Solve the absolute value equation. 4 − |x| = 1 25 POINTS

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

Andrej [43]

For this case we have the following expression:
 $\frac{n ^ 4-11n ^ 2 + 30}{ n ^ 4-7n ^ 2 + 10} 

$
 We are going to make the following change of variables:
 $x = n ^ 2
$
Rewriting the expression we have:
 $\frac{(x ^ 2-11x + 30)}{(x ^ 2-7x + 10)} 

$
Factoring the expression we have:
 $\frac{(x-5) (x-6)}{(x-5) (x-6)} 
$
Canceling similar terms we have:
 $\frac{x-6}{x-2} 
$
Returning the change we have:
 $\frac{n ^ 2-6}{n ^ 2-2} 

$
 The resctrictions of the function are those that make the denominator equal to zero.
We have then:
 $n ^ 2-2 = 0

n = +/- \sqrt{2} 
$
 Answer:
The simplified expression is:
 $\frac{n ^ 2-6}{n ^ 2-2}$
The restrictions are:
 $n = \sqrt{2} 
$
$n = - \sqrt{2}$

7 0

3 years ago

HELP HELP!!!! YOU WILL GET BRAINLIEST!! PLEASE!!!

LiRa [457]

Um idk sorry lol that’s way to hard for me

5 0

3 years ago

5 % of 170 is what number?

Darina [25.2K]

Answer: 3400

Step-by-step explanation:

We have, 5% × x = 170

or,

5

100

× x = 170

Multiplying both sides by 100 and dividing both sides by 5,

we have x = 170 ×

100

5

x = 3400

If you are using a calculator, simply enter 170×100÷5, which will give you the answer.

4 0

3 years ago

Read 2 more answers

I don’t know how to do this. can someone please help me :)

Kaylis [27]

The surface area of a cylinder is the sum of the area of the two ends and the lateral area.
.. surface area = 2*(end area) +(lateral area)
.. = 2*(π*r^2) +(2π*r*h)
.. = 2π*r*(r +h)
.. = 2*3.14*(8 in)*(8 in +8 in)
.. = 3.14*256 in^2
.. ≈ 803.8 in^2

The 3rd selection is appropriate.

8 0

4 years ago

Ellis is painting wooden fenceposts before putting them in his yard. They are each 5 feet tall and have a diameter of 1 foot. Th

Naya [18.7K]

Answer:

39.25 cubic feet of paint will be needed by Ellis.

Step-by-step explanation:

Volume of a cylinder:

The volume of a cylinder of radius r and height h is given by:

$V = \pi r^2h = 3.14r^2h$