I need help with some math stuff. Catapult Launch
In this activity, you will write and solve a system of linear equations given two tables of data. You will then analyze the solution of the system to draw a conclusion.

Part A
While building his catapult, Aiden tested several different designs. He varied the arm length of his catapult and recorded the horizontal distance between where the ball was launched and where it landed for each arm length.

The table presents Aiden’s data showing the length of the catapult arm in relation to the horizontal distance the catapult launched the tennis ball.

Length of Catapult Arm (cm) Horizontal Distance (cm)
60 320
80 352.4
100 386.8
60 288.1
70 315
75 322
90 362
100 390
85 350
95 398

Use the graphing tool to determine the line of best fit for Aiden’s data.

Question
What is the equation of the line of best fit for Aiden’s data?

Enter the correct answer in the box by replacing m and b in the equation. Round each number to the nearest tenth.

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Part B
Natalie also made a catapult, but she used stronger elastic bands than Aiden did. As a result, she was able to send her ball farther with a shorter arm length. She also varied the length of her catapult arm while measuring the horizontal distance between where the tennis ball was launched and where it landed. The table presents the data she recorded while using her catapult.

Length of Catapult Arm (cm) Horizontal Distance (cm)
25 290.8
35 325.4
30 315.2
60 420
65 435.8
50 385.1
45 355
40 362
50 378.3
40 333.9

Use the graphing tool to determine the line of best fit for Natalie’s data.

Question
What is the equation of the line of best fit for Natalie’s data?

Enter the correct answer in the box by replacing m and b in the equation. Round each number to the nearest tenth.

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Part C
Question
If Aiden and Natalie each set the arm length of their catapults to 55 centimeters, which statement is true?

Aiden’s catapult will launch the tennis ball farther than Natalie’s catapult will.
Natalie’s catapult will launch the tennis ball farther than Aiden’s catapult will.
Both Aiden’s and Natalie’s catapults will launch the tennis ball the same horizontal distance.
There is not enough information to determine whose tennis ball will launch farther at this arm length.
Part D
Question
Write and solve a system of equations made up of Aiden’s and Natalie’s lines of best fit that they can use to find the catapult arm length that they could both use to launch their tennis balls the same distance. What is the solution to the system?

Type the correct answer in the box. Round each number to the nearest tenth.

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Part E
The solution to the system of equations representing Aiden’s and Natalie’s data is shown on the graph.

Analyze the solution to the system to determine whether there is a catapult arm length that Aiden and Natalie can both use to launch their tennis balls the same distance. Explain your reasoning.

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