Final answer:
The equation that shows 9 is a factor of 72 is (d) 72 = 81 - 9, which, when rearranged, gives us the correct relationship in the form of 72 = 9 x 8.
Step-by-step explanation:
The question asks which equation shows that 9 is a factor of 72. In mathematics, when we say that a number is a factor of another, it means that the first number can be multiplied by some other whole number to get the second number. To say 9 is a factor of 72, we should be able to express 72 as a product of 9 and another integer.
The correct equation is 72 = 9 x 8, which is a multiplication expression and can be derived by dividing 72 by 9, which equals 8. This means that 9 multiplied by 8 gives us 72, confirming that 9 is indeed a factor of 72. This concept is sometimes referred to as divisibility. Choice (d) 72 = 81 - 9 is the equation that shows this relationship, as rearranging it gives us the expression that 9 multiplied by any integer (in this case, 8) results in 72. None of the other options provided show the correct factor relationship between 9 and 72.