For some integer m, every odd integer is of the form a) m b) m + 1 c) 2m d) 2m + 1
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d) 2m + 1

Step-by-step explanation:

'n' is a positive integer which is divided by 2 we get some quotient 'm' and remainder 'r'

Where r = 0 and 1

n = 2m+r (i)

putting r = 0 in eq (i)

n = 2m+0

m = 2m ( Divisible by 2)

It is an even number.

putting r = 1 in eq(i)

n = 2m+1 ( not divisible by 2)

It is an odd number.

So every odd number is in the form of (2m+1). where m is any positive integer.

Every even number is in the form of (2m) where m is any positive integer.

HOPE IT HELPS!!!

d) 2m+1

Step-by-step explanation:

for example:

m be 2 then. 2×2+1=5

m be 3 then. 2×3+1=7

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

about 0.75 hours

step-by-step explanation: