In a set of data, if the data is perfectly symmetrical then the mean is equal to the median. In this case, the median would be 50.
For example, consider the data set: {25, 50, 75}
The mean is going to be 50 because = 50
The median is also 50 because that is the middle number when ordered numerically.
Hope this helped! Let me know if you have any more questions.
Answer: x = 2
=============================================================
Explanation:
Refer to the diagram below.
I've added points D,E,F,G. This helps with labeling the segments and angles, and identifying the proper triangles (to see which are congruent pairs).
Triangle GEA is congruent to triangle GFA. We can prove this using the AAS congruence theorem. We have AG = AG as the pair of congruent sides, and the congruent pairs of angles are marked in the diagram (specifically the blue pairs of angles and the gray right angle markers)
Since triangle GEA is congruent to triangle GFA, this means the corresponding pieces segment GF and GE are the same length.
The diagram shows GF = 3x-4, so this means GE = 3x-4 as well.
----------------------
Through similar steps, we can show that triangle GEC is congruent to triangle GDC. We also use AAS here as well.
The congruent triangles lead to GD = GE. So GD = 3x-4. The diagram shows that GD = 6x-10
Since GD is equal to both 3x-4 and 6x-10, this must mean the two expressions are equal.
----------------------
Now let's solve for x
6x-10 = 3x-4
6x-3x = -4+10
3x = 6
x = 6/3
x = 2
Answer
Find out the how long did they rest in 8 hours.
To prove
As given
contestants in a dance-a-thon rest for the same amount of time every hour.
A couple rests for 25 minutes in 5 hours .
As
25 mintues = 5 hours
1 hours = 5 mintues
Thus in 1hours a the dance -a-thon rest for 5 mintues.
Now for 8 hours.
8 hours = 8 × 5 mintues
= 40 mintues
Therefore in 8 hours a dance-a-thon rest for 40 mintues.
Answer:
Step-by-step explanation:
Equilateral triangles have 3 congruent sides, so all 3 sides have the same length. Therefore, we know that . We are given the lengths of all 3 sides in terms of
, but we only need to set two of them equal to each other to solve for
. Let's use
and
to solve for
. We know that
,
, and
. Therefore, we can write the following equation to solve for
(Substitute given values into equation)
Solving for , we get:
(Subtract
from both sides of the equation to isolate constants)
(Simplify)
(Subtract
from both sides of the equation to isolate
)
(Simplify)
(Divide both sides of the equation by
to get rid of
's coefficient)
(Simplify)
Therefore, , and
. Hope this helps!