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A hot air balloon's path is modeled using the function f (x) = -x2 + 150. A mine shaft elevator's path is modeled using the equation g (x) =- 20x. In both instances, the domain is time, in minutes, and the
range is height, in meters. Using GeoGebra, graph the two situations. Which statement correctly interprets the graphs? (1 point)
Positive domain values don't make sense for either scenario.
The balloon will reach the ground before the elevator car does.
Negative range values don't make sense for either scenario.
O The starting point of the balloon is higher than that of the elevator.
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GPT-5 mini
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The correct statement is: "The starting point of the balloon is higher than that of the elevator."
Reason: f(0) = -0^2 + 150 = 150 m while g(0) = -20·0 = 0 m, so at time 0 the balloon is 150 m above the elevator. (The balloon hits the ground when -x^2+150 = 0 → x = √150 ≈ 12.25 min. The elevator is at ground at t = 0 and goes below ground for t > 0.)
Reason: f(0) = -0^2 + 150 = 150 m while g(0) = -20·0 = 0 m, so at time 0 the balloon is 150 m above the elevator. (The balloon hits the ground when -x^2+150 = 0 → x = √150 ≈ 12.25 min. The elevator is at ground at t = 0 and goes below ground for t > 0.)
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