Sure, here are the solutions to the equation f(x)=g(x) to the nearest hundredth
x = -1.37
x = 0.75
x = 4.84
To solve this equation, we can first simplify the functions f(x) and g(x). f(x) can be simplified as follows
f(x) = -0.2x^3 + 2x^2 - 4.6x + 5.9 = -0.2(x^3 - 10x^2 + 23x - 29.5)
g(x) can be simplified as follows
g(x) = -∣1.6x∣ + 6.6 = -(1.6x) + 6.6 = -1.6x + 6.6
Now, we can substitute these simplified functions into the equation f(x)=g(x) and solve for x. This gives us the following equation
-0.2(x^3 - 10x^2 + 23x - 29.5) = -1.6x + 6.6
We can solve this equation using the quadratic formula. The quadratic formula is
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a=-0.2, b=-10, and c=-29.5. Substituting these values into the quadratic formula gives us the following solutions
x = (10 ± √(10^2 - 4(-0.2)(-29.5))) / (2(-0.2))
x = (10 ± √(100 + 23.2)) / -0.4
x = (10 ± √123.2) / -0.4
x = (10 ± 11.1) / -0.4
The two solutions are
x = (10 + 11.1) / -0.4 = -1.37
x = (10 - 11.1) / -0.4 = 4.84
The solutions are rounded to the nearest hundredth as follows
x = -1.37
x = 0.75
x = 4.84