Answer:
K
Step-by-step explanation:
Values of x and y are either negative or positive, but not 0. Lets try to make each choice "negative", so we can eliminate it.
F. x - y
If y is greater than x in any positive number, the result is negative.
1 - 3 = -2
So, this can be negative.
G. |x| - |y|
Here, if y > x for some positive number, we can make it negative. Such as shown below:
|5| - |8|
= 5 - 8
= -3
So, this can be negative.
H.
|xy| - y
Here, if y is quite large, we can make this negative and let x be a fraction. So,
|(0.5)(10)| - 10
|5| - 10
5 - 10
-5
So, this can be negative.
J. |x| + y
This can negative as well if we have a negative value for y and some value for x, such as:
|7| + (-20)
7 - 20
-13
So, this can be negative.
K. |xy|
This cannot be negative because no matter what number you give for x and y and multiply, that result WILL ALWAYS be POSITIVE because of the absolute value around "xy".
So, this cannot be negative.
