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Dovator [93]
3 years ago
7

The waiting time to a roller coaster is 20 minutes when 150 people are in line. How long is the waiting time when 240 people are

in line?
Mathematics
1 answer:
scoray [572]3 years ago
5 0
So, the first thing you want to find out is how many seconds each person adds to the wait time. Find out how many seconds are in 20 minutes.. 20*60=120. 120/150=0.8 seconds. Each person adds 0.8 seconds to the wait time. Now, multiply that by 240.. 240*0.8=192 seconds. Lastly, find out how many minutes 192 seconds is... 192/60=32 minutes.
I hope I did that right! And if I did, I hope that helped!
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Grab the image of the rectangle DEFG reflection across the line x= 3​
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Answers:

  • D ' at (9, -9)
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Refer to the diagram below

========================================

Explanation:

For points D,E,F,G we will follow these steps

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  2. Reflect across the y axis using the rule (x,y) \to (-x,y). Here we have the x coordinate flip in sign from positive to negative, or vice versa. The y coordinate stays the same.
  3. Shift everything 3 units to the right so we effectively undo the first step. This places the points in the proper final position.

Let's go through an example:

Point D is located at (-3, -9). Apply the three steps mentioned above.

  1. Shift point D three units to the left to arrive at (-6, -9)
  2. Reflect over the y axis to go from (-6, -9) to (6, -9)
  3. Lastly, shift 3 units to the right to move to (9, -9) which is the location of D'

In short, D(-3,-9) reflects over the line x = 3 to land on D ' (9, -9)

The other points E, F, G will follow the same steps to get the answers you see at the top.

The diagram below visually summarizes everything.

-------------

Side notes:

  • The distance from D to the line of reflection is the same as the distance from D' to the line of reflection. Put another way, the line of reflection bisects segment DD'. Points E,F,G follow the same property.
  • Going from D to E to F to G has us go counterclockwise. Going from D' to E' to F' to G' has us go clockwise. Any reflection transformation will flip the orientation.

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