<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
Let,
the no. of adults be "x"
then, the no. of childern = total people - total adults
= (30 - x)
Now,
According to the quesiton,
2 (30 - x) + 5x = 87
60 - 2x + 5x = 87
60 + 3x = 87
3x = 87 - 60
3x = 27
x = 27 / 3
x = 9
So, there were 9 adults in the group
Answer:315 bulbs planted and 7 left over
Step-by-step explanation:322/15 = 21.44
Roughly around 21 rows.
21 x 15 = 315 bulbs planted
322 - 315 = 7 bulbs left over
Hello!
So you need to find the sin of the angle:
sin20 = x / 10
10 x sin20 = x
x = 3.4
Hope this helps :))
Answer:
<h2>(3 + i)(4 + 2i) = 10 + 10i</h2>
Step-by-step explanation:
Use FOIL: (a + b)(c + d) = ac + ad + bc + bd
and i² = -1
