<img src="https://tex.z-dn.net/?f=%5Csqrt%7B36%7D%20%2B%204%20%2F%20%5Csqrt%7B100%7D" id="TexFormula1" title="\sqrt{36} + 4 / \s

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Black_prince [1.1K]

3 years ago

qrt{100}" alt="\sqrt{36} + 4 / \sqrt{100}" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

pentagon [3]3 years ago

4 0

The answer is 2√19 I think

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9^x=1/3<br><br> How much is x?

kumpel [21]

Answer:

x = -1/2

Step-by-step explanation:

This question can be solved by applying the laws of indices

In a^n, a - base

n - index

Given

9^x = 1/3

According to the laws of indices, a/b = b^(-a)

Hence we can write, 1/3 = 3^(-1)

9^x = 3^(2x)

Again according to the laws of indices,

a^b = a^n can be written as;

b = n

That is, if in an equation the bases are the same, the indices are also equal.

So we can write,

3^(2x) = 3^(-1)

2x = -1

Divide both sides of the equation by 2, the coefficient of x

2x/2 = -1/2

x = -1/2

6 0

3 years ago

35 out of 48 people chose Nike as their favorite brand.If you were to ask 528 people how many would pick Nike?

professor190 [17]

Answer:

352

Step-by-step explanation:

4 0

3 years ago

Rationalise the denominator of:<br>1/(√3 + √5 - √2)

Paul [167]

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} }$

can be re-arranged as

$\rm :\longmapsto\:\dfrac{1}{ \sqrt{3} - \sqrt{2} + \sqrt{5} }$

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} }$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{1}{( \sqrt{3} - \sqrt{2} ) + \sqrt{5} } \times \dfrac{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }{( \sqrt{3} - \sqrt{2} ) - \sqrt{5} }$

We know,

$\rm :\longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}$

So, using this, we get

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ {( \sqrt{3} - \sqrt{2} )}^{2} - {( \sqrt{5}) }^{2} }$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{3 + 2 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{5 - 2 \sqrt{6} - 5}$

$\rm \: = \: \dfrac{ \sqrt{3} - \sqrt{2} - \sqrt{5} }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{ - ( - \sqrt{3} + \sqrt{2} + \sqrt{5}) }{ - 2 \sqrt{6}}$

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}}$

On rationalizing the denominator, we get

$\rm \: = \: \dfrac{- \sqrt{3} + \sqrt{2} + \sqrt{5}}{2 \sqrt{6}} \times \dfrac{ \sqrt{6} }{ \sqrt{6} }$

$\rm \: = \: \dfrac{- \sqrt{18} + \sqrt{12} + \sqrt{30}}{2 \times 6}$

$\rm \: = \: \dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}$

$\rm \: = \: \dfrac{- 3\sqrt{2} + 2 \sqrt{3} + \sqrt{30}}{12}$

Hence,

$\boxed{\tt{ \rm \dfrac{1}{ \sqrt{3} + \sqrt{5} - \sqrt{2} } =\dfrac{- \sqrt{3 \times 3 \times 2} + \sqrt{2 \times 2 \times 3} + \sqrt{30}}{12}}}$

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<h3><u>More Identities to </u><u>know:</u></h3>

$\purple{\boxed{\tt{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}}}}$

$\purple{\boxed{\tt{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}}}}$

$\purple{\boxed{\tt{ {(x + y)}^{3} = {x}^{3} + 3xy(x + y) + {y}^{3}}}}$

$\purple{\boxed{\tt{ {(x - y)}^{3} = {x}^{3} - 3xy(x - y) - {y}^{3}}}}$

$\pink{\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}}$

$\pink{\boxed{\tt{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}}}$

6 0

3 years ago

How many more students watch 6 to 7 hours of tv a week then watch 2 to 3 hours of Tv a week.

faltersainse [42]

To calculate this, we need to find how many students watch 6-7 hours of tv a week, and how many students watch 2-3 hours a week.
We have 10 students watching 6-7 hours a week, and 3 students watching 2-3 hours a week. The question is asking "How many more 6-7 than 2-3", which means to subtract 3 from 10.
I will now write out the equation as I rewrite the entire question.
How many more students watch 6-7 (10-) hours of tv a week than to how many watch 2-3 (3) hours a week? (=?)
Now, write out what we have in parenthesis.
10-3=?
Subtract 3 from 10.
10-3 = 7.
There are 7 more 6-7 hours of tv a week than there are 2-3 hours of tv a week.
I hope this helps!

4 0

3 years ago

Read 2 more answers

What are the next 4 multiples of the fraction 1/6

Bad White [126]

Answer:

1/6, 2/6, 3/6, 4/6, 5/6

Step-by-step explanation:

2 X 1/6 = 2/6

3 X 1/6 = 3/6

4 X 1/6 = 4/6

5 X 1/6 = 5/6