Answer:
1. 2,3; -2, 3
2. Both points share common values, but their absolute values for the x-value vary.
3. 2,3; 2, -3
4. Both points share common values, but their absolute values for the y-value vary.
Step-by-step explanation:
For 1, the answer is thus:
-On the graph, the original point is 2, 3.
-A reflection over the y-axis changes the x-value, so it would be -2,3.
Similar for the next chart:
-The initial point is 2,3.
-A reflection over the x-axis changes the y-value, so the reflected point would be 2, -3.
The explanation is:
Both points have similar values except with differences in the absolute value.
Hope this helps you.
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
_____
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.
_____
<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:
65+19=84
Step-by-step explanation:
Emily has $84
Answer and step-by-step explanation:
Break the bracket out would be the first step to evaluate this expression:
3(x-1)
= 3x - 3
Hope this helped :3
Answer:
The combined score was 191
Explanation:
91 (Colin’s score) + 9 (how many more Brian had than Colin) = 100 (Brian’s score)
91 (Colin’s score) + 100 (Brian’s score) = 191 (combined score)