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3 years ago

Simplify 4sqrt(6) / sqrt(30) by rationalizing the denominator.

2 answers:

8 0

Given question is 4√6/√30
by rationalizing the denominator
4√6x√30/√30x√30
= 4√6x30/√30²
=4x√180/30 (i)
by solving the √180
√180=6√5
putting the value of √180 in (i)
=4x6√5/30
=24√5/30
=4√5/5 is the right answer.

sweet-ann [11.9K]3 years ago

6 0

Answer:

4/\sqrt{5}

Step-by-step explanation:

Given -

$4/\sqrt{5}/ ( \sqrt{30} \\= 4/\sqrt{5}/ (\sqrt{6} * \sqrt{5} )\\= 4/\sqrt{5}\\$

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2.789 in expanded form

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3 years ago

et f(x) = x + |2x − 3|. Find all solutions to the equation f(x) = 12. (Enter your answers as a comma-separated list. If an answe

Alinara [238K]

Answer:

1. {5,-9}

2.{4}

3.{9/2}

Step-by-step explanation:

The equation $f(x)=x+\lvert 2x-3 \rvert=12$ can be solved as follows:

$x+\lvert 2x-3 \rvert =12\,\,\,\text{(given equation)}$

$\lvert 2x-3 \rvert =12-x$

$2x-3=12-x\,\,\text{or}\,\,2x-3=-(12-x)$

$3x=15\,\,\text{or}\,\,\x=-9$

Then, the solutions of the equation are $x=5, x=-9$ .

Now, if $g(x)=5x-3+\lvert x+4\rvert$ , we can solve the equation $g(a)=4a+9$ as follows:

$5a-3+\lvert a+4 \rvert =4a+9$

$\lvert a+4\rvert =4a+9-5a+3$

$a+4 =-a+12\,\,\text{or}\,\,a+4=-(-a+12)$

$2a=8\,\,\text{or}\,\,4=12$

So, the unique solution of this last equation is $a=4$

The last equation is $h(x-1)=x-3$ , where $h(x)=\lvert x \rvert -2x+5.$ . To solve this equation we can proceed as follows:

$h(x-1)=x-3$

$\lvert x-1\rvert -2(x-1)+5=x-3$

$\lvert x-1 \rvert -2x+2+5=x-3$

$\lvert x-1\rvert =3x-10$

$x-1=3x-10\,\,\text{or}\,\,x-1=-(3x-10)$

$-2x=-9\,\,\text{or}\,\,4x=11$

$x=9/2\,\,\text{or}\,\,x=11/4$

But, x=11/4 is not a solution of this equation. So the unique solution is x=9/2.

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3 years ago

on a certain planet, objects weight about 7/12 of what they weigh on earth. an object weights 13 5/12 pounds on the planet. solv

Cloud [144]

Although the concept here is physics, the solution is technically just algebra. You have two situations that are related to each other which can be expressed in equation form. Actually, the equation is already given which is <span>7/12 w= 13 5/12. So, basically, all you have to do is solve for w.

Let's simplify 13 5/12 first into an improper fraction.You do this by multiplying the denominator with the whole number and adding to it the numerator. This will be your new numerator, The denominator would still be 12. So, this is equal to (12*13 + 5)/12 = 161/2. Then,

(7/12) w = 161/12

By cross multiplication,

7*12*w = 161*12
w = 161/7 = 23

Therefore, w = 23 pounds which is the weight of the object on Earth.

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3 years ago

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suter [353]

Answer:

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4. Why studying central tendency alone is insufficient and calculating dispersion is always needed in both descriptive and infer

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Answer:

Check below for the answer and explanation.

Step-by-step explanation:

Studying the central tendency alone is not sufficient because apart from calculating the value of the central point of a group of data ( which is what the measure of central tendency does), it is important to also understand the spread of these data about the average(mean) value.The measure of dispersion will help us to know the range of error that is recorded in both descriptive and inferential statistics and this will enable the statistician to assess the validity of the data generated from the experiment performed.

A small value of standard deviation indicates that each of the values in the dataset is close to the average (mean) value.

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