Do 27 divided by 4 1/2 or 4.5. That will be your answer. Let me know if this helps!
6.5 = - 1/2(5) + 9
6.5 = - 2.5 + 9 which is the same as 6.5 = 9 - 2.5
6.5 = 6.5
So yes, this ordered pair IS a solution.
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.
The correct choice would be 128.
If there are 6 options and the person can pick any number of toppings, we need to know the number of subsets that can be formed with 6. That would be 2^6 or 64.
Since there is a pan or hand-tossed option, we need to multiply 64 by 2 to find the total.
64 x 2 = 128