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deff fn [24]
3 years ago
13

Multiply 3/sqrt17- sqrt2 by which fraction will produce an equivalent fraction with rational denominator

Mathematics
2 answers:
zzz [600]3 years ago
3 0

Answer:

B.

Step-by-step explanation:

To simplify something that looks like \frac{\text{whatever}}{\sqrt{a}-\sqrt{b}} you would multiply the top and bottom by the conjugate of the bottom. So you multiply the top and bottom for this problem I just made by:

\sqrt{a}+\sqrt{b}.

If you had  \frac{\text{whatever}}{\sqrt{a}+\sqrt{b}}, then you would multiply top and bottom the conjugate of \sqrt{a}+\sqrt{b} which is \sqrt{a}-\sqrt{b}.

The conjugate of a+b is a-b.

These have a term for it because when you multiply them something special happens.  The middle terms cancel so you only have to really multiply the first terms and the last terms.

Let's see:

(a+b)(a-b)

I'm going to use foil:

First:  a(a)=a^2

Outer: a(-b)=-ab

Inner:  b(a)=ab

Last:    b(-b)=-b^2

--------------------------Adding.

a^2-b^2

See -ab+ab canceled so all you had to do was the "first" and "last" of foil.

This would get rid of square roots if a and b had them because they are being squared.

Anyways the conjugate of \sqrt{17}-\sqrt{2} is

\sqrt{17}+\sqrt{2}.

This is the thing we are multiplying and top and bottom.

omeli [17]3 years ago
3 0

For this case we have the following expression:

\frac {3} {\sqrt {17} - \sqrt {2}}

We must rationalize the expression, so we multiply by:

\frac {\sqrt {17} + \sqrt {2}} {\sqrt {17} + \sqrt {2}}

So, we have:

\frac {3} {\sqrt {17} - \sqrt {2}} * \frac {\sqrt {17} + \sqrt {2}} {\sqrt {17} + \sqrt {2}} =\\\frac {3 (\sqrt {17} + \sqrt {2}} {17- \sqrt {17} * \sqrt {2} + \sqrt {17} * \sqrt {2} -2} =\\\frac {3 (\sqrt {17} + \sqrt {2}} {15}

Thus, the correct option is option B.

Answer:

OPTION B

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labwork [276]

Answer:

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Step-by-step explanation:

(2m ^6)^3 is the same as ;

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hope this helps :)

8 0
3 years ago
Read 2 more answers
Change the fraction to a percent.
ziro4ka [17]
The fraction in the picture is  1/8 . 
That's equivalent to 12.5 %.
____________________________________

Maybe what you want is the whole mixed number changed to percent.

-- The  5  alone is  500% .

-- The  1/8  alone is  12.5% .

-- When you puttum together and addum up,

                 (5 + 1/8)  =  (500%  +  12.5%)  =  512.5%  .
8 0
3 years ago
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Sam invests $800 at 6%/a compounded annually for 5 years. What is the total interest<br> earned?
s2008m [1.1K]
<h3>Answer:    270.58 dollars</h3>

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

Work Shown:

  • A = account value after t years
  • P = principal or amount deposited = 800
  • r = interest rate in decimal form = 0.06
  • n = number of times we compound per year = 1
  • t = number of years = 5

So,

A = P*(1+r/n)^(n*t)

A = 800*(1+0.06/1)^(1*5)

A = 1070.58046208

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After five years, the account will have $1,070.58 in it.

The amount of interest earned is A-P = 1070.58 - 800 = 270.58 dollars.

4 0
2 years ago
Use the following data set to answer numbers 1 - 4.
alukav5142 [94]

Answer:

1. 13+18+13+14+13+16+14+21+13

= 145/9

=16.11

2. Range =145

3. Mode =13

4. Median =14

Step-by-step explanation:

6 0
2 years ago
I don’t understand these 3 questions and I need help.
rjkz [21]
Not sure about the first one but the second one is option c (or -3). You just have to factor and find the solutions (so it would be -7 and 4 and then u just add them)

For question 39 the answer is c
6 0
3 years ago
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