Answer: A. divided the difference of the two quantities by the sum of the two quantities.
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Explanation:
The difference of the quantities is 20-15 = 5
The sum of the quantities is 20+15 = 35
Dividing those results leads to 5/35 = 0.142857 which rounds to 0.1429
That converts to 14.29%
This is likely the path Adam took. This path is incorrect. The correct steps are shown below
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Difference = 20-15 = 5
Divide the difference over the original quantity
5/20 = 1/4 = 0.25 = 25%
We have a 25% decrease because the new quantity (15) is smaller than the old quantity (20)
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Here's another way to approach the problem
A = old value = 20
B = new value = 15
C = percent change
C = [ (B-A)/A ] * 100%
C = [ (15-20)/20 ] * 100%
C = (-5/20)*100%
C = -0.25*100%
C = -25%
The negative C value means we have a negative percent change, ie we have a percent decrease. So this is another way to get a 25% decrease.
Your answer is 21 for this one.
Problem 1
x = measure of angle N
2x = measure of angle M, twice as large as N
3(2x) = 6x = measure of angle O, three times as large as M
The three angles add to 180 which is true of any triangle.
M+N+O = 180
x+2x+6x = 180
9x = 180
x = 180/9
x = 20 is the measure of angle N
Use this x value to find that 2x = 2*20 = 40 and 6x = 6*20 = 120 to represent the measures of angles M and O in that order.
<h3>Answers:</h3>
- Angle M = 40 degrees
- Angle N = 20 degrees
- Angle O = 120 degrees
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Problem 2
n = number of sides
S = sum of the interior angles of a polygon with n sides
S = 180(n-2)
2700 = 180(n-2)
n-2 = 2700/180
n-2 = 15
n = 15+2
n = 17
<h3>Answer: 17 sides</h3>
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Problem 3
x = smaller acute angle
3x = larger acute angle, three times as large
For any right triangle, the two acute angles always add to 90.
x+3x = 90
4x = 90
x = 90/4
x = 22.5
This leads to 3x = 3*22.5 = 67.5
<h3>Answers:</h3>
- Smaller acute angle = 22.5 degrees
- Larger acute angle = 67.5 degrees
