Answer:
The number represented by x may be rational or irrational
Step-by-step explanation:
Rational and irrational numbers
For this answer, we must remind that a rational number is such that it can be expressed as a fraction. Irrational numbers cannot. Examples of rational numbers are
[tex]-2,\frac{3}{4},0,3.21,1.3333...[/tex]
Examples of irrational numbers are
[tex]\sqrt{2},\pi, 1+\sqrt{3}, e^5,sin1[/tex]
To help us to better explain this answer, let's suppose
[tex]x=1+\sqrt{2}\ ,\ y=1-\sqrt{2}[/tex]
They both are irrational and their sum is rational as shown:
[tex]x+y=1+\sqrt{2}+1-\sqrt{2}=2[/tex]
The first option: "The number represented by y must be rational" is false because y is not rational
The second option: "The number represented by X must be rational." and the last option: "The number represented by x must be rational and the number
represented by y must be rational" are equally false.
The only true option is: "The number represented by x may be rational or irrational".
We can clearly see one member of a sum doesn't necessarily define it as irrational
Answer:
Option B is the correct answer.
Step-by-step explanation:
A rational number is the one that can be made by dividing two numbers with no fractional part, for example, .75 or 1/2.
An irrational number is a real number that can't be made by dividing two numbers that don't have fractional part.
In this case, the answer is the number represented by x may be rational or irrational because one part of the sum doesn't have to be defined as irrational.
