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o-na [289]
3 years ago
14

Write the following number in expanded form 46,371

Mathematics
1 answer:
Anarel [89]3 years ago
8 0
46,371 = 40,000 + 6,000 + 300 + 70 + 1
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Simplify: [5×(25)^n+1 - 25 × (5)^2n]/[5×(5)^2n+3 - (25)^n+1​]​
Alekssandra [29.7K]

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

<u>Given expression is </u>

\rm :\longmapsto\:\dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }

can be rewritten as

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

We know,

\purple{\rm :\longmapsto\:\boxed{\tt{  {( {x}^{m} )}^{n}  \: = \:   {x}^{mn}}}} \\

And

\purple{\rm :\longmapsto\:\boxed{\tt{ \:  \:   {x}^{m} \times  {x}^{n} =  {x}^{m + n} \: }}} \\

So, using this identity, we

\rm \:  =  \: \dfrac{5 \times  {5}^{2n + 2}  - {5}^{2n + 2} }{{5}^{2n + 3 + 1}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 4}  -  {5}^{2n + 2} }

can be further rewritten as

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 2 + 2}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2}  - 1)}

\rm \:  =  \: \dfrac{4}{25 - 1}

\rm \:  =  \: \dfrac{4}{24}

\rm \:  =  \: \dfrac{1}{6}

<u>Hence, </u>

\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }  =  \frac{1}{6} }}

4 0
2 years ago
Help plz i need an answer thx if you do
RoseWind [281]

Answer:

\frac{1}{16} or in decimals: 0.0625

Step-by-step explanation:

4*4*4 is 4³ or 16*4 or 64

4*4*4*4*4 is 4^{5} or 16*16*4 or 256*4 or 1024

We have \frac{64}{1024} which divided by 8 is \frac{8}{128} which divided by 8 again is \frac{1}{16}

5 0
3 years ago
Read 2 more answers
How do I solve 15+5-5/12. please give me the steps
gregori [183]
1) You must do division first. So divide 5/12 and get .41666666... 
2) Then you add 15+5 and get 20.
3) Finally you subtract 20 and .41666666... and you get 19.5833333...
4) you can simplify 19.583333... to 19.584 if you need to.
7 0
3 years ago
A train is traveling at a constant speed. The diagram represents the train's distance and time. What is the speed of the train?
Over [174]
240÷6=40 so the answer would be "The train is traveling 40 miles per hour."
6 0
3 years ago
Read 2 more answers
The radius of a circle is 16 cm. Find its area in terms of pi
anzhelika [568]
Area is 804.25 if the radius is 16cm
8 0
2 years ago
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