Answer:
If
is divisible by 3, the n is also divisible by 3.
Step-by-step explanation:
We will prove this with the help of contrapositive that is we prove that if n is not divisible by 3, then,
is not divisible by 3.
Let n not be divisible by 3. Then
can be written in the form of fraction
, where x and y are co-prime to each other or in other words the fraction is in lowest form.
Now, squaring

Thus,


It can be clearly seen that the fraction
is in lowest form.
Hence,
is not divisible by 3.
Thus, by contrapositivity if
is divisible by 3, the n is also divisible by 3.
<u>Given</u>:
The equation of the circle is 
We need to determine the center and radius of the circle.
<u>Center</u>:
The general form of the equation of the circle is 
where (h,k) is the center of the circle and r is the radius.
Let us compare the general form of the equation of the circle with the given equation
to determine the center.
The given equation can be written as,

Comparing the two equations, we get;
(h,k) = (0,-4)
Therefore, the center of the circle is (0,-4)
<u>Radius:</u>
Let us compare the general form of the equation of the circle with the given equation
to determine the radius.
Hence, the given equation can be written as,

Comparing the two equation, we get;


Thus, the radius of the circle is 8
409,821,735,673.....the value of the 4 in this number is 400 billion
Given:
The bases of a trapezoid lie on the lines


To find:
The equation that contains the midsegment of the trapezoid.
Solution:
The slope intercept form of a line is

Where, m is slope and b is y-intercept.
On comparing
with slope intercept form, we get

On comparing
with slope intercept form, we get

The slope of parallel lines are equal and midsegment of a trapezoid is parallel to the bases. So, the slope of the bases line and the midsegment line are equal.

The y-intercept of one base is 7 and y-intercept of second base is -5. The y-intercept of the midsegment is equal to the average of y-intersects of the bases.




So, the y-intercept of the required line is 1.
Putting m=2 and b=1 in slope intercept form, we get

Therefore, the equation of line that contains the midsegment of the trapezoid is
.