daniel is on an airplane flying to a destination 825 miles away. after one hour, the pilot announces that the plane is 495 miles away from its destination airport. in another hour, the pilot announces that the plane will begin its half-hour descent for the final 165 miles.

which equation represents the remaining distance, in miles, to the destination in terms of (t), the time, in hours, since leaving the airport?

(d = 825 - 165t)
(d = 825 - 330t)
(d = 825 + 165t)
(d = 825 + 330t)

Question

daniel is on an airplane flying to a destination 825 miles away. after one hour, the pilot announces that the plane is 495 miles away from its destination airport. in another hour, the pilot announces that the plane will begin its half-hour descent for the final 165 miles.

which equation represents the remaining distance, in miles, to the destination in terms of (t), the time, in hours, since leaving the airport?

(d = 825 - 165t)
(d = 825 - 330t)
(d = 825 + 165t)
(d = 825 + 330t)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Rate of Change", "Linear Modeling" ], "new_concepts": [], "current_concepts": [ "Linear Rate of Change", "Linear Modeling" ] } ## Determine the initial value and rate of change $$ \begin{aligned} d_0 &= 825 \ d_1 &= 495 \ r &= \frac{d_1 - d_0}{1 - 0} = \frac{495 - 825}{1} = -330 \end{aligned} $$ ## Formulate the linear equation $$ \begin{aligned} d &= d_0 + r \cdot t \ d &= 825 - 330t \end{aligned} $$ ## Verify with the second data point $$ \begin{aligned} t &= 2 \ d &= 825 - 330(2) = 825 - 660 = 165 \end{aligned} $$

d = 825 - 165t

d = 825 - 330t

d = 825 + 165t

d = 825 + 330t

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Modeling" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the initial value and rate of change

Formulate the linear equation

Verify with the second data point

Answer: