Simplify and evaluate without a calculator. 3*(m-4)-n*(m-4) if m=5 and n=3
2 answers:
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Applying the segment addition theorem, the length of line segment VW is: 2 units.
<h3>What is the Segment Addition Theorem?</h3>The segment addition theorem states that the sum of the lengths of two segments that make up a larger line segment equals the measure of the larger line segment, if the point on the line segments are collinear.
UV = 8x
VW = x+1
UW = 10
UV + VW = UW (segment addition theorem)
Substitute the values
8x + (x + 1) = 10
Open bracket
8x + x + 1 = 10
Combine like terms
9x + 1 = 10
Subtract 1 from both sides
9x + 1 - 1 = 10 - 1
9x = 9
Divide both sides by 9
9x/9 = 9/9
x = 1
VW = 8x + (x + 1)
Plug in the value of x
VW = x + 1
VW = 1 + 1
VW = 2 units.
Therefore, applying the segment addition theorem, the length of line segment VW is: 2 units.
Learn more about the segment addition theorem on:
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Answer:
Option D.
Step-by-step explanation:
Suppose that we have a set of N values:
{x₁, x₂, ..., xₙ}
The median is the value in the middle, and the mean is calculated as:
Because here we have "the median" then we will assume that N is odd, and there is only one median, the value "k" (if N was even, the median would be the mean of the two middle values, that case is really similar to the case where N is odd, so solving only one of the cases is enough)
Now we add 7 to all the values greater than the median
We subtract 7 to all values smaller than the median.
Then the median remains unchanged (because we did not add nor subtract anything to the median).
The new mean will be:
So the mean does not change.
Because the mean is computed as the sum of the numbers divided by N, and the mean does not change, and N does not change, then the sum of the numbers does not change.
Finally, the standard deviation is computed as:
Because M does not change, if we add or subtract numbers to some of the values, the standard deviation will change (Because all the terms are squared, so the added and subtracted sevens don't cancel like in the previous cases)
Then the only value that does not have the same value in both the original and new data sets is the standard deviation.
If you're looking for the dashed line, here it is.
