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You such a lie Pewds
which one is g?
3. The length, in feet, of a small train at an amusement park can be modeled by the function f(c) = 9c + 14, where c is the number of passenger cars attached to the locomotive. The original passenger cars were replaced, and the length of the train is now modeled by the function h(c) = 12c + 14. Based on this information, which statement describes the change in this situation? F. The locomotive is now 9 feet long, and the length of each passenger car remained the same. *G. The locomotive is now 12 feet long, and the length of each passenger car remained the same. * H. Each passenger car is now 9 feet long, and the length of the locomotive remained the same. J. Each passenger car is now 12 feet long, and the length of the locomotive remained the same.
Thanks, much easier to read. Why do you think G is the right answer?
g and c are my go to answer when idk the answer tbh
Let's say the train has 0 cars. The function that describes the length of the train is now \[h(c) = 12c+14\] if we have 0 cars, then \(c=0\) and \[h(0) = \]
0? imma blonde and I suck at math im sorry
\[h(c) = 12c+14\]that means to find \(h(0)\) you replace \(c\) with \(0\) \[12(0) + 14 = \]
26(0) ? what
12(0) = 12*0 =
good. If \[12(0) = 0\]what does \[12(0)+14=\]
Right. So that means a train with 0 cars and the engine is 14 feet long. If that is the case, then the engine is 14 feet long. Engine 14 feet long is not compatible with answer choice G, is it?
If we use the first formula to find the length of a train with 0 cars, we have \[f(c) = 9c+14\]\[f(0) = 9(0)+14 = 9*0+14 = 0+14 = 14\] So with the original formula, a train with no cars is ALSO 14 feet long, meaning the engine is 14 feet long. Now we know that our answer has to be one where the engine stays the same length. That narrows it down to the 3rd and 4th choices. If the number of cars is \(c\), we can figure out how long each car is by looking at the number in front of \(c\) in the formula. Each car adds that number of feet to the train. If we have 0 cars, the train is the length of the locomotive. If we have 1 car, the train is the length of the locomotive + the length of 1 car. If we have 2 cars, the train is the length of the locomotive + the length of 2 cars, and so on. If we look at our formula \[h(c) = 12c+14\]with that in mind, it should be clear that one term (\(12c\)) represents the part where we add the length of the \(c\) cars, and the other term (\(+14\)) represents the part where we add the length of the engine.