Final answer:
Given the equation (6)(3T) = 1817, and solving for T, we find that T is an irrational number resulting from dividing 1817 by 18. None of the answer choices accurately describe this scenario, so the correct answer is (d) None of the above.
Step-by-step explanation:
The equation given is (6)(3T) = 1817. To assess which rule applies to the equation, we need to determine the nature of the numbers involved. First, we notice that 6 is a rational number. To solve for T, we divide both sides of the equation by 18 (since 6 times 3 equals 18), yielding T = 1817 / 18. Since 1817 is not a multiple of 18, T will not be a whole number, and we'll get a decimal that does not terminate or repeat; hence T is an irrational number.
Considering the answer choices, none of the options directly describes the scenario where a rational number is multiplied by a variable that results in an irrational number. The correct answer must be (d) None of the above.