If \(xy < 0\) and \(y > 0\) which of the following must be positive?

Explanation: If \(xy < 0\) and \(y > 0\), then \(x\) must be negative. Let's test the options: A) \(x-y\): (Negative) - (Positive) = Negative. Must be negative. B) \(2x+3y\): (Negative) + (Positive). Can be positive or negative. C) \(\frac{x+10}{y+2}\): If $x=-5$, $\frac{5}{\text{Positive}} = \text{Positive}$. If $x=-15$, $\frac{-5}{\text{Positive}} = \text{Negative}$. Can be positive or negative. D) \(\frac{x}{-y-2}\): \(x\) is Negative. \(-y\) is Negative. \(-y-2\) is Negative. \(\frac{\text{Negative}}{\text{Negative}} = \text{Positive}\). Must be positive. E) \(2y^2+x\): (Positive) + (Negative). Can be positive or negative. \(\therefore \frac{x}{-y-2}\) must be positive.