two rational numbers. this means a, b, c, and d are (integers/irrational numbers? )
and (b is not 0, d is not 0/ b and d are 0? )
the
sum of the numbers is
ad+bc/bd, where bd is not 0. because integers are closed under (addition and multiplication/ addition and division? )
the sum is the
ratio of two integers, making it a rational number.

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column

answer: the correct option is d.

explanation:

it is given that the triangle j'k'l' shown on the grid below is a dilation of triangle jkl using the origin as the center of dilation.

from the given graph it is noticed that k(4,8) and k'(2,4). let origin is defined by o and scale factor is defined by k, then

    (1)

distance formula,

put these values in equation (1).

therefore scale factor is     and option d is correct.