Final answer:
To determine if the relation K = {(2.3m + 45, 0), (-67m - 8.9, 0)} is a function, we need to check if there are any duplicate x-values. The relation is a function if each input value has a unique output value. By solving the equation, we find that m must be equal to -0.7774 (approximately) for the relation to be a function.
Step-by-step explanation:
In order for the relation K = {(2.3m + 45, 0), (-67m - 8.9, 0)} to be a function, each input value must have a unique output value.
The relation represents a set of ordered pairs, where the first element in each pair is the x-value, and the second element is the y-value.
To determine if the relation is a function, we need to check if there are any duplicate x-values.
In this case, we have two ordered pairs: (2.3m + 45, 0) and (-67m - 8.9, 0).
If the x-values of these ordered pairs are equal, then the relation is not a function. Therefore, we need to solve the equation:
2.3m + 45 = -67m - 8.9
This equation can be solved to find the values of m for which the relation K is a function.
By simplifying the equation, we get:
69.3m + 53.9 = 0
Now, we can solve for m:
69.3m = -53.9
m = -53.9/69.3 = -0.7774 (approximately)
So, for the relation K to be a function, m must be equal to -0.7774 (approximately).