<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
C) 2
1) Given the table, let's find out that missing data picking 2 points (2,-10) and (6,-4)
Since we have the slope, let's work on finding the linear coefficient
plugging point (2,-10) into that:
y= mx +b
-10 =3/2(2) +b
-10 =6/2 +b
-10= 3 +b
-10-3 =b
b= -13
2) So the rule of that function is y= 3/2x -13
Plugging x= 10 we have
y= 3/2(10) -13
y=2
3) So the missing y-coordinate is 2.
The answer is C let me know if it was wrong but it should be correct :)
When converting to milimeter from micrometer you will divide by 1000. i.e
I think number 2 not sure tho
