<h2>
Step-by-step explanation:</h2>
As per the question,
Let a be any positive integer and b = 4.
According to Euclid division lemma , a = 4q + r
where 0 ≤ r < b.
Thus,
r = 0, 1, 2, 3
Since, a is an odd integer, and
The only valid value of r = 1 and 3
So a = 4q + 1 or 4q + 3
<u>Case 1 :-</u> When a = 4q + 1
On squaring both sides, we get
a² = (4q + 1)²
= 16q² + 8q + 1
= 8(2q² + q) + 1
= 8m + 1 , where m = 2q² + q
<u>Case 2 :-</u> when a = 4q + 3
On squaring both sides, we get
a² = (4q + 3)²
= 16q² + 24q + 9
= 8 (2q² + 3q + 1) + 1
= 8m +1, where m = 2q² + 3q +1
Now,
<u>We can see that at every odd values of r, square of a is in the form of 8m +1.</u>
Also we know, a = 4q +1 and 4q +3 are not divisible by 2 means these all numbers are odd numbers.
Hence , it is clear that square of an odd positive is in form of 8m +1
Answer:
Protractor
Step-by-step explanation:
A POSTULATE, LAW OR THEORY SHOULD NEVER BE ALTERED
∴ The protractor postulate states that the measurement of an angle between two rays can be designated as a unique number, and this number would be between 0 and 180 degrees, Hence for every angle A, there corresponds a positive real number less than or equal to 180. This postulate guarantee the use of a protractor to measure angles.
Hence, Given line AB and point O on that line in such a way that any ray that can be drawn with its endpoint at O can be put into a one- to-one correspondence with the real numbers between 0 and 180 is a statement that explains Protractor's Postulate.
Answer:
B) 29
Step-by-step explanation:
Given:
AC= 58
Point D and E are the midpoints of side AB and BC Respectively.
Solution:
According to Midpoint theorem which states:
"The segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side."
DE= 
AC
DE= 
Hence length of DE is 29.
If you divid 8.4 x 107 and 3 x 103 you should get 2.8 x 104
