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Colt1911 [192]
3 years ago
5

Simplify the rational expression. State any restrictions on the variable n^4-11n^2+30/ n^4-7n^2+10

Mathematics
2 answers:
LenKa [72]3 years ago
7 0

Answer:

(n^2-6)/(n^2-2), n cannot be +-sqrt 5, +-sqrt 2

Step-by-step explanation:

djyliett [7]3 years ago
5 0
To factor both numerator and denominator in this rational expression we are going to substitute n^{2} with x; so n^{2} =x and n ^{4} =  x^{2}. This way we can rewrite the expression as follows:
\frac{n^{4}-11n^{2} +30 }{n^{2}-7n^{2} +10 } =  \frac{ x^{2} -11x+30}{ x^{2} -7x+10}
Now we have two much easier to factor expressions of the form a x^{2} +bx+c. For the numerator we need to find two numbers whose product is c (30) and its sum b (-11); those numbers are -5 and -6. (-5)(-6)=30 and -5-6=-11.
Similarly, for the denominator those numbers are -2 and -5. (-2)(-5)=10 and -2-5=-7. Now we can factor both numerator and denominator:
\frac{ x^{2} -11x+30}{ x^{2} -7x+10} = \frac{(x-6)(x-5)}{(x-2)(x-5)}
Notice that we have (x-5) in both numerator and denominator, so we can cancel those out:
\frac{x-6}{x-2}
But remember than x= n^{2}, so lets replace that to get back to our original variable:
\frac{n^{2}-6 }{n^{2}-2 }
Last but not least, the denominator of rational expression can't be zero, so the only restriction in the variable is n^{2} -2 \neq 0
n^{2}  \neq 2
n \neq +or- \sqrt{2}
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3 years ago
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Alik [6]

Answer:

  • x + y ≤ 600
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Step-by-step explanation:

a) We can write two inequalities, one for the number of tickets, and one for the necessary revenue.

  x + y ≤ 600 . . . . . . . limit imposed by available seating

  5x +7y ≥ 3500 . . . . required revenue to meet expenses

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b) For x = 330, the first inequality puts one limit on y:

  330 +y ≤ 600

  y ≤ 270

And the second inequality puts another limit on y:

  5(330) +7y ≥ 3500

  7y ≥ 1850 . . . . subtract 1650

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The number of tickets that must be sold to meet expenses is 265, which is less than the number that can be sold, 270. It is possible to meet expenses.

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3 years ago
How would you do this???
Kobotan [32]

Answer:

8.3 L/s

Step-by-step explanation:

To find the answer you need to find the slope also known as the rate of change. When you find slope it is always change in y over change in x.

\frac{399-150}{40-10}

Then simplify

\frac{249}{30}

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Ms. galendez's backyard is a rectangle whose length is twice the width. if the perimeter is 720 ft, what are the dimensions of h
Talja [164]

Answer:

120ft and 240ft

Step-by-step explanation:

720 = 2L + 2W

Since L = 2W, we get

720 = 2(2W) + 2W

6W = 720

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The dimensions of the yard are 120 feet and 240 feet

3 0
3 years ago
A polling company reported that ​% of surveyed adults said that Complete parts​ (a) through​ (d) below.
SOVA2 [1]

Answer:

a) 376.66

b) Option 2: No, the result from part (a) could not be the actual number of adults who said that rising gas prices are "quite annoying" because a count of people must result in a whole.

c) 377

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Step-by-step explanation:

a) 37% of 1018 is;

37/100 × 1018 = 376.66

b) Thus, the result in a above is not a whole number. Thus;

No, the result from part (a) could not be the actual number of adults who said that rising gas prices are "quite annoying" because a count of people must result in a whole.

c) from a above a, we got a value of 376.66.

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3 years ago
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