Math Problem Statement

When the Peregrine Falcon is in a dive, it can reach speeds of [242] [\text{mph}], making it the fastest member of the animal kingdom. The graph below shows a proportional relationship between distance and time. How does the speed (miles per hour) represented by this relationship compare to that of the Peregrine Falcon? Choose 1 answer: Choose 1 answer: (Choice A) The speed represented by the graph is less than the speed of the Peregrine Falcon. A The speed represented by the graph is less than the speed of the Peregrine Falcon. (Choice B) The speed represented by the graph is greater than the speed of the Peregrine Falcon. B The speed represented by the graph is greater than the speed of the Peregrine Falcon. (Choice C) The speed represented by the graph is equal to the speed of the Peregrine Falcon. C The speed represented by the graph is equal to the speed of the Peregrine Falcon. A coordinate plane. The x-axis represents the time, in hours, runs from 0 to 5 and is scaled by 1. The y-axis represents the distance, in miles, runs from 0 to 250 and is scaled by 25. A graph of a line intersects the points (0, 0) and (1, 200). Image of a peregrine falcon. Related content Report a problem

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Solution

To solve this problem, we need to find the speed represented by the graph and compare it to the speed of the Peregrine Falcon, which is 242 mph.

Step 1: Calculate the speed from the graph.

The speed of an object is given by the formula: Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}} From the graph, we are given two points: (0,0)and(1,200)(0, 0) \quad \text{and} \quad (1, 200) This means that in 1 hour, the object travels 200 miles.

So the speed is: Speed=200 miles1 hour=200 mph\text{Speed} = \frac{200 \text{ miles}}{1 \text{ hour}} = 200 \text{ mph}

Step 2: Compare the speeds.

  • The speed from the graph is 200 mph.
  • The speed of the Peregrine Falcon is 242 mph.

Since 200 mph is less than 242 mph, the speed represented by the graph is less than the speed of the Peregrine Falcon.

Final Answer:

The correct choice is: A - The speed represented by the graph is less than the speed of the Peregrine Falcon.

Would you like more details or have any questions about this? Here are 5 related questions to further explore:

  1. How can you calculate the speed from a different pair of points on a graph?
  2. What is the formula for determining the slope of a line, and how does it relate to speed?
  3. How can you use proportional relationships to predict other distances at different times?
  4. What other animals have impressive speeds, and how do they compare to the Peregrine Falcon?
  5. How do real-world factors, such as wind resistance, affect the speed of birds or vehicles?

Tip: When analyzing graphs of proportional relationships, the slope of the line represents the speed or rate of change in many contexts like distance over time.

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Math Problem Analysis

Mathematical Concepts

Proportional Relationships
Rates of Change
Slope of a Line

Formulas

Speed = Distance / Time

Theorems

Proportionality Theorem

Suitable Grade Level

Grades 6-8