Which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9
1 answer:
Notice that we can simplify both numerator and denominator of our rational function. In the numerator we have a quadratic expression of the form 
. To to simplify it, we are going to find tow numbers that add to 2 and multiply to -8; those numbers are 4 and -2.
In the denominator we have a difference of squares:
Now we can rewrite our function:
From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at
and 
We can conclude that the graphic of our rational function is:
In the denominator we have a difference of squares:
Now we can rewrite our function:
From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at
We can conclude that the graphic of our rational function is:
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Hello,
Making an equation would be a good method to solve this problem.
The area of a rectangle is equal to
, where l is the length and w is the width of the rectangle.
If the area of the wall is 280280, we know = 280280
We also know that the length is 88 feet longer than twice the width. Twice the width is equal to
, and the length is 88 feet longer than that, so 
.
So, we have a system of equations:
Using the first equation, we can find the value of l and we get
We then plug in this value of l into the second equation, and we have:
Now, we can multiply by w on both sides, and subtract 280280 on both sides, and use the quadratic formula to get w ≈ 353, -397
The width of a wall cannot be negative, so the answer is 353 feet.
To find l, and make sure of our answers, we should check it with the original problem to make sure it checks out.
Doing this, we get:
Divide by 353 on both sides to get:
Now, we should check it with the equation
794 = 2(353) + 88
794 = 794, checks out.
So, the width of the wall of the barn is 353 feet, and the length of the wall of the barn is 794 feet.
Hope this helps! Feel free to contact me with any questions you may have.
Making an equation would be a good method to solve this problem.
The area of a rectangle is equal to
If the area of the wall is 280280, we know
We also know that the length is 88 feet longer than twice the width. Twice the width is equal to
So, we have a system of equations:
Using the first equation, we can find the value of l and we get
We then plug in this value of l into the second equation, and we have:
Now, we can multiply by w on both sides, and subtract 280280 on both sides, and use the quadratic formula to get w ≈ 353, -397
The width of a wall cannot be negative, so the answer is 353 feet.
To find l, and make sure of our answers, we should check it with the original problem to make sure it checks out.
Doing this, we get:
Divide by 353 on both sides to get:
Now, we should check it with the equation
794 = 2(353) + 88
794 = 794, checks out.
So, the width of the wall of the barn is 353 feet, and the length of the wall of the barn is 794 feet.
Hope this helps! Feel free to contact me with any questions you may have.