Suppose you earn $12 each time you mow the lawn which function describes the relationship between your total earnings E and the number of times you mow the lawn, m
1.E(m) = m + 12
2. m + 12E
3.E(m) = m - 12
4. E(m) = 12m
4. E(m) = 12m
explain why
The given problem states that you earn $12 each time you mow the lawn. This means that your earnings are directly proportional to the number of times you mow the lawn. The formula for directly proportional relationships is y = kx, where "y" is the dependent variable (total earnings), "x" is the independent variable (number of lawn mows), and "k" is the constant of proportionality (how much you earn per lawn mow).
In this case, "k" is equal to $12, since that is the amount earned per lawn mow. Therefore, the equation for the relationship between your earnings E and the number of times you mow the lawn, m, can be written as:
E = km
Substituting $12 for "k", we get:
E = $12m
This is the same as:
E(m) = 12m
So, the correct function that describes the relationship between your total earnings E and the number of times you mow the lawn, m, is E(m) = 12m.
The correct answer would be:
4. E(m) = 12m
The correct function that describes the relationship between your total earnings E and the number of times you mow the lawn, m, is option 4. E(m) = 12m.
To understand why this is the correct option, let's break it down. In this case, you earn $12 each time you mow the lawn. So, for every m times you mow the lawn, you earn 12 dollars for each time. Therefore, your total earnings E can be calculated by multiplying the number of times you mow the lawn (m) by the amount you earn each time ($12), resulting in E(m) = 12m.
It's important to note that option 1, E(m) = m + 12, is not the correct function in this case. This equation implies that your earnings E are equal to the number of times you mow the lawn (m) plus 12, which is not the correct way to calculate your earnings based on the given information.