Prove that
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Proof in explanation.

Step-by-step explanation:

I'm going to assume you mean "greater than or equal to".

We know .

We know this because any real number squared will result in a positive or zero result.

Let's expand the left hand side:

Distribute:

Combine like terms:

Commutative property of addition:

Add on both sides:

Now we wanted to show . Our right hand side almost appeared that way except the factor of 2 present there.

Let's go back to our inequality that we got:

Divide both sides by 2:

Note: Half of a positive number is less than that positive number.

This inequality says we would like it to say in the end:

Step-by-step explanation:

hello :

note : add for your statement : x>0 and y>0

look this solution :

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

e) none of the above because the measure of angle cba is 101°