Final answer:
For two quantities A and B that vary directly with x, the ratio A/B will be a constant since the variable x cancels out. Thus, the correct choice is d) A/B = k.
Step-by-step explanation:
When we state that A varies directly as x, we can write this as A = k1 × x, where k1 is a constant of proportionality for A. Similarly, as B varies directly as x, we express this as B = k2 × x, where k2 is the constant of proportionality for B. To find how A/B varies with x, we divide the equation for A by the equation for B:
A/B = (k1 × x) / (k2 × x). x terms cancel out, leaving us with: A/B = k1 / k2. We can denote k1 / k2 as a new constant, let's call it 'k'. Therefore, we rewrite the equation as: A/B = k.
This shows that the ratio A/B is constant when A varies directly as x, and B also varies directly as x, but with a different proportionality constant. Hence, A/B does not vary with x, and instead, it remains constant, represented by k. Thus, the correct choice is d) A/B = k.