1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
hodyreva [135]
2 years ago
8

Could anyone help me with this question? Thank you!

Mathematics
1 answer:
shutvik [7]2 years ago
4 0

Answer:

C

Step-by-step explanation:

We want to simplify the rational expression:

\displaystyle \frac{n^4-11n^2+30}{n^4-7n^2+10}

First, we can factor both the numerator and the denominator. This yields:

\displaystyle =\frac{(n^2-6)(n^2-5)}{(n^2-2)(n^2-5)}

Cancel like terms:

\displaystyle =\frac{(n^2-6)}{(n^2-2)}

However, since we canceled a term from our expression, we must place restrictions in order to stay true to the original expression.

Rational expressions are undefined whenever the denominator equals 0. The denominator is (before canceling):

(n^2-2)(n^2-5)=0

Solve for n. By the zero product property:

n^2-2=0\text{ and } n^2-5=0

Therefore:

n^2=2\text{ and } n^2=5

By taking the square root of both sides (since we are taking an even root, it is required to have plus/minus):

n=\pm\sqrt{2}\text{ and } n=\pm\sqrt5

Therefore, our fully simplified expression is:

\displaystyle \frac{n^2-6}{n^2-2}\, ,n\neq \pm\sqrt5, \pm\sqrt2

Hence, our answer is C!

You might be interested in
How do you write range on a graph?
Ratling [72]

The range of a function is the set of all possible outputs.

When the quadratic functions are in standard form, they generally look like this:

f(x) = ax^{2}  + bx + c

If a is positive, the function opens up; if it’s negative, the function opens down. In this form, the y-coordinate of the vertex is found by evaluating f(−\frac{b}{2a}). For example, consider this function:

f(x) = -2x^{2} + 8x -3\\

So we’re gonna do: −b/2a=−8/2(−2)=−8/−4=2

Then, we plug this in:

f(2) = -2(2)^{2} +8(2) -3 = 5

a is negative, so the range is all real numbers less than or equal to 5.

Learn more about range at

brainly.com/question/2264373

#SPJ4

4 0
1 year ago
Round 2. 873 to the nearest tenth
PtichkaEL [24]
2.873 ≈2.9 (nearest tenth)
6 0
3 years ago
Read 2 more answers
Please help me with maths !!!
zlopas [31]

Answer:

  • 170.7 cm

Step-by-step explanation:

Let the original water level is x.

<u>Use below equation to find its value:</u>

  • x + 2.4 + 3 1/2 = 162 + 14.6
  • x + 2.4 + 3.5 = 176.6
  • x + 5.9 = 176.6
  • x = 176.6 - 5.9
  • x = 170.7 cm
3 0
3 years ago
Simplify This expression
REY [17]

Answer:

9

Step-by-step explanation:

10-2×3+5

10-6+5

4+5

9

5 0
3 years ago
Read 2 more answers
Evaluate 7r- 15/8 when r=3 and s=5
HACTEHA [7]

Answer:

Which is equal to 18.

Step-by-step explanation:

7(3) - 15/(5). 7 x 3 is equal to 21, 15/5 is equal to 3. you are now left with 21-  3,

6 0
3 years ago
Other questions:
  • What is the value of x in the equation 1/4x+2=-5/8x-5
    8·2 answers
  • A class of 25 students include 12 boys does the ratio of girls to students represent a fraction does the ratio of boys to girls
    14·2 answers
  • Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 4 h, and Car B traveled the dista
    14·1 answer
  • The function given by Upper A left parenthesis t right parenthesis equals 0.0265 t cubed minus 0.444 t squared plus 1.774 t plus
    5·1 answer
  • Laila read 36 pages in 4 hours. Which expression can be used to find the number of pages she read per hour?
    11·2 answers
  • If a 12-sided regular polygon rotates about its center, at which angle of rotation will the image of the polygon coincide with t
    8·1 answer
  • 3x+4/5=7-2x what does x=
    15·1 answer
  • What is the volume of the image below?<br> V = arh<br> 6 in<br> 11 in
    11·1 answer
  • at a party, everyone shook hands with everybody else. there were 66 handshakes. How many people shook hands?
    5·1 answer
  • Does America live up to its core values?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!