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dawsoncarlisle
30.09.2020 •
Mathematics
The functions below represent the amounts of water released from two reservoirs over x weeks:
Reservoir A
f(x) = x2 – 7x + 5
Reservoir B
g(x) = 3x2 – 6x + 2
The function h(x) = f(x) – g(x) represents the difference in the amounts of water released.
Determine which statements about h(x) and about the reservoirs are true. Check all that apply.
h(x) = –2x2 – 13x + 6
h(x) = –2x2 – x + 3
Reservoir A releases less water than Reservoir B over 1 week.
Reservoir A releases the same amount of water as Reservoir B over 1 week.
Reservoir A releases more water than Reservoir B over 1 week.
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Ответ:
Step-by-step explanation:
Given:
f(x) = x^2 -7x +5
g(x) = 3x^2 -6x +2
h(x) = f(x) -g(x)
Find:
h(x)
h(1)
Solution:
The expression for h(x) is found by evaluating its definition:
h(x) = (x^2 -7x +5) -(3x^2 -6x +2)
h(x) = x^2(1 -3) +x(-7 -(-6)) +(5 -2)
h(x) = -2x^2 -x +3
Then h(1) is found by substituting 1 for x:
h(1) = -2(1^2) -(1) +3 = -2 -1 +3
h(1) = 0 . . . . difference in release amounts after 1 week is 0
The true statements are ...
h(x) = -2x^2 -x +3Reservoir A releases the same amount of water as Reservoir B over 1 weekОтвет:
-250
Step-by-step explanation:
We could solve the problem above using integers. Integers are the set of whole numbers and their opposites. The number line is used to represent integers. So, when it is a 'decrease' it is negative.