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Julli [10]
3 years ago
12

What are the coordinates of the endpoints of the midsegment for DEF that is parallel to DE

Mathematics
1 answer:
Nutka1998 [239]3 years ago
6 0

Answer:

\left(\dfrac{x_D+x_F}{2},\dfrac{y_D+y_F}{2}\right),  \left(\dfrac{x_E+x_F}{2},\dfrac{y_E+y_F}{2}\right).

Step-by-step explanation:

Let points D, E and F have coordinates (x_D,y_D),\ (x_E,y_E) and (x_F,y_F).

1. Midpoint M of segment DF has coordinates

\left(\dfrac{x_D+x_F}{2},\dfrac{y_D+y_F}{2}\right).

2. Midpoint N of segment EF has coordinates

\left(\dfrac{x_E+x_F}{2},\dfrac{y_E+y_F}{2}\right).

3. By the triangle midline theorem, midline MN is parallel to the side DE of the triangle DEF, then points M and N are endpoints of the midsegment for DEF that is parallel to DE.

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3 years ago
A data set of 27 different numbers has a mean of 33 and a median of 33. A new data set is
Svetllana [295]

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:

M = \frac{(x_1 + x_2 + x_3 ... + x_n)}{N}

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:

M' = \frac{(x_1 - 7) + (x_2 - 7) + ... + (x_{k}) + ... + (x_n + 7)}{N} = \frac{(x_1 + x_2 + ... + x_n) + (-7)*(n/2 - 0.5) + 7*(n/2 - 0.5)}{N}  = \frac{(x_1 + x_2 + ... + x_n)}{N} = M

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:

SD = \sqrt{\frac{(x_1 - M)^2 + ... + (xn - M)^2}{N} }

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.

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2 years ago
Read 2 more answers
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MrRa [10]

Step-by-step explanation:

-2x - 5 = 4

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2 years ago
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I was sick today at school and I didn’t learn anything about this I need help!!
Harrizon [31]

Answer:

Assuming 16 and 17.  5  books in 5 shelves, do you need help making an array?  for 17, composite since you can divide the new number by either prime number, and a prime number can only be divided by 1 and itself.

Step-by-step explanation:

What are the prime numbers in between 21 and 30?  


Well all numbers are 21, 22,23,24, 25, 26, 27, 28, 29, 30.

We know right away prime numbers can't be even so now we have 21, 23, 25, 27, 29.

Fives are easy to check for too so we can get rid of 25.

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the only way 25 splits up is 5x5, so that means there are 5 books per shelf and 5 shelfs.


for 17 the defenition of prime is that it can only be divided by 1 and itself.  If you multiply two different numbers to get a new number, then this new number can be dived by the two you used.  For example 3 and 2 multiply to get 6.  Because of that you can divide 6 by 2 to get 3 or divide 6 by 3 to get 2, so since it is divisible by more than just 1 and itself, it is not prime.  Let me know if you need any more help with this.  

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