You have 13 toppings. You can choose 3. How many combinations are there?
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Answer:
see attached
Step-by-step explanation:
Each point moves 3 times the distance from the center of dilation that it was.
You can compute the new coordinates by ...
L = P - O . . . . . the length from O to P is P-O for some point P and origin O
Then 3 times that distance is
3L = 3P -3O
We want to find the point P' that is 3L from O, so we add this distance to the coordinates of O. We get ...
P' = 3L +O = 3P -3O +O
P' = 3P -2O
So, for the lower left point A(-2, -7), the dilated image point A' is ...
A' = 3(-2, -7) -2(2, -7) = (-6, -21) +(-4, 14) = (-10, -7)
That is, ...
A' = 3A +(-4, 14)
The coordinates of the remaining points can be found similarly.
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On a graph, it is usually fairly easy to count the grid squares in each direction between the point of interest and the center of dilation. The image point is 3 times the distance in each direction (horizontally, vertically).
Some theoretical probability of a rolling primary color could be these:
