Answer:
- x = ±√3, and they are actual solutions
- x = 3, but it is an extraneous solution
Step-by-step explanation:
The method often recommended for solving an equation of this sort is to multiply by the product of the denominators, then solve the resulting polynomial equation. When you do that, you get ...
... x^2(6x -18) = (2x -6)(9)
... 6x^2(x -3) -18(x -3) = 0
...6(x -3)(x^2 -3) = 0
... x = 3, x = ±√3
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Alternatively, you can subtract the right side of the equation and collect terms to get ...
... x^2/(2(x -3)) - 9/(6(x -3)) = 0
... (1/2)(x^2 -3)/(x -3) = 0
Here, the solution will be values of x that make the numerator zero:
... x = ±√3
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So, the actual solutions are x = ±3, and x = 3 is an extraneous solution. The value x=3 is actually excluded from the domain of the original equation, because the equation is undefined at that point.
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<em>Comment on the graph</em>
For the graph, we have rewritten the equation so it is of the form f(x)=0. The graphing program is able to highlight zero crossings, so this is a convenient form. When the equation is multiplied as described above, the resulting cubic has an extra zero-crossing at x=3 (blue curve). This is the extraneous solution.
Answer:
Answer is ...Obtuse
Step-by-step explanation:








We get,
m<ABC =

Hence <ABC is obtuse
30% of 22.40 is 6.72. 6.72 plus 22.40 is 29.12. Therefore the answer is 29.12.
Answer:

The interval of convergence is:
Step-by-step explanation:
Given


The geometric series centered at c is of the form:

Where:
first term
common ratio
We have to write

In the following form:

So, we have:

Rewrite as:


Factorize

Open bracket

Rewrite as:

Collect like terms

Take LCM


So, we have:

By comparison with: 



At c = 6, we have:

Take LCM

r = -\frac{1}{3}(x + \frac{11}{3}+6-6)
So, the power series becomes:

Substitute 1 for a


Substitute the expression for r

Expand
![\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n]](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B3x%20%2B%202%7D%20%3D%20%20%5Csum%5Climits%5E%7B%5Cinfty%7D_%7Bn%3D0%7D%5B%28-%5Cfrac%7B1%7D%7B3%7D%29%5En%2A%20%28x%20-%20%5Cfrac%7B7%7D%7B3%7D%29%5En%5D)
Further expand:

The power series converges when:

Multiply both sides by 3

Expand the absolute inequality

Solve for x

Take LCM


The interval of convergence is:
Answer:
15 boys and 20 girls
Step-by-step explanation:
1. Since we cant simplify 3:4 we will leave it just like that.
2. 3x+4x=35
3. We add them both to give us 7x=35
4. We divide by 7 to get x by itself which results in 35/7=5.
x=5
5. Now we found x we can create 2 seperate soulutions:
3(5)=
and 4(5)=
Therefore there are 15 boys and 20 girls in the class. This makes sense because 15/20 reduced is 3 over 4.