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Murljashka [212]
2 years ago
12

Simplify expression x8y-26/x14y-5 × x-39y-21

Mathematics
1 answer:
koban [17]2 years ago
3 0

The simplified form of the expression is x^{-45} y^{-42}

<h3>Simplifying an expression</h3>

From the question, we are to simplify the given expression

The given expression is

\frac{x^{8}y^{-26}  }{x^{14}y^{-5}  } \times x^{-39} y^{-21}

The expression can be simplified as shown below

\frac{x^{8}y^{-26}  }{x^{14}y^{-5}  } \times x^{-39} y^{-21}

\frac{x^{8} \times x^{-39} \times  y^{-26} \times  y^{-21}  }{x^{14} \times y^{-5}  }

\frac{x^{8+-39} \times  y^{-26+-21}  }{x^{14} \times y^{-5}  }

\frac{x^{8-39} \times  y^{-26-21}  }{x^{14} \times y^{-5}  }

\frac{x^{-31} \times  y^{-47}  }{x^{14} \times y^{-5}  }

Then,

\frac{x^{-31} }{x^{14} } \times \frac{ y^{-47} }{ y^{-5} }

x^{-31-14} \times y^{-47--5}

x^{-31-14} \times y^{-47+5}

x^{-45} \times y^{-42}

x^{-45} y^{-42}

Hence, the simplified form of the expression is x^{-45} y^{-42}

Learn more on Simplifying an expression here: brainly.com/question/2320607

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Answer:

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Step-by-step explanation:

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3 years ago
List the first 10 terms of each of these sequences.
harina [27]
Q1)
the sequence should start with 10, after that each term is calculated by subtracting 3 from the previous term.
1st term - 10
2nd term - 10 - 3 = 7
3rd term  - 7 - 3 = 4
4th term - 4 - 3 = 1
5th term  - 1 - 3 = -2
6th term - -2 - 3 = -5
7th term - -5 - 3 = -8 
8th - -8 - 3 = -11
9th - -11 - 3  = -14
10th -14 - 3 = -17
the sequence is - 10,7,4,1,-2,-5,-8,-11,-14,-17

Q2) 
<span>the sequence whose nth term is the sum of the first n positive integers
In this we get the term by adding all the integers of the terms before that term 
1st term - n = 1 no terms before this , therefore 0 + n(1)  = 1
2nd term -n =2  sum of integers before - 1 + n( 2) = 3
3rd - 3+3 = 6
4th - 6+4 = 10 
5th - 10 + 5 = 15
6th - 15 + 6 = 21
7th  - 21 + 7 = 28
8th - 28 + 8 = 36
9th - 36 + 9 = 45
10th -  45 + 10 = 55
this is a triangular number pattern
this number pattern can be found out using ; n = (n x (n+1))/2

sequence is - 1,3,6,10,15,21,28,36,45,55

Q3)
</span>the sequence whose nth term is 3n − 2n
general term for this sequence is 3n − 2n
to find 1st term , n = 1
substituting n = 1 in the general term 
1st term - 3x1 - 2x1 = 3-2 = 1
2nd - 3x2- 2x2 = 6 - 4 = 2
3rd - 3x3 - 2x3 = 9-6 = 3
4th - 3x4 - 2x4 = 12 - 8 = 4
5th - 3x5 - 2x5 = 15 - 10 = 5
6th - 3x6 - 2x6 = 18 - 12 = 6
7th - 3x7 - 2x7 = 21 - 14 = 7
8th - 3 x8 - 2x8 = 24 - 16 = 8
9th - 3x9 - 2x9 = 27 - 18 = 9
10th - 3x10 - 2x10 = 30-20 = 10

sequence is 1,2,3,4,5,6,7,8,9,10

Q4)
<span>the sequence whose nth term is √ n
when n=1 1st term is </span>√1 = 1
1st term - √1 = 1
2nd term - √2 = 1.41
3rd - √3 = 1.73
4th - √4 = 2
5th - √5 = 2.23
6th- √6 = 2.44
7th - √7 = 2.65
8th- √8 = 2.82
9th - √9 = 3
10th - √10 = 3.16

The sequence is 1, 1.41, 1.73, 2, 2.23, 2.44, 2.65, 2.82, 3, 3.16

Q5)T<span>he sequence whose first two terms are 1 and 5 and each succeeding term is the sum of the two previous terms
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2nd term - 5
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4th term - add 2nd and 3rd terms (5+6) = 11
5th - add 3rd and 4th (6+11) = 17
6th - (11+17) = 28
7th - (17 + 28) = 45
8th - 45 + 28 = 73
9th - 73 + 45 = 118
10th - 73+ 118 = 191

sequence is - 1,5,6,11,17,28,45,73,118,191
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184500 $ are to be divided between 2 people. One person has 80% of what the other person has. How much does each one receive in
Annette [7]

Given:

$184500 are to be divided between 2 people.

One person has 80% of what the other person has.

To find:

The amount each one receive in $.

Solution:

Let $x be the amount received by first person. Then,

Amount received by the second person = 80% of x

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Total amount = Amount received by first person + by second person

                      =x+0.80x

                      =1.80x

Total amount is 184500. So,

1.80x=184500

x=\dfrac{184500}{1.80}

x=102500

So, the amount received by the first person is $102,500.

0.80x=0.80\times 102500

0.80x=82000

So, the amount received by the second person is $82,000.

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3 years ago
Preston writes 3 songs in 2 days, working 7 hours each day. He spends the same amount of time on each song. How long does he spe
Alekssandra [29.7K]

Answer:

Step-by-step explanation:

In 2 days he spends 2*7 = 14 hours total

He divides the number of hours on each song evenly

14 /3 = 4 2/3 hours on each song.

What is 2/3 of an hour?

2/3 * 60 = 120 / 3 = 40 minutes

Total time spent on each song 4 hours and 40 minutes

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2 years ago
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Blababa [14]

Answer:10


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