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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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If Usain Bolt can run a marathon (26.2) in 2 hours and 15 minutes, how fast would he run if he ran at the same constant rate?
inn [45]

Answer:

The speed of Usain Bolt is 0.194 miles per minutes to complete the marathon.

Step-by-step explanation:

Given as :

The Distance of marathon = 26.2 unit

The time taken to complete marathon = 2 hours and 15 minutes

                                                                = 120 + 15 = 135 minutes

Let The constant speed of Usain Bolt = S unit per minutes

So, Speed = \frac{Distance }{Time}

Or, S  = \frac{26.2 }{135}

∴   S = 0.194  unit per minutes

Hence The speed of Usain Bolt is 0.194 miles per minutes to complete the marathon.   Answer

8 0
3 years ago
If you scale down the ratio on the left, what will you get for the unknown quantity on the right? 434 miles14 gallons = ?2 gallo
jarptica [38.1K]

Answer:

option (A) 62 miles

Step-by-step explanation:

Data provided in the question:

Ratio on the left = 434 miles : 14 gallons

ratio on the right = ?? : 2 gallons

Now,

The ratio on the both sides are equal

let the unknown value in the ratio be 'x'

Now, the ratio a : b can also be represented as \frac{a}{b}

therefore,

434 miles : 14 gallons = x : 2 gallons

or

⇒ \frac{\textup{434 miles}}{\textup{14 gallons}}  = \frac{\textup{x}}{\textup{2}}

or

⇒ x =  \frac{\textup{434 miles}}{\textup{14 gallons}}\times2 gallons}

or

⇒ x = 62 miles

Hence,

the correct answer is option (A) 62 miles

7 0
2 years ago
HELP!!!!!!!! Select an expression that id equivalent to 4squareroot of 2x^2 • 4squareroot of 2x^3
earnstyle [38]

Answer:

B

Step-by-step explanation:

\sqrt[4]{2x^2} *\sqrt[4]{2x^3} =(2x^2)^{1/4}*(2x^3)^{1/4}\\= 2^{1/4}*(x^2)^{1/4} *2^{1/4} * (x^3)^{1/4}\\

combine like terms

= 2^{2/4} *x^{2/4}*x^{3/4}\\= 2^{2/4} * x^{5/4}

these steps use exponent laws

a few key ones i used:

(x^y^z) = x^(y*z)

x^y * x^z = x^(y+z)

let me know if you have any questions!

8 0
1 year ago
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