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.
An expression is defined as a set of numbers, variables, and mathematical operations. The correct options are A and C.
<h3>What is an Expression?</h3>
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given exponential (6⁻¹⁰/6⁻⁴) function can be simplified as shown below,
(6⁻¹⁰/6⁻⁴)
= 6⁻¹⁰ × 6⁴
= 6⁽⁻¹⁰⁺⁴⁾
= 6⁻⁶
= 1/6⁶
Hence, the correct options are A and C.
Learn more about Expression:
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Answer:$154.73
Step-by-step explanation:
Take 65 and multiple .15 and that will give you the 15% off of the case. When u do that you get 9.75 so then 65-9.75= 55.25 multiply .08 for the sales tax on the case = 4.42 add to 55.25= 59.67 then add the sales tax for the laptop 320 multiplied by .08 = 25. 60 for a total of 345.60 then add that to 59.67 = 405.27 then u have to subtract that from 560 and Josh has $154.73