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deadea46
31.07.2020 •
Mathematics
A clock loses 5 seconds every 12 minutes. At this rate, how many minutes will the clock lose in a 24-hour period?
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Ответ:
10 minutes
Step-by-step explanation:24h = 24x60min = 1440min
5 sec 12 min
x sec 1440 min
x = 1440*5/12 = 600 sec = 10 min
Ответ:
x = -b/2a
We can solve this problem by:
1) Looking at the given graphs of the polynomial functions and looking at where each parabola is cut in half
2) Solving for each axis of symmetry algebraically by first putting each given function into the standard form of ax² + bx + c then solving for the axis of symmetry.
In this problem, I'll be solving for each axis of symmetry algebraically.
The first function: f(x)
f(x) = -4(x - 8)² + 3
f(x) = -4(x - 8)(x - 8) + 3
f(x) = -4(x² - 16x + 64) + 3
f(x) = -4x² + 64x - 256 + 3
f(x) = -4x² + 64x - 253
Axis of symmetry: x = -b / 2a
x = -(64) / 2(-4)
x = -64 / -8
x = 8
Axis of symmetry: x = 8
The second function: g(x)
g(x) = 3x² + 12x + 15
The function function is already in standard form, so just substitute the values into the formula for the axis of symmetry.
x = -b / 2a
x = -(12) / 2(3)
x = -12 / 6
x = -2
Axis of symmetry: x = -2
The third function: h(x)
h(x) = -1(x - 3)² + 2
h(x) = -1(x² - 6x + 9) + 2
h(x) = -x² + 6x - 9 + 2
h(x) = -x² + 6x - 7
Axis of symmetry: x = -b / 2a
x = -b / 2a
x = -(6) / 2(-1)
x = -6 / -2
x = 3
Axis of symmetry: x = 3
Solution: The ranking of the functions based on their axis of symmetry from smallest to largest is g(x), h(x), and f(x).