Answer:
Step-by-step explanation:
cos (2α)*sin (α-β)-cos(β-α)*sin(2α)
cos (β-α)=cos {-(α-β)}=cos (α-β)
[cos (-x)=cos x]
sin(α-β)*cos (2α)-cos (α-β)*sin (2α)=sin (α-β-2α)=sin (-α-β)
=sin {-(α+β)}
=-sin (α+β)
<h3>
Answer: 0.5</h3>
This is equivalent to the fraction 1/2
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Explanation:
The distance from A to B is 3 units. We can count out the spaces, or subtract the x coordinates of the two points and apply absolute value.
|A-B| = |-5-(-8)| = |-5+8| = |3| = 3
or
|B-A| = |-8-(-5)| = |-8+5| = |-3| = 3
We can say that segment AB is 3 units long.
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The distance from A' to B' is 1.5 units because...
|A'-B'| = |-2.5-(-4)| = |-2.5+4| = |1.5| = 1.5
or
|B'-A'| = |-4-(-2.5)| = |-4+2.5| = |-1.5| = 1.5
The absolute values ensure the distance is never negative.
We can say A'B' = 1.5
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Now divide the lengths of A'B' over AB to get the scale factor k
k = (A'B')/(AB)
k = (1.5)/(3)
k = 0.5
0.5 converts to the fraction 1/2.
The smaller rectangle A'B'C'D' has side lengths that are exactly 1/2 as long compared to the side lengths of ABCD.
Answer:
C. 4:13
Step-by-step explanation:
there are 4 students in the 4th grade and 4+9= 13 so it is 4:13
Number of vertices of hexagon is 6
