Maria figure that the bowling balls on a rack weighed a total of 240 lb how many 16 pound bowling balls weigh a total of 240 lbs
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If -3+5i is a solution, then by the conjugate root theorem, -3-5i is also a solution. We find the polynomial by multiplying together the factors. If x = -4, then x + 4 is the factor. If x = -3+5i, then (x-(-3+5i)) is a factor, and so is (x-(-3-5i)). Simplifying those down gives us as the first factor as (x+3-5i) and the second as (x+3+5i). We can FOIL those 2 together to get their product, and then FOIL in x+4. FOILing the 2 complex factors together gives us . If we combine like terms and cross out things that cancel it's much easier than what it looks like there! It simplifies down to
. Since i^2 = -1, it simplifies further to
and finally, to
. Now we will FOIL in x+4.
. Our final simplified third degree polynomial is
So we are given a system:
Substitute x = 2 we get the system:
Multiply the first equation by -5 and the second by 2 we get the system:
Adding the two equations we get :
We find the value of y by using any of the other equations like this:
Final solution:
Substitute x = 2 we get the system:
Multiply the first equation by -5 and the second by 2 we get the system:
Adding the two equations we get :
We find the value of y by using any of the other equations like this:
Final solution: