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nasty-shy [4]
3 years ago
7

Simplify this equation Thanks a lot!!!

Mathematics
1 answer:
den301095 [7]3 years ago
4 0

Answer:

-1

Step-by-step explanation:

We need to simplify the given expression . The given expression is ,

\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}

Here we can see that the power of the both exponent is same that is (2n+1) . Recall the property of exponents ,

\bf\implies a^m \times b^m = (ab)^m

Using this property , we have ,

\rm\implies ( 2 \sqrt6 +5)^{2n-1} ( 2\sqrt6 - 5)^{2n-1}

This can be written as ,

\rm\implies\{( 2 \sqrt6 +5) ( 2\sqrt6 - 5)\}^{2n-1}

Simplifying using ( a+b)(a-b) = a² - b² ,

\rm\implies\{( 2 \sqrt6)^2 -5^2 \}^{2n-1}\\\\\rm\implies ( 24 - 25)^{2n-1}

Subtracting the numbers inside the brackets ,

\rm\implies (-1)^{2n - 1 }

Now we know that every odd number is in the form of 2n -1 , where n is any integer. Therefore , the <u>power is odd</u> .

Since the base is (-1) , for even power it is 1 and for odd power it is -1 . Therefore the final answer is ,

\rm\implies\boxed{\quad \red{ -1 }\quad }

<u>Hence </u><u>the</u><u> </u><u>required</u><u> answer</u><u> is</u><u> </u><u>(</u><u>-</u><u>1</u><u>)</u><u> </u><u>.</u>

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94.92 + 20.00 = 114.92 Eva spent and Martha spent $94.92

Step-by-step explanation:

5 0
3 years ago
If average of m numbers is n^2 and average of n numbers is m^2 then average of m+n numbers is 
kkurt [141]
The sum of the m numbers divided by m (which is the average) equals n^2. Then, the sum of the m numbers equals mn^2.
The sum of the n numbers divided by n (which is the average) equals m^2. Then, the sum of the n numbers equals nm^2.
The average of m+n numbers which is the sum of the m numbers plus the sum of the n numbers divided by (m+n) equals (mn^2+nm^2)/(m+n). This is mn(n+m)/(m+n). Then the factor (m+n) can be ruled out and the result is mn.
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3 years ago
X + 16 at X= 4<br> 20<br> 21<br> 15
Colt1911 [192]

Answer:

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Step-by-step explanation:

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4 0
3 years ago
Read 2 more answers
PLEASE HELP!! I WILL BRAINLIEST
ArbitrLikvidat [17]

Answer:

81.8%

Step-by-step explanation:

Mean = \mu = 40

Standard deviation = \sigma = 5

Now we are supposed to find out what percent of the numbers fall between 35 and 50

z = \frac{x-\mu}{\sigma}

Substitute the values

z = \frac{x-40}{5}

Now for P(35<x<50)

Substitute x = 35

z = \frac{35-40}{5}

z =-1

Substitute x = 50

z = \frac{50-40}{5}

z =2

So, P(-1<z<2)

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=0.9772-0.1587

=0.8185

= 0.818 \times 100

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Hence  81.8% percent of the numbers fall between 35 and 50

7 0
3 years ago
What is the center of the data?
satela [25.4K]

Answer:

Median = 13

Step-by-step explanation:

Given

See attachment for dot plot

Required

The center of data

This implies that, we calculate the median

From the attached plot,

n = 13 --- number of observation

So, the median is:

Median = \frac{n + 1}{2}

Median = \frac{13 + 1}{2}

Median = \frac{14}{2}

Median = 7th

The median is at the 7th position

At the  7th position, is 13

Hence:

Median = 13

5 0
3 years ago
Read 2 more answers
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