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
Musya8 [376]
3 years ago
5

Rationalize the denominator of √3+√2\ 5+√2 ​

Mathematics
1 answer:
hammer [34]3 years ago
5 0

Answer:

\frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{23}

Step-by-step explanation:

\frac{\sqrt3 \ + \ \sqrt2 }{5 \ +  \ \sqrt2 } \\\\=\frac{\sqrt3 \ + \ \sqrt2 }{5 \ +  \ \sqrt2 } \times \frac{5 \ - \ \sqrt2 }{5 \ -  \ \sqrt2 } \\\\=\frac{( \sqrt3 \ + \ \sqrt2)(5 \ -  \ \sqrt2)}{(5 \ + \  \sqrt2)( 5 \  - \  \sqrt 2 )}\\\\=\frac{( \sqrt3 \ + \ \sqrt2)(5 \ -  \ \sqrt2)}{(5 \ + \  \sqrt2)( 5 \  - \  \sqrt 2 )}\\\\=\frac{5 \sqrt3 \ + \ 5\sqrt 2 \ - \ \sqrt{ 3\times 2 } \ - \ \sqrt{2 \times 2}}{(5)^2 \ - \ (\sqrt2)^2}\\\\= \frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{25 - 2}\\\\

= \frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{23}

You might be interested in
The ratio of students in Class X to Class Y is 2 : 5. There are 24 more students in Class Y than Class X. How many students must
Natalka [10]

Answer: 12 students

Step-by-step explanation:

Let X and Y stand for the number of students in each respective class.

We know:

X/Y = 2/5, and

Y = X+24

We want to find the number of students, x, that when transferred from Y to X, will make the classes equal in size. We can express this as:

(Y-x)/(X+x) = 1

---

We can rearrange X/Y = 2/5 to:

X = 2Y/5

The use this value of X in the second equation:

Y = X+24

Y =2Y/5+24

5Y = 2Y + 120

3Y = 120

Y = 40

Since Y = X+24

40 = X + 24

X = 16

--

Now we want x, the number of students transferring from Class Y to Class X, to be a value such that X = Y:

(Y-x)=(X+x)

(40-x)=(16+x)

24 = 2x

x = 12

12 students must transfer to the more difficult, very early morning, class.

7 0
3 years ago
How do i solve this???
Leni [432]

This will help u and hope its right .

6 0
3 years ago
Suppose you want to accumulate $25,000 as down payment on a house and the best you can do is to put aside $200 a month. If you d
Sunny_sXe [5.5K]

Answer:

It will take 88.2 months to accumulate the amount

Step-by-step explanation:

Given;

Future value of money, FV = $25,000

investment per compound period, P = $200

interest rate, i = 0.75% x 12 = 9%

The number of monthly installments required to amount to FV is given by;

n = \frac{ln(FVi +cp)-ln(cp)}{ln(c+i)-ln(c)}\\\\ n = \frac{ln(25000*0.09 +200*12)-ln(200*12)}{ln(12+0.09)-ln(12)}\\\\n = \frac{8.4446 -7.7832}{2.4924-2.4849}\\\\n = 88.2 \ months

Therefore, it will take 88.2 months to accumulate the amount.

7 0
4 years ago
The Cunninghams are moving across the country. Mr. Cunningham leaves 3 hours before Mrs. Cunningham. If he averages 40mph and sh
svp [43]
Recall your d = rt, distance = rate * time

now, if say, by the time they meet, Mr Cunningham has travelled "d" miles, that means Mrs Cunningham must also had travelled "d" miles as well.

However, he left 3 hours earlier, so by the time he travelled "d" miles, and took say "t" hours, for her it took 3 hour less, because she started driving 3 hours later, so, she's been on the road 3 hours less than Mr Cunningham, so by the time they meet, Mrs Cunningham has travelled then "t - 3" hours.

\bf \begin{array}{lccclll}
&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\
&------&------&------\\
\textit{Mr Cunningham}&d&40&t\\
\textit{Mrs Cunningham}&d&80&t-3
\end{array}
\\\\\\
\begin{cases}
\boxed{d}=40t\\
d=80(t-3)\\
----------\\
\boxed{40t}=80(t-3)
\end{cases}
\\\\\\
\cfrac{40t}{80}=t-3\implies \cfrac{t}{2}=t-3\implies t=2t-6\implies 6=2t-t
\\\\\\
6=t
5 0
3 years ago
a recipe for soup calls for 4 3/4 cup of water 1/2 teaspoon of salt, and 2 1/2 cups of mixed vegetables. if the recipe yields tw
tekilochka [14]
All we have to do is multiply by two

4 3/4 * 2 = 9 1/2 
1/2 * 2 = 1
2 1/2 * 2 = 5
7 0
3 years ago
Other questions:
  • 10 POINTS + BRAINLIEST ANSWER!!
    14·1 answer
  • How to solve this problem
    15·1 answer
  • Pabia made $270.00 for 18 hours of work
    6·1 answer
  • Help me please ? w pic
    11·2 answers
  • Plz help me with this question ​
    14·1 answer
  • Choose Yes or No to tell if the fraction
    7·1 answer
  • I just need a quick explanation pls and thank you!
    13·1 answer
  • Solve for x. Thank you
    12·2 answers
  • Hellp by the way this is homewoerk
    12·2 answers
  • PLEASE NEED HELP ASAP
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!