Question
The number z is irrational. Which statement about 9+z is true? 9+z is rational. 9+z is irrational. 9+z can be rational or irrational , depending on the value of z.
Answer
4.5
(234 Votes)
Nesta
Master · Tutor for 5 years
Answer
B -
is irrational.
Explanation
## Step 1The problem states that the number
is irrational. An irrational number is a number that cannot be expressed as a ratio of two integers.## Step 2The number '9' is a rational number because it can be expressed as the ratio of two integers. ## Step 3According to the principles of number theory, the sum of a rational number and an irrational number is always irrational. ## Step 4To elaborate, irrational numbers are numbers that cannot be written down as simple fractions but are expressed in decimals that go on forever without repeating. Rational numbers, such as fractions, integers, and whole numbers, have a finite or repetitive decimal representation.## Step 5Based on these mathematical principles, the sum of the rational number '9' and the irrational number 'z' will always be an irrational number.