Answer:
64°
Step-by-step explanation:
<em>So supplement angles are equal to 180, so first our two angles added together will be 180:</em>
x + x = 180
<em>Now one of these angles is 6 greater than half:</em>
x + (x/2 + 6) = 180
<em>Then we will solve for x:</em>
x + (x/2 + 6) = 180
x + x/2 + 6 = 180
x + x/2 = 174
x = 174
x = 116
<em>Plug it back in:</em>
x + (x/2 + 6) = 180
/\
x/2 + 6
(116)/2 + 6
64
<em>To check:</em>
116 + 64 = 180 ✓
Given polynomial function:
.
We need to apply Descartes' rule of sign to identify the number of complex roots.
The given polynomial is f(x)=x^3-96x^2+400
Let us see the number of sign changes in f(x)
There are 2 sign changes in f(x). One from plus to minus and second from plus to minus. Hence, there 2 or 0 positive roots.
Now, let us see the number of sign changes in f(-x)
f(-x)=-x^3-96x^2+400
There are only one sign change. Hence, there will be 1 negative roots.
The degree of the polynomial is 3.
Hence, there will be exactly 3 zeros.
<em>Therefore, the possible numbers of zeros are:</em>
<em>2 positive, 1 negative and 0 complex</em>
<em>0 positive, 1 negative and 2 complex.</em>
Let us see the graph:
In the graph, we can see that the graph cuts the x axis at three points (2 positive, 1 negative points).
<h3>Hence, the number of complex zeros for the given polynomial is zero.</h3>