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The teacher spend some amount on buying costumes and microphones for 6 cast members.
<u>GiveN</u><u>:</u>
- Cost of each costume = $38
- Cost of each microphone = $c
- Total money spent = $354
Let's frame the equation. Total money is the total amount spent for 6 cast members.
Money spent on costumes = $38 × 6
Money spent on microphone = $c × 6
<u>Equation:</u>
Taking 6 as common,
Dividing 6 from both sides,
Solving further,
So, the cost of each microphone = <u>$21</u>
The teacher spent this much on each microphone.
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The coordinates of the point S' is (2,1)
Explanation:
Given that the RST has vertices R(0,0), S(10,5) and T(5,-5)
The image R'S'T' is the image of RST after a dilation with center (0,0) and scale factor
We need to determine the coordinates of the point S'
The coordinates of S' can be determined by multiplying both the x and y - coordinates of the point S with the scale factor
Let us consider the x - coordinate of the point S and multiply it with the scale factor
Thus, we have,
x - coordinate of the point S' is given by
Thus, the x - coordinate of the point S' is 2
Similarly, the y - coordinate of the point S' can be determined by multiplying the point S with the scale factor
Thus, we have,
The y - coordinate of the point S' is given by
Thus, the y - coordinate of the point S' is 1
Hence, the coordinates of the point S' is (2,1)
A and B must be disjoint. You have, by the inclusion/exclusion principle, that
where the last term is required to prevent double counting. When
and 
are disjoint, you have 
and 
, leaving you with
where the last term is required to prevent double counting. When