Answer:
The sign is negative
Step-by-step explanation:
Given
[tex]Expression = 3xy[/tex]
[tex]x > 0[/tex]
[tex]y<0[/tex]
Required
Determine the sign
The expression can be split into 3 factors
[tex](3) (x) (y)[/tex]
If x > 0 then x is positive and If y < 0 then y is negative
So, the expression becomes:
[tex](+3) (+x) (-y)[/tex]
Leave only signs
[tex](+) (+) (-)[/tex]
[tex]+ * + = -[/tex]
So, we have:
[tex](+*+) (-)[/tex]
[tex](+) (-)[/tex]
[tex]+ * - = -[/tex]
So, we have:
[tex](+) (-) = -[/tex]
Hence, the sign of the expression is negative
Take for instance;
[tex]x = 2[/tex]
[tex]y = -4[/tex]
The expression would be:
[tex]3 *2 * - 4 =-24[/tex] -- negative
