If one of our zeros is 4, then the factor is x-4. If the second zero is 5i, then the conjugate root theorem says there HAS to be a root that is -5i. So our 3 factors are (x-4)(x+5i)(x-5i). We will FOIL out these factors to get the polynomial. Let's start with the ones that contain the imaginary numbers. Doing that mutliplication we get x^2-25i^2. i^2 is equal to -1, so what that expression simplifies down to is
. Now we will multiply in that last factor of (x-4):
. FOILing out we have
. There you go!
Of course it is c. range would show the difference between the highest and lowest scores, there is no mode in her data set, and the median is the middle point of the data set
When you move the 40 to the other side ur subtracting and so -40 - 5 is -45, after you divide -45 and 5 and get -9.
Answer:
Since y is a solution of the homogeneus system then satisfies Ay=0.
Since z is a solution of the system Ax=b then satisfies Az=b.
Now, we will show that A(y+z)=b.
Observe that A(y+z)=Ay+Az by properties of the product of matrices.
By hypotesis Ay=0 and Az=b.
Then A(y+z)=Ay+Az=0+b=b.
Then A(y+z)=b, this show that y+z is a solution of the system Ax=b.
