A health fitness research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend eac
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Answer:
The point where all three lines meet is (8, 11)
Step-by-step explanation:
The given functions are;
f(x) = x²⁽ˣ ⁻ ⁵⁾ + 3
g(x) = 2·x - 5
h(x) = 8/x + 10
Equating the simpler functions g(x) to h(x) to find the points of the same value gives;
2·x - 5 = 8/x + 10
2·x - 15 = 8/x
2·x² - 15·x = 8
2·x² - 15·x - 8 = 0
With the aid of an online application, we have;
(2·x + 1)(x - 8) = 0
x = -1/2, or x = 8
The y-values at the point of intersection, is given as follows;
g(x) = 2·x - 5 = 2×(-1/2) - 5 = -6 or g(x) = 2·x - 5 = 2×(8) - 5 = 11
The points where g(x) and h(x) meet are (-1/2, -6) and (8, 11)
To check where the point of intersection of the two functions g(x) ang h(x) meet f(x), we have;
At x = -1/2, f(x) = = 3.0442
At x = -1/2, f(x) = 2⁽⁸⁻⁵⁾ + 3 = 8 + 3 = 11
Therefore, the point where all three lines meet = (8, 11).