Question

Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necessary. show work
f(x) = - 0.5x + 2
g(x) = x^3 - 5x^2 + 3

Answer 1

The points of intersection for the two functions and round to the nearest tenth are (0.5, 1.4) and (4.85, -0.3)

System of equations

Given the following function

f(x) = - 0.5x + 2

g(x) = x^3 - 5x^2 + 3

The point of intersection is the point where f(x) = g(x)

x^3 - 5x^2 + 3 = - 0.5x + 2

x^3 - 5x^2 + 3 + 0.5x - 2 = 0

x^3 - 5x^2 + 0.5x + 1 = 0

Factorize and determine the value of x

x = 0.53 and 4.85

If x = 0.53

f(0.53) = -0.5(0.53) + 2

f(0.53) = -0.265 + 2

f(0.53) = 1.375

If x = 4.85

f(4.85) = -0.5(4.85) + 2

f(4.85) = -2.425 + 2

f(4.85) = -0.245

Hence the points of intersection for the two functions and round to the nearest tenth are (0.5, 1.4) and (4.85, -0.3)

Learn more on functions here: brainly.com/question/10439235

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