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Ipatiy [6.2K]
2 years ago
6

Rationalize the denominator.

="\frac{9}{\sqrt{x+3} }" alt="\frac{9}{\sqrt{x+3} }" align="absmiddle" class="latex-formula"> Simplest form
Mathematics
1 answer:
Jobisdone [24]2 years ago
6 0

The result after rationalizing is \frac{9\sqrt{x+3} }{x+3}.

<h3>What is Rationalization?</h3>

Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction.

Here, given fraction

 \frac{9}{\sqrt{x+3} }

Multiply and divide by \sqrt{x+3}, we get

\frac{9}{\sqrt{x+3} } \frac{\sqrt{x+3} }{\sqrt{x+3} }  =  \frac{9\sqrt{x+3} }{x+3}

Thus, the result after rationalizing is \frac{9\sqrt{x+3} }{x+3}.

Learn more about Rationalization from:

brainly.com/question/15837135

#SPJ1

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HELP PLS!! <br> Adding and subtracting vectors in component form
tino4ka555 [31]
<h3>Answers:</h3>
  1. u+v = <3,12>
  2. w+g = <7,0>
  3. g-z = <2,4>
  4. v-u = <9,4>
  5. y+v = <7,9>
  6. u+v+y = <4,13>

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

Explanation:

Problem 1

If we had the two vectors u = <a,b> and v = <c,d>, then adding them gives us

u+v = <a+c,b+d>

The corresponding coordinates pair up and add together.

In this case we have

u = <-3,4>

v = <6,8>

So,

u+v = <-3+6,4+8>

u+v = <3,12>

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

Problem 2

We follow the same idea as the previous problem.

w = <8,-1>

g = <-1,1>

w+g = <8+(-1),-1+1>

w+g = <7,0>

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

Problem 3

Similar to addition, subtracting vectors has us subtract the corresponding coordinates.

The general template is:

u = <a,b>

v = <c,d>

u-v = <a-c,b-d>

With this in mind, we can say the following:

g = <-1,1>

z = <-3,-3>

g-z = <-1-(-3),1-(-3)>

g-z = <-1+3,1+3>

g-z = <2,4>

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

Problem 4

Follow the same idea as problem 3 above.

v = <6,8>

u = <-3,4>

v-u = <6-(-3),8-4>

v-u = <6+3,8-4>

v-u = <9,4>

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

Problem 5

Refer to problem 1.

y = <1,1>

v = <6,8>

y+v = <1+6,1+8>

y+v = <7,9>

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

Problem 6

u = <-3,4>

h = v+y = y+v = <7,9>

u+v+y = u + h

u+v+y = <-3,4> + <7,9>

u+v+y = <-3+7,4+9>

u+v+y = <4,13>

Notice how I built off the result of problem 5 when I used h = v+y. The vector v+y is the same as y+v because the order of addition doesn't matter. Also, the idea mentioned in problem 1 can be extended for more than two vectors.

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Answer: X = 4

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On the left side, notice that the 5's cancel out, so we are simply left with z. On the right side, we have 20 divided by 5 which gives us 4.

Now we have X = 4.

Finally, remember to check your answer by substituting a 4 back into the original equation.

So we have 5 (4) = 20 which is a true statement.

This means that our answer, x = 4 is correct.

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