Let p and q be integers and define r = pq + p + q. Prove that r is even if and only if p and q are both even.

The value of r can only be even if both value of P and q are even

Exploring the 3 possible scenarios:

If p is even and q is odd:

the value of Pq is even and P ₊ q is odd

Hence, the value of r (r = pq + p + q) is : even number ₊ odd number = odd number

e.g if p=2 and q=3

r = pq + p + q = 2*3 + 2+3 =6 +5 =11

and If p is odd and q is odd:

the value of Pq is odd and P ₊ q is even

Hence, the value of r (r = pq + p + q) is : odd number ₊ even number= odd number

e.g if p=5 and q=3

r = pq + p + q = 5*3 + 5+3 =15 + 8 = 23

If p is even and q is even:

the value of Pq is even and P ₊ q is even

Hence, the value of r (r = pq + p + q) is : even number ₊ even number= even number

e.g if p=2 and q=4

r = pq + p + q = 2*4 + 2+4 =8 + 6= 14

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation: