.3 3. True or False? For any integer m, 2m(3m + 2) is divisible by 4. Explain to get credit.

Mathematics

1 answer:

Sav [38]3 years ago

4 0

Answer with explanation:

We have to prove that, For any integer m, 2 m×(3 m + 2) is divisible by 4.

We will prove this result with the help of Mathematical Induction.

⇒For Positive Integers

For, m=1

L HS=2×1×(3×1+2)

=2×(5)

=10

It is not divisible by 4.

⇒For Negative Integers

For, m= -1

L HS=2×(-1)×[3×(-1)+2]

=-2×(-3+2)

= (-2)× (-1)

It is not divisible by 4.

False Statement.

You might be interested in

Find the percent change from 30to 39

ankoles [38]

I want to say 9% but idrk what your asking

8 0

4 years ago

Read 2 more answers

ella drew a rectangle that was 3 units wide and 4 units long. Draw a different rectangle that has the same perimeter but a diffe

RUDIKE [14]

First we can find the perimeter of the given rectangle

P=2L+2W (L=length and W=width)
P=2*3+2*4
P=6+8
P=14

So now we want to come up with a different combination of numbers that would give up a perimeter of 14. We know that 14 is divisible by 2 so let's make out width 2. If we plug in 2 as the width and 14 as the perimeters, we can solve for length

14=2L+2*2
14=2L+4
10=2L (subtract 4 from both sides)
L=5

So the dimensions are 5 units and 2 units

Hope this helps!

5 0

4 years ago

Brian bought a 15 pound bag of concrete he split the bag into smaller bags that each hold 2(1/2) pounds.how many smaller bags di

GaryK [48]

He filled up 6 small bags of concrete

7 0

3 years ago

Hi pls help thank you very much

nignag [31]

If-then are the two answers

8 0

3 years ago

Given y=x^2 how would the graph of y=x^2+4 differ?

satela [25.4K]

A) The graph will move up by 4 units

6 0

3 years ago