The surface area of a composite figure

Could anyone help me with this question? Thank you!

shutvik [7]

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!

4 0

2 years ago

Answer this question I will Mark brilliant and gets 70 PTS do number one or two or do both

yanalaym [24]

Answers And Explanations:

Question 1.

Pulling out like terms :

1.1 Pull out like factors :

12y - 10 = 2 • (6y - 5)

Equation at the end of step 1 :

Divide both sides by 2

Divide both sides by 6

y-(5/6) > 0

Add 5/6 to both sides

y > 5/6.

Therefore, y = 5/6

__________________________________

Question 2.

To make fractions improper with whole numbers, you must multiply the Denominator by the whole number, then add the Numerator to the Product.

First we multiply 32 by 5.

32 x 5 = 160.

Then we add the Numerator which is 1.

160 + 1 = 161, then we put it over the Denominator, your final answer is 161/5.

Therefore, 161/5 is your final answer.

Have any questions? Feel free to comment below!

Thank you and Best of Luck to you!

7 0

2 years ago

URGENT!! Find the solutions by completing the square x^2-5x+4=y

rosijanka [135]

Answer:

y=x^2-5x+4 i am not sure but a im try

5 0

1 year ago

An Italian restaurant offers small, medium and large calzones. The choices of filings are cheese, sausage, spinach, or vegetable

larisa86 [58]

Answer:

A) 12 toppings.

Step-by-step explanation:

That would be the answer if there are no combinations of toppings.

You would simply take the number of sizes (3) and the number of toppings (4) and multiply them together to get 12 combinations.

8 0

2 years ago

FACTORED POLYNOMIAL ONLY

Leto [7]

Answer: $5x^{3}$ ( $x^{3}$ +2x+3)

3 0

3 years ago