How does Brandon's sound intensity level compare to ahmad's?
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The mathematical mistake that Riley made is that:
"She used the wrong common denominator." (Option A)
A common denominator is a factor that is similar to all the fractions in the sequence of equations.
Hence the correct answer is:
(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))
See the correct sequence of steps below:
Step One - the Expression is given as:
(x/(x-3)(x-2)) + (3/(x+3))
Step 2 - Find the common denominator and rewrite the expression so that the numerators are above the common denominators.
Hence we have: (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)
Step 3 Apply the Law of Multiplicative Distribution:
Hence we have (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)
Step 4 - Collect Like Items
This gives us: (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)
Step 5 Sort for like coefficients
This gives us: ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)
Step 6 - check for the sum or difference
This gives us: (4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)
We simplify and factor the expression to get
(2(2x²-6x+6)/(x-3)(x-2)(x+3).
See the attached for full question.
Learn more about Common Denominators at:
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>