To determine which statement must be true given that the product of 23 and another variable xy is a valid mathematical expression, we first need to understand what this statement implies.
Starting with the equation, if 23 * xy is a valid expression, then it means that xy must also yield a finite and defined value when multiplied by 23. This could lead us to realize that for the entire expression to hold true, either x or y (or both) must take on values that ensure the expression is defined.
For example, if both x and y are real numbers or if either is not equal to zero, then the multiplication results in a valid output. Hence, we conclude that:
- Both x and y must be non-zero.
- xy must be defined.
Ultimately, this inquiry revolves around the conditions under which the multiplication holds. Therefore, while specific options for the answer weren’t provided, generally speaking, we can say that:
- If 23 xy is a true mathematical statement, then xy should not be zero.
This is a fundamental rule in algebra, as the division or multiplication involving zero typically leads to undefined expressions.