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2 years ago

What has to be the same in order to add fractions?

Mathematics

1 answer:

RUDIKE [14]2 years ago

8 0

Answer: The denominator

Explanation: you can’t add 3/12 and 2/6. You would have to change it to 3/12 + 4/12.

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If AC equals 48 meters, what is the perimeter of the field

Alinara [238K]

Remark

A kite is constructed such that AB = BC and AD = DC. AB = sqrt( (1/2)AC + 18^2) see diagram. AD = sqrt(24^2 + 32^2)

Step One

Solve for AB

1/2 AC = 24 (AC is given as 48)

18 is a given length

AB = sqrt(24^2 + 18^2) = sqrt(576 + 324) = sqrt(900) = 30

Step Two

Find the length of AD

AD = sqrt(32^2 + 24^2) = sqrt(1024 + 576) = sqrt(1600) = 40

Step Three

Find the Perimeter.

P = 2 * 30 + 2*40 = 60 + 80 = 140

P = 140 <<<<< Answer

5 0

2 years ago

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Consider these three numbers written in scientific notation: 6.5 × 103, 5.5 × 105, and 1.1 × 103. Which number is the greatest,

zavuch27 [327]

I think the answer would be B that’s the only one I consider

6 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

2 years ago

A fruit packing plant

Alborosie

Huh??? what does that mean

4 0

2 years ago

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Kwan hiked up a hill at 4 km/h and back down at 6 km/h. His total hiking time was 3 hours. How long did the trip up the hill tak

Leya [2.2K]

Let the time to hike up the hill = t

As given that the total time time up and down is 3 hrs, therefore

The time down the hill = 3-t

The distance up and down is the same.

Distance = speed * time

$4t=6(3-t)$

$4t=18-6t$

$10t=18$

t=1.8

Hence, time taken to uphill = 1.8 hours

Time taken to down hill = 3-18 = 1.2 hours

3 0

2 years ago

What has to be the same in order to add fractions?​

What has to be the same in order to add fractions?