If r is a positive number and s is a negative number, all of the following must represent positive numbers EXCEPT:
A. -r+s
B. r-s
C. rs^2
D: (rs)^2
if r is positive -r is negative
negative + negative is still more negative
So the answer is a?
yes
To determine which of the given options represents a positive number, we need to understand the properties of positive and negative numbers.
A positive number is greater than zero, while a negative number is less than zero. When adding a positive number to a negative number, the result can be either positive, negative, or zero, depending on the magnitudes of the numbers being added.
Now, let's evaluate each of the given options:
A. -r + s:
If r is a positive number, and s is a negative number, then -r is a negative number and s is also a negative number. When we add two negative numbers, the result is always negative. So, -r + s is a negative number.
B. r - s:
In this case, we are subtracting a negative number from a positive number. When we subtract a negative number, it is equivalent to adding its absolute value. Since the absolute value of a negative number is positive, the result is positive. Therefore, r - s is a positive number.
C. rs^2:
Here, we are multiplying a positive number, r, with a negative number, s^2. The square of any number, positive or negative, is always positive. So, s^2 is a positive number. When we multiply a positive number (r) by a positive number (s^2), the result is positive. Therefore, rs^2 is a positive number.
D. (rs)^2:
In this case, we are squaring the product of r and s. The product of a positive number (r) and a negative number (s) is always negative. When we square a negative number, the result is positive. So, (rs)^2 is a positive number.
To summarize:
A. -r + s is a negative number.
B. r - s is a positive number.
C. rs^2 is a positive number.
D. (rs)^2 is a positive number.
Therefore, the correct answer is A. -r + s, as it represents a negative number.