The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three time
1 answer:
<h3>Answers:</h3>
- x = 45
- y = 53
- z = 82
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Explanation:
The three angles add to 180, so x+y+z = 180
The second and third angles add to 3 times the measure of the first, so y+z = 3x
The third angle is 29 more than the second, so z = y+29
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The system of equations is
For now, let's focus on the second and third equations only.
Start with y+z = 3x. Replace z with y+29 which is valid because of the third equation.
So we'll have
y+z = 3x
y+y+29 = 3x
2y+29 = 3x
Let's isolate y
2y+29 = 3x
2y = 3x-29
y = (3x-29)/2
y = 3x/2 - 29/2
y = 1.5x - 14.5
We'll use this later.
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Go back first equation of the system. Plug in z = y+29
x+y+z = 180
x+y+y+29 = 180
x+2y+29 = 180
Then plug in y = 1.5x - 14.5 we found earlier
x+2y+29 = 180
x+2(1.5x-14.5)+29 = 180
x+3x-29+29 = 180
4x = 180
x = 180/4
x = 45
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We can use this x value to find y
y = 1.5x - 14.5
y = 1.5*45 - 14.5
y = 53
and use this to find z
z = y+29
z = 53+29
z = 82
As a check, x+y+z = 45+53+82 = 180 to help confirm the answer. I'll let you check the other equations.
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Step-by-step explanation:
We are given the following data-set:
70, 65, 71, 78, 89, 68, 50, 75
Deviations from the mean
–0.75, –5.75 , 0.25, 7.25, 18.25, –2.75, –20.75, 4.2
Sample size, n = 8
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Sum of squares of differences =
0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5
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where are data points,
is the mean and n is the number of observations.
Sum of squares of differences =
0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5
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Some examples:
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