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
hichkok12 [17]
2 years ago
8

What is the following quotient?

Mathematics
1 answer:
seropon [69]2 years ago
4 0

Answer:  Choice B) \frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\

==========================================

Work Shown:

\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\

This shows why choice B is the answer.

---------------

Explanation:

  • In the second step, I multiplied top and bottom by (\sqrt{11}+\sqrt{3})
  • This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
  • In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.

So in general, if the denominator is \sqrt{a}-\sqrt{b} and you want to rationalize the denominator, then you should multiply top and bottom by \sqrt{a}+\sqrt{b}. The same applies in reverse as well.

This leads to the denominator becoming (\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}) = (\sqrt{a})^2-(\sqrt{b})^2 = a-b

Keep in mind that a \ge 0 and b \ge 0

You might be interested in
Find an equation of the line through (1,8) and parallel to y = 4x +3. Write the equation using function notation.
brilliants [131]

Answer:

f(x) = 4x + 4

Step-by-step explanation:

When a line is parallel to another line, the slopes are always equal. Therefore,  the coefficient for x has to be four. If you multiply the y-coordinate by 4, you get 4. To get 8, you have to add four, so the equation is simply f(x) = 4x+4.

5 0
2 years ago
Read 2 more answers
Bill spent $42 on fruit at the grocery store. He spent a total of $60 at the store. What percentage of the total did he
Neporo4naja [7]

Answer:

70%

Step-by-step explanation:

To find the total percentage of his $60 dollars that he spent on fruit, we simply take the amount of money spent on fruit divided by the total spent.

% spent on fruit = 42 / 60

% spent on fruit = 0.7

% spent on fruit = 70 %

Cheers.

3 0
3 years ago
Read 2 more answers
Ida is cutting a 11/12 foot wooden board into 3/16 foot sections to do some detail work on a model she is building. How many who
zlopas [31]
You have to give them the same denominator so multiply 11/12 by 4 and 3/16 by 3. giving you 44/48 and 9/48. then divied 44 by 9 giving you 4.8888
there for there are 4 whole 3/16 sections of the 11/12 board
3 0
3 years ago
Read 2 more answers
Kool-aide is made from flavored powder and water, with the ratio of powder to water 3:2 based on weight. If 120g of flavored pow
MAXImum [283]

The given ratio of powder to water is 3:2 based on weight for Kool-aide. It is also given that 120g of flavored powder is needed for a certain amount of Kool-aide.

Let us assume that the amount of water (by weight) required to maintain the given ratio of 3:2 be represented by the letter x. Thus, from the given information we can conclude that:

\frac{Powder Weight}{Water Weight}=\frac{3}{2}=\frac{120}{x}

\therefore \frac{3}{2}=\frac{120}{x}

Cross-multiplying we get:

3x=240

\therefore x=\frac{240}{3}=80 grams.

Thus, the amount of water in grams in that Kool-aide is 80 grams.

5 0
3 years ago
Read 2 more answers
7 , 14 , 21 , 28 __ __ __​
kotegsom [21]
35, 42, and 49 jagskahskahslahslabajak
4 0
2 years ago
Other questions:
  • How many square inches does an 11" x 13" area encompass?
    5·1 answer
  • Travis has a savings account that his parents opened for him. It pays 6% annual interest. His uncle also opened an account for h
    5·1 answer
  • 9-x-x=-1<br> Solve for x
    12·2 answers
  • The actual length of Wall C is 4 m. To represent Wall C, Noah draws a segment 16 cm long. What scale is he using? Explain or sho
    5·1 answer
  • Please help please please help
    14·1 answer
  • PLEASE HELP ON A TIMER!!!!!!
    5·2 answers
  • The article: “Motion Sickness in Public Road transport: the Effect of Driver, Route and Vehicle” (Ergonomics (1999):1646-1664) r
    6·1 answer
  • I need help finding the length of the segment RS.​
    6·1 answer
  • Math
    13·2 answers
  • bobs gift shop sold 350 cards for mothers day one saleman henry sold 4% of the cards sold for mothers day how many cards did hen
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!