Consider the claim: if m is an even integer, then m^2+5m-1 is an odd integer.
(a.) prove the claim using a direct proof.
(b.) state the converse. is the converse true? provide a proof or give a counterexample.
i have read the previous examples and am having trouble with them so don't copy and paste a retired answer.

Rewriting the expression using m=2p we have:

is an odd integer but the converse is not true.

Step-by-step explanation:

Even numbers are written as 2n where n is any integer, while odd numbers are written as 2n-1 where n is any integer.

a) To prove that is an odd integer, we have to prove that it can be written as 2n-1.

By hypothesis, m is an even integer so we will write it as 2p.

Rewriting the original expression using we have:

Solving the expression and factorizing it we get

And this last expression is an expression of the form 2n-1, and therefore is an odd integer.

b) The converse would be: if is an odd integer, then m is an even integer.

We'll give a counterexample, let's make , then

is an odd integer but m is odd.

Therefore, the converse is not true.

she gotta workk that a 2

step-by-step explanation:

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1