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Afina-wow [57]
2 years ago
13

D%7D%7B5%C3%97%285%29%5E%7B2n%2B3%20%7D-%20%2825%29%5E%7Bn%2B1%E2%80%8B%7D%7D%20%5C%5C%20" id="TexFormula1" title="Simplify: \frac{ 5×(25)^{n+1} - 25 × (5)^{2n}}{5×(5)^{2n+3 }- (25)^{n+1​}} \\ " alt="Simplify: \frac{ 5×(25)^{n+1} - 25 × (5)^{2n}}{5×(5)^{2n+3 }- (25)^{n+1​}} \\ " align="absmiddle" class="latex-formula">
Need help please"....."​
Mathematics
1 answer:
Katen [24]2 years ago
4 0

\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} }}

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What is 0.66666666666 as a fraction
stellarik [79]

To turn 0.(6)=0.6666... into a fraction you should do such steps:

1 step. Set up an equation by representing the repeating decimal with a variable. Using your example, you will let x represent the repeating decimal 0.(6), so you have x=0.666... .

2 step. Identify how many digits are in the repeating pattern, or n digits. Multiply both sides of the equation from Step 1 by 10^n to create a new equation. Again, using your example, you see that the repeating pattern consists of just one digit: 6. Now multiply both sides of the equation by 10^1 = 10. Thus, you have 10x = 10 \cdot 0.666... or 10x = 6.666.....

3 step. Subtract the equation in Step 1 from the equation in Step 2. Notice that when we subtract these equations, our repeating pattern drops off. Therefore, 10x-x=6.666...-0.666...\\ 9x=6.

4 step. You now have an equation that you can solve for x and simplify as much as possible, using x as a fraction: 9x = 6. If you divide both sides by 9, you get x=\dfrac{6}{9}. When simplified, you get that x=\dfrac{2}{3}.

Answer: 0.(6)=0.666... =\dfrac{2}{3}.

8 0
3 years ago
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Help my math please<br> Due date is in 3 hours
Bumek [7]

Answer:

see explanation

Step-by-step explanation:

(a)

To change a mixed number to an improper fraction

Multiply the whole number by the denominator of the fraction and add the numerator. This value is the numerator of the improper fraction while the denominator remains unchanged, that is

(2 × 13) + 12 = 26 + 12 = 38 ← numerator

2 \frac{12}{13} = \frac{38}{13}

(b)

To change an improper fraction to a mixed number

divide the numerator by the denominator, noting the remainder, which forms the numerator of the fraction in the mixed number.

\frac{47}{19} = 2 remainder 9, hence

\frac{47}{19} = 2 \frac{9}{19}



7 0
3 years ago
Nichol walks at a constant pace of 1.2 m/s and takes 15 minutes to get to school.
liraira [26]

Answer:

The difference between the distances they walked is 600 meters.

Step-by-step explanation:

Let's calculate the distance traveled by Nichol and Sakura with the following equation:

d = v*t

Where:

v: is the speed

t: is the time

The distance traveled by Nichol is:

d_{n} = 1.2 m/s*15min*\frac{60 s}{1 min} = 1080 m

And the distance traveled by Sakura is:

d_{s} = 1.4 m/s*20 min*\frac{60 s}{1 min} = 1680 m

Hence, the difference between the distances they walked is:

d_{t} = d_{s} - d_{n} = 1680 m - 1080 m = 600 m

Sakura traveled 600 meters more than Nichol.

Therefore, the difference between the distances they walked is 600 meters.

               

I hope it helps you!                    

4 0
2 years ago
Baldo is paid $80 per day at his job, plus $15 per hour for every hour (h) that he works overtime. One day, his total earnings w
Flauer [41]
15h + 80 = 140

If you wanted to solve how many hours he worked:
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yuradex [85]

Answer:

Step-by-step explanation:

Considering the complete question attached in figure.

Consider

Hadley = x

Parker = y

Greenville = z

Distance between Greenville and Parker = yz = 29

Given that distance between Hadley and Greenville is 13 miles less than the distance between Parker and Greenville.

                                        xz = yz -13 --- (1)

Distance between hardley and greenville = xz  = ?

From (1)

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                                         xz = 16 miles

So Alan is right that distance between Hadley and Greenville is 16 miles

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