Question

PLEASE HELP! I’m almost finished with this assignment if someone could answer these questions correctly I’ll give you Brainliest for saving me haha!
c. When a rational and an irrational number are added, is the sum rational or irrational?
Explain.
Type your response here:
d. When a nonzero rational and an irrational number are multiplied, is the product rational or
irrational? Explain.
Type your response here:
e. Which system of numbers is most similar to the system of polynomials?
Type your response here:
f. For each of the operations—addition, subtraction, multiplication, and division—determine
whether the set of polynomials of order 0 or 1 is closed or not closed. Consider any two
polynomials of degree 0 or 1.
Type your response here:

Answer 1

Answer:
C. The sum of any rational number and any irrational number will always be an irrational number.

Explanation: Each time they assume the sum is rational; however, upon rearranging the terms if their equation, they get a contradiction (that an irrational number is equal to a rational number). Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.

Answer:
D. Any nonzero rational number times an irrational number is irrational.

Explanation: Assume r is nonzero and rational, and x is irrational. If rx = q, and q is rational, then x = q/r, which is rational. This is a contradiction.

Answer:
E. The system of polynomials is almost the same with the system of whole numbers.

Explanation: We count with and use a base 10 (decimal) system. Polynomials such as the function above are a “base x” system.

Answer:
F. Addition, subtraction, and multiplication would all be closed because every answer would be a polynomial. Division is not closed because when we divide numbers, sometimes they don’t divide evenly, leaving us with a remainder, which we can write as a fraction.

Explanation: (in answer)

I hope this at least semi helps!