If the sumof two numbers, n and m, is rational, which statement is true?

Option B:

Both n and m must be rational.

Solution:

Given information:

Sum of two numbers, n and m are rational.

To find which statements are true:

Option A: Both n and m may be rational but do not have to be.

It is not true because n and m given is rational.

It have to be rational.

Option B: Both n and m must be rational.

Yes, n and m must be rational then only the sum of numbers are rational.

It is true.

Option C: Both n and m must be irrational.

Sum of irrationals will be sometimes irrational and sometimes can't add.

So it is not true.

Option D: One number is rational and the other is irrational.

Rational and irrational cannot be add.

So it is not true.

Option B is true.

Both n and m must be rational.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.