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.
Answer:
One possible answer would be they sold 80 student tickets and 30 adult tickets
Step-by-step explanation:
set up two inequalities, one to show number of tickets that can be sold, and the other is how much money they need to make
5x+10y G than or = 700
x+y L than or = 110
The first inequality shows that each student (x) ticket sells for $5, and each adult (y) ticket sells for $10, and the amound has to be greater or equal to 700.
The second inequality shows that both student and adult tickets sold have to be less than or equal to 110.
First find either x or y, in this case finding y was easier
y is g than or = to 30
This means that they sold at least 30 adult tickets= $300
With y, plug into the inequality x+y L than or = to 110 to find x
x is less than or = to 80
This means that they sold at most 80 student tickets = $400
Hope this helps!
The first step in solving quadratic equations by finding square roots is; C:square root both sides to isolate x
<h3>How to solve quadratic equations?</h3>
To answer this question, we will take an example of a quadratic equation that we need to find the square root as;
x² = 36
Now, to get the roots which are the values of x, we will first have to take the square root of both sides to Isolate x. Thus;
√x² = √36
x = ±6
Read more about quadratic equations at; brainly.com/question/1214333
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For example:
(4/9) x=8
Now can solve this equation multiplying each side by 9/4.
(9/4)(4/9)x=(9/4)8
x=18
To check:
(4/9)(18)=(4*18)/9=72/9=8
Answer:
16 ft³
Step-by-step explanation:
4ft x 2ft x 2ft = 4ft x 4ft = 16 ft³
