Using algebraic methods, prove that the sum of 2 consecutive odd integers is always a multiple of 4.

This statement will always be true practically.

Step-by-step explanation:

Let the odd number be:

=2x - 1

So the next odd will be:

= 2x + 1

Now for getting sum of two odd numbers we will add them:

= (2x -1)+(2x + 1)

Opening brackets:

= 2x -1 +2x +1

A dding like terms, Both 1's  will be cancelled out

= 4x

Now this proves that adding two odd numbers will deduce to a result which will always a multiple of 4

Hence proved.

I hope it will help you!

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi