Determine whether the statement is true, false, or sometimes true. Explain or show why.

If x is positive and y = -x, then xy is negative.

Is this always true or sometimes true?

False. If x is positive and you put a negative in front of it, you have to divide by negative one which would then give you positive x again. If you multiply a positive x and a positive y then xy is positive. False. Hope that helps.!!!:)

If y = -x, the xy = x(-x).

What do you get when you multiply a positive by a negative?

The statement is always true.

To show this, let's assume that x is a positive number. Given that y is defined as y = -x, we can substitute the value of y into the equation xy.

xy = x * (-x)

Multiplying a positive number (x) by a negative number (-x) results in a negative value because of the product of a positive and negative number rule.

Therefore, we can conclude that if x is positive and y = -x, then xy will always be negative.

To determine whether the statement is true, false, or sometimes true, we need to consider all possible cases. Let's break it down:

1. If x is positive:
- In this case, y = -x would be negative, as it has a negative sign in front of x.
- When we multiply x (positive) by y (negative), we get a negative product. This happens because multiplication of a positive number by a negative number always results in a negative number.

2. If x is negative:
- Here, y = -x would be positive, as it has a negative sign in front of x, but the negative signs cancel each other out, resulting in a positive value for y.
- When we multiply x (negative) by y (positive), we get a negative product. This happens because multiplication of a negative number by a positive number always results in a negative number.

Therefore, we can conclude that regardless of the value of x (positive or negative), the product xy will always be negative. Hence, the given statement is always true.