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
Anon25 [30]
3 years ago
15

Rationalize the denominator and simplify.

Mathematics
1 answer:
cestrela7 [59]3 years ago
4 0
If you're using the app, try seeing this answer through your browser:  brainly.com/question/3151018

——————————
 
     \mathsf{\dfrac{3\sqrt{6}+5\sqrt{2}}{4\sqrt{6}-3\sqrt{2}}}


Multiply and divide by the conjugate of the denominator, which is  \mathsf{4\sqrt{6}+3\sqrt{2}:}

     \mathsf{=\dfrac{\big(3\sqrt{6}+5\sqrt{2}\big)\cdot \big(4\sqrt{6}+3\sqrt{2}\big)}{\big(4\sqrt{6}-3\sqrt{2}\big)\cdot \big(4\sqrt{6}+3\sqrt{2}\big)}}


Expand those products and eliminate the brackets:
 
     \mathsf{=\dfrac{\big(3\sqrt{6}+5\sqrt{2}\big)\cdot 4\sqrt{6}+ \big(3\sqrt{6}+5\sqrt{2}\big)\cdot 3\sqrt{2}}{\big(4\sqrt{6}-3\sqrt{2}\big)\cdot 4\sqrt{6}+ \big(4\sqrt{6}-3\sqrt{2}\big)\cdot 3\sqrt{2}}}\\\\\\ \mathsf{=\dfrac{12\cdot \big(\sqrt{6}\big)^2+20\sqrt{2}\cdot \sqrt{6}+9\cdot \sqrt{6}\cdot \sqrt{2}+15\cdot \big(\sqrt{2}\big)^2}{16\cdot \big(\sqrt{6}\big)^2-12\cdot \sqrt{2}\cdot \sqrt{6}+ 12\cdot \sqrt{6}\cdot \sqrt{2}-9\cdot \big(\sqrt{2}\big)^2}}\\\\\\ \mathsf{=\dfrac{12\cdot 6+20\sqrt{2\cdot 6}+9\sqrt{6\cdot 2}+15\cdot 2}{16\cdot 6-12\sqrt{2\cdot 6}+ 12\sqrt{6\cdot 2}-9\cdot 2}}\\\\\\ \mathsf{=\dfrac{72+20\sqrt{12}+9\sqrt{12}+30}{96-12\sqrt{12}+12\sqrt{12}-18}}

     \mathsf{=\dfrac{72+29\sqrt{12}+30}{96-18}}\\\\\\ \mathsf{=\dfrac{102+29\sqrt{2^2\cdot 3}}{78}}\\\\\\ \mathsf{=\dfrac{102+29\cdot \sqrt{2^2}\cdot \sqrt{3}}{78}}\\\\\\ \mathsf{=\dfrac{102+29\cdot 2\sqrt{3}}{78}} 

     \mathsf{=\dfrac{102+58\sqrt{3}}{78}}\\\\\\ \mathsf{=\dfrac{\,\diagup\!\!\!\! 2\cdot \big(51+29\sqrt{3}\big)}{\diagup\!\!\!\! 2\cdot 39}} 

     \mathsf{=\dfrac{51+29\sqrt{3}}{39}}\quad\longleftarrow\quad\textsf{this is the answer.}


I hope this helps. =)

You might be interested in
How to divide fractions with whole numbers?
ad-work [718]
<span>1.Multiply the bottom number of the fraction by the whole number.
<span>2.Simplify the fraction (if needed)</span></span>
7 0
3 years ago
-8x^2+4x+5=0 using quadratic formula
daser333 [38]
So you want to solve for x?

It would be nice if this would easily factor:
(-4x + 5)(2x +1)  = 0    This will not work!

So you need to use the quadratic formula:
a = -8, b = 4, c = 5

x = \frac{-b+/-  \sqrt{b^{2}-4ac} }{2a}

x = (-4 +/- \sqrt{16-4(-8)(5)})/2(-8)
   = (-4 +/- \sqrt{16 + 160})/-16
   = (-4 +\sqrt{176})/-16
   = 1/4 - \sqrt{11}/4

6 0
3 years ago
Start with the following statement: Vertical angles are congruent. a.State the conditional and three other forms of the statemen
WARRIOR [948]
There are three kinds of statement that we could construct base on the given where as Vertical angels are congruent. First is converse: If angle 1 is 90 degree then angle 2 is 90. Second is Inverse: If angle 2 is not 90 then angle 1 is not. Third is Contrapositive: If angle 2 is not 90 then angle 1 is not 90 also.
8 0
3 years ago
The service department of a luxury car dealership conducted research on the amount of time its service technicians spend on each
mart [117]

Answer:

Probability that the mean service time is between 1 and 2 hours is 0.96764.

Step-by-step explanation:

We are given that a systematic random sample of 100 service appointments has been collected.

The 100 appointments showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.

<u><em>Let </em></u>\bar X<u><em> = sample mean service time</em></u>

The z-score probability distribution for sample mean is given by;

                             Z = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \mu = average preparation time = 90 minutes

           \sigma = standard deviation = 140 minutes

           n = sample of appointments = 100

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, probability that the mean service time is between 60 and 120 minutes is given by = P(60 minutes < \bar X < 120 minutes)

P(60 minutes < \bar X < 120 minutes) = P(\bar X < 120 min) - P(\bar X \leq 60 min)  

  P(\bar X < 120 min) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{120-90}{\frac{140}{\sqrt{100} } } ) = P(Z < 2.14) = 0.98382

  P(\bar X \leq 60 min) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } \leq \frac{60-90}{\frac{140}{\sqrt{100} } } ) = P(Z \leq -2.14) = 1 - P(Z < 2.14)

                                                        = 1 - 0.98382 = 0.01618

<em>The above probability is calculated by looking at the value of x = 2.14 in the z table which has an area of 0.98382.</em>

Therefore, P(60 min < \bar X < 120 min) = 0.98382 - 0.01618 = <u>0.96764</u>

7 0
3 years ago
How do you provide the value of k that makes each equation true?
Verdich [7]

Answer:

sorry dont know

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Don't understand the question.
    5·2 answers
  • There are 9 more turtles in the water than on a log. 13 turtles are on the water. How many turtles are on a log? Please explain
    15·1 answer
  • A super train travels 1,500 miles in 12.5 hours. How many miles does it travel in one hour?
    9·1 answer
  • What is the mass of an object that has a force of 100 Newtons and acceleration of 25 m/s2
    9·1 answer
  • What is the related rate of the ratio 90 to 3?
    6·1 answer
  • 1) Find 25% of 80.
    13·2 answers
  • What is the center of dilation?
    9·1 answer
  • Translation four units down and two units right
    7·2 answers
  • How do you find line segments? I'm having trouble with summer homework going into sixth grade AAAAA
    9·1 answer
  • 9 ft19 ftPlease refer to the rounding rules in the instructions.Circumference of the base = 59.5feetArea of the base = 254.3squa
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!