Points A,B, and C are collinear. Points M and N are the midpoints of segments AB and AC. Prove that BC = 2MN
2 answers:
Look at the picture.
1)|AM| = |MB| = x
|AN| = |NC| = y
|BC| = 2y - 2x = 2(y - x)
|MN| = y - x
Therefore |BC| = 2|MN|
2)|AM| = |MB| = x
|AN| = |NC| = y
|BC| = 2y - 2x = 2(y - x)
|MN| = y - x
Therefore |BC| = 2|MN|
1)|AM| = |MB| = x
|AN| = |NC| = y
|BC| = 2y - 2x = 2(y - x)
|MN| = y - x
Therefore |BC| = 2|MN|
2)|AM| = |MB| = x
|AN| = |NC| = y
|BC| = 2y - 2x = 2(y - x)
|MN| = y - x
Therefore |BC| = 2|MN|
Hello ! (<span>I attached a picture of the drawing)</span>
<span>First, we draw a line with 3 points B,A,C in this order.Then </span><span>we will note the middle of AB with M and also the middle of AC with N.
</span>
<span></span><span>We can notice that BC = AB + AC
</span>
<span>M - the middle of AB ⇒ AM=MB=AB/2</span>
<span>N - the middle of AC ⇒ AN=NC=AC/2
</span>
<span>We can write MN as AM+AN , which means AB/2 + AC/2 . We can also write AB as BC-AC , so we will have :
</span>
<span>MN = AB/2 + AC/2</span>
<span>MN = (BC-AC)/2 + AC/2</span>
<span>MN = BC/2 - AC/2 + AC/2 ( AC/2 with -AC/2 are reduced)</span>
MN = BC/2 or BC = 2·MN
<span>First, we draw a line with 3 points B,A,C in this order.Then </span><span>we will note the middle of AB with M and also the middle of AC with N.
</span>
<span></span><span>We can notice that BC = AB + AC
</span>
<span>M - the middle of AB ⇒ AM=MB=AB/2</span>
<span>N - the middle of AC ⇒ AN=NC=AC/2
</span>
<span>We can write MN as AM+AN , which means AB/2 + AC/2 . We can also write AB as BC-AC , so we will have :
</span>
<span>MN = AB/2 + AC/2</span>
<span>MN = (BC-AC)/2 + AC/2</span>
<span>MN = BC/2 - AC/2 + AC/2 ( AC/2 with -AC/2 are reduced)</span>
MN = BC/2 or BC = 2·MN
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So we will be using dimensional analysis to solve it as such:
In short, 23,843 kL is 6,291,029.02 (6,291,029 rounded to the whole gallon) gallons.
Answer:
The degrees of freedom are given by:
The p value for this case would be given by:
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes
Step-by-step explanation:
Information given
represent the sample size
represent the confidence level
represent the sample variance
represent the value that we want to verify
System of hypothesis
We want to test if the true deviation for this case is lesss than 5minutes, so the system of hypothesis would be:
Null Hypothesis:
Alternative hypothesis:
The statistic is given by:
And replacing we got:
The degrees of freedom are given by:
The p value for this case would be given by:
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes