What is the sign of 3 x y 3xy3, x, y when x > 0 x>0x, is greater than, 0 and y < 0 y<0
1 answer:
Answer:
The sign is negative
Step-by-step explanation:
Given
![Expression = 3xy](https://tex.z-dn.net/?f=Expression%20%3D%203xy)
![x > 0](https://tex.z-dn.net/?f=x%20%3E%200)
![y](https://tex.z-dn.net/?f=y%3C0)
Required
Determine the sign
The expression can be split into 3 factors
![(3) (x) (y)](https://tex.z-dn.net/?f=%283%29%20%28x%29%20%28y%29)
If x > 0 then x is positive and If y < 0 then y is negative
So, the expression becomes:
![(+3) (+x) (-y)](https://tex.z-dn.net/?f=%28%2B3%29%20%28%2Bx%29%20%28-y%29)
<em />
Leave only signs
![(+) (+) (-)](https://tex.z-dn.net/?f=%28%2B%29%20%28%2B%29%20%28-%29)
![+ * + = -](https://tex.z-dn.net/?f=%2B%20%2A%20%2B%20%3D%20-)
So, we have:
![(+*+) (-)](https://tex.z-dn.net/?f=%28%2B%2A%2B%29%20%28-%29)
![(+) (-)](https://tex.z-dn.net/?f=%28%2B%29%20%28-%29)
![+ * - = -](https://tex.z-dn.net/?f=%2B%20%2A%20-%20%3D%20-)
So, we have:
![(+) (-) = -](https://tex.z-dn.net/?f=%28%2B%29%20%28-%29%20%3D%20-)
<em>Hence, the sign of the expression is negative</em>
<em></em>
Take for instance;
![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
![y = -4](https://tex.z-dn.net/?f=y%20%3D%20-4)
The expression would be:
-- negative
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