f(x) = 4x - x^2
1)
f(4) = 4(4) - 4^2 = 16 - 16 = 0
f(-4) = 4(-4) - (-4)^2 = -16 - 16 = -32
f(4) - f(-4) = 0 - (-32) = 32
2)
f(3/2) = 4(3/2) - (3/2)^2
f(3/2) = 6 - 9/4 = 15/4
√f(3/2) = √(15/4) = √15 / 2
3)
f(x + h) = 4(x + h) - (x + h)^2
= 4x + 4h -(x^2 + 2xh + h^2)
= 4x + 4h -x^2 - 2xh - h^2
f(x - h) = 4(x - h) - (x - h)^2
= 4x - 4h -(x^2 - 2xh + h^2)
= 4x - 4h -x^2 + 2xh - h^2
So
[f(x + h) -f(x - h) ] / 2h
= [4x + 4h -x^2 - 2xh - h^2 - ( 4x - 4h -x^2 + 2xh - h^2 )] / 2h
=( 4x + 4h -x^2 - 2xh - h^2 - 4x + 4h + x^2 - 2xh + h^2 ) / 2h
= (8h - 4xh) / 2h
= 2h(4 -2x) / 2h
= 4 - 2x
Answer: [f(x + h) -f(x - h) ] / 2h = 4 - 2x
Using it's concept, the experimental probability that the next client to get a haircut Manuel's salon will have brown hair is 1/2.
<h3>
What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>. For an experimental probability, these number of outcomes are taken from previous trials.
In this problem, out of 12 haircuts, 6 were with brown hair, hence the probability is given by:
p = 6/12 = 1/2.
More can be learned about probabilities at brainly.com/question/14398287
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Answer:
“two negatives = positive” rule works for multiplication and division.
Step-by-step explanation:
-5 + (-3) example
imagine a number line with 0 in the center. From (0) You move left 5 places to (-5) on the number line. Now you move another 3 more to the left (-3) and land on (-8).
You are combining the negatives. I hope this helps.
Answer:
In 12 months
Step-by-step explanation:
Let a = year when average the average cost of owning a freezer would be less than $117
($850 + $40a) / a < $117
$850 + $40a < $117a
collecting like terms
$850 < $77a
a = 11.04 months
The coefficients in order are 2 2 1
