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3 years ago

Can u help me the s solve this problem If 5x-8=37,the x=9

Mathematics

1 answer:

SVEN [57.7K]3 years ago

8 0

Answer:x=9

Step-by-step explanation:

X=9-8=37

(5x9)-8=37

45-8=37

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What is the sum of the first 51 consecutive odd positive integers?

Angelina_Jolie [31]

We call:

$a_{n}$ as the set of the first 51 consecutive odd positive integers, so:

 $a_{n} = \{1, 3, 5, 7, 9...\}$

Where:
$a_{1} = 1$
$a_{2} = 3$
$a_{3} = 5$
$a_{4} = 7$
$a_{5} = 9$
and so on.

In mathematics, a sequence of numbers, such that the difference between two consecutive terms is constant, is called Arithmetic Progression, so:

3-1 = 2
5-3 = 2
7-5 = 2
9-7 = 2 and so on.

Then, the common difference is 2, thus:

 $a_{n} = \{ a_{1} , a_{1} + d, a_{1} + d + d,..., a_{1} + (n-2)d+d\}$

Then:

 $a_{n} = a_{1} + (n-1)d$

So, we need to find the sum of the members of the finite series, which is called arithmetic series:

There is a formula for arithmetic series, namely:

 $S_{k} = ( \frac{a_{1} + a_{k}}{2} ).k$

Therefore, we need to find:
 $a_{k} = a_{51}$

Given that $a_{1} = 1$ , then:

$a_{n} = a_{1} + (n-1)d = 1 + (n-1)(2) = 2n-1$

Thus:
$a_{k} = a_{51} = 2(51)-1 = 101$

Lastly:

$S_{51} = ( \frac{1 + 101}{2} ).51 = 2601$

4 0

3 years ago

The Roosevelt Branch Library is open daily from 9:00 A.M. until 4:30 P.M., 255 days a year. How many hours in all is the library

kramer

Lets look at the hours they are open from. 9 am - 4:30 pm which is 7 and a half hours a day. Now we multiply 7 1/2 by the number of days they are open, which will be 7 1/2 * 255 = 1,912.5. This means that the library is open 1,912 1/2 hours a year.

I hope I've helped! :)

3 0

2 years ago

Read 2 more answers

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Bezzdna [24]

The first number that you see between Michael and John is 40

6 0

3 years ago

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Lesson 4: Practice Problems

gtnhenbr [62]

Answer:

a).1

b).1

c).111

Step-by-step explanation:

a) anything to the zero power is 1

b) any number divided by itself is one

c) 100+10+1=111

3 0

2 years ago

Write the explicit formula and define the formula please explain and help thanks

schepotkina [342]

Remark

The formula for this series is

t_n = n^2 - 1

Explanation

If the series ends at 288, then the highest value n can have is 17

So you would write t_n = n^2 - 1 {n| 1 ≤ n ≤17}

If you said this to someone, you would say "t_n = n squared minus 1 where n is such that 1 is greater than or equal to 1 or less than or equal to 17"

Example

What is the 4th term in this series?

t_4 = 4^2 - 1

t_4 = 16 - 1

t_4 = 15

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3 years ago