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2 years ago

.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]2 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.

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2 years ago

Explain weather 14t-3t is equivalent to 3t-14t. Support your sender by evaluating the expression for t=2.

m_a_m_a [10]

Answer:

Solving 14t-3t we get 22 and 3t-14t we get -22

So, 14t-3t is not equivalent to 3t-14t.

Step-by-step explanation:

We need to explain weather 14t-3t is equivalent to 3t-14t. Support your sender by evaluating the expression for t=2.

<em>Equivalent expressions are those that have same values for any value of variable substituted.</em>

Now, We check if our expressions are equivalent, by evaluating the expression for t=2.

If they are equivalent, they would have same result after evaluation.

First, put t=2 into 14t-3t

$14t-3t\\Put\:t=2\\=14(2)-3(2)\\=28-6\\=22$

Now put t=2, into 3t-14t

$3t-14t\\Put\:t=2\\=3(2)-14(2)\\=6-28\\=-22\\$

For solving 14t-3t we get 22 and 3t-14t we get -22

So, 14t-3t is not equivalent to 3t-14t.

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2 years ago