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.
She used 180 beads because 45x4 =180
1. I think the underlined number is 2. So It will be hundredths.
2. (8 x 100) + (6 x 10) + (3 x 1) + (1/10) + (4/100) + (1/1000)
Or 800 + 60 + 3 + 0.1 + 0.04 + 0.001
Answer:
684
Step-by-step explanation:
57 times 12
12 weeks times 57 pages= 684 pages in 12 weeks
Hey!
The sum of four times a number and -2
Let us take the number as ' x '
( 4x - 2 )
Six times a number and 3
( 6x + 3 )
The sum = ( 4x - 2 ) + ( 6x + 3 )
Hope helps!