Solve for w. 6+(w−10)=5
2 answers:
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Answer:
65,280
Step-by-step explanation:
Consider the 4×4 grid ...
where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.
The same will be true of 270° rotational symmetry, for the same reason.
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For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)
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The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...
65,536 -256 = 65,280 . . . . colorings not rotationally symmetric
The two angles are 155 degrees and 25 degrees
<h3><u>Solution:</u></h3>Given that two supplementary angles are in ratio 31 : 5
Let the first angle be 31a
Let the second angle be 5a
Two Angles are Supplementary when they add up to 180 degrees.
Therefore,
first angle + second angle = 180 degrees
<em><u>Therefore the angles are:</u></em>
first angle = 31a = 31(5) = 155 degrees
second angle = 5a = 5(5) = 25 degrees
Thus the two angles are 155 degrees and 25 degrees