Use five different colors to paint the four rectangles A, B, C and D shown in the figure. No two rectangles sharing an edge can
be the same color. How many ways are there to color the rectangles?
1 answer:
There are 120 ways to color the 4 rectangles
<h3>How to determine the number of ways?</h3>The given parameters are:
Paints, n = 5
Rectangles, = 4
The number of ways to color the rectangles is
This gives
Apply the permutation formula
Evaluate the expression
Ways = 120
Hence, there are 120 ways to color the 4 rectangles
Read more about permutation at:
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Answer:
B. a reflection across X axis and then a dilation by a scale factor of 1.5
Step-by-step explanation:
As clear from the graph all the coordinates of image 2 are 1.5 times of image 1 so shape 2 is dilated by the scale factor 1.5.
It is evident from the graph that lines AO and A"O"are parallel to each other so shape 2 is the reflection of shape 1.
Now we calculate the magnitude of line AB
m1 = (y2-y1)/(x2-x1)
=(-3+6)/(-4.5=9)
=3/4.5
=1/1.5
=2/3
Next we calculate magnitude m2 of A"B"
m2= (2-4) /(-3+6)
=(-2/3)
Then we know Tan(180-∅) = -tan∅
similarly if m1=(-m2)
then the one line having magnitude m2 is the rotated image through X axis by 180° of the line having magnitude m1.
So the answer is B.
