Final answer:
The graph representing this scenario is continuous and the viable solutions are (10, 50) and (0.5, 40.5).
Step-by-step explanation:
1. The graph is continuous.
This statement is true. The equation t = c + 40 defines a linear relationship between temperature (t) and cricket chirps (c). Linear relationships are continuous, meaning there are no gaps or jumps in the graph. Therefore, the temperature can change smoothly as the number of cricket chirps increases.
2. All values of t must be positive.
This statement is false. While the number of cricket chirps (c) can be 0 or even negative (in case of silence), the temperature (t) calculated by adding 40 will always be positive. So, the graph may have a positive y-intercept but can extend below the x-axis.
3. A viable solution is (–2, 38).
This statement is false. As mentioned earlier, the number of cricket chirps cannot be negative. Therefore, a negative value for c is not a viable solution. Consequently, the point (-2, 38) would not be on the graph.
4. A viable solution is (0.5, 40.5).
This statement is true. If you hear half a cricket chirp in 14 seconds, the temperature would be 40 + 0.5 = 40.5 degrees Fahrenheit. Therefore, (0.5, 40.5) is a valid point on the graph.
5. A viable solution is (10, 50).
This statement is true. Hearing 10 cricket chirps in 14 seconds translates to a temperature of 50 degrees Fahrenheit (40 + 10 = 50). Therefore, (10, 50) represents a valid solution on the graph.
In conclusion, the two statements that are true about the graph are:
The graph is continuous.
A viable solution is (0.5, 40.5).
A viable solution is (10, 50).