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3 years ago

What is the value of x

Mathematics

1 answer:

Archy [21]3 years ago

8 0

I think it might be a 10

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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

Pls follow the steps and show work

WINSTONCH [101]

1st box: 2a (subtract 2a from both sides)
2nd box: 3 (add 3 to both sides)
3rd box: 10 (add 7+3)
4th and 5th box: 2 (divide both by 2)
6th box: 5 (10/2=5)

8 0

2 years ago

HELP ME!!!!!!!!!!!!!!!!!!!!111

Vlad1618 [11]

Answer:

-40

Step-by-step explanation:

(-40) divided by 5 is (-8)

4 0

2 years ago

Read 2 more answers

Members of the theater club sold tickets for the spring

Tpy6a [65]

so basically what i was thinking of was they sold them in the spring

8 0

3 years ago

As part of a survey, 150 students were asked to name their favorite class. 50 points

disa [49]

A:40%
If you put 60 over 150 and x(percent of students) over 100 and cross multiply 100 and 60, you will get 6000. You then divide that by 150 which leaves you with 40 as x and 40 over 100 is 40%.

5 0

2 years ago