Check the picture below.
well, g(x) + 1 is simply a vertical shift upwards of 1 unit, if the vertex before that had a y-coordinate of 4, then later on became 4+1 or 5, so the new vertex is simply (3 , 5).
How do I solve x+2y=8
2 answers:
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Answer:
34 cm
Step-by-step explanation:
The actual question is How many inches of ribbon Peter will need to make the "X".
Using the Pythagorean theorem, the length of the diagonal of a square with 12 cm sides is:
Since the "X" requires two diagonals, the length of ribbon required is:
The length required, rounded to the nearest centimeter, is 34 cm.
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.
