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2 years ago

Simplify the following expression. X^2/9 . X^-4/9 x^2/9 . X^-4/9

Mathematics

1 answer:

Lynna [10]2 years ago

4 0

Answer:

Step-by-step explanation:

i hope it is b if its not im sorry

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A ECD is

FinnZ [79.3K]

Answer: SAS

Step-by-step explanation:

The Side Angle Side (SAS) postulates that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent

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3 years ago

How is the series 5+11+17…+251 represented in summation notation?

NISA [10]

Answer:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

Step-by-step explanation:

Given:

Series 5+11+17+...+251

To find:

Summation notation of the given series

Summation Notation:

$\displaystyle \large{\sum_{k=1}^n a_k}$

Where n is the number of terms and $\displaystyle \large{a_k}$ is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

Arithmetic Series

A series that has common difference.

Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

11-5 = 6
17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

<u>Arithmetic Sequence</u>

$\displaystyle \large{a_n=a_1+(n-1)d}$

Where $\displaystyle \large{a_n}$ is the nth term, $\displaystyle \large{a_1}$ is the first term and $\displaystyle \large{d}$ is the common difference:

So for our general term:

$\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}$

And for number of terms, substitute $\displaystyle \large{a_n}$ = 251 and solve for n:

$\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}$

Now we can convert the series to summation notation as given the formula above, substitute as we get:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

5 0

2 years ago

Find the median, first quartile, third quartile, and interquartile range of the data.

jasenka [17]

Answer:

Median: 55

First quartile: 26.5

Third quartile: 93

Interquartile range: 66.5

5 0

3 years ago

Read 2 more answers

Convert degrees Fahrenheit (F) into degrees Celsius (C) using the formula C = 5/9(F - 32). Rewrite the equation to convert degre

marissa [1.9K]

To answer the question above, isolate F on the other side of the equation by multiplying both sides by 9/5. This gives,
(9/5) C = F - 32
Next, transpose -32 to left side.
(9/5)C + 32 = F
Rearrange the equation to give an answer of
F = (9/5)C + 32

4 0

3 years ago

jolie can read around 14 sentences per minute of her current novel. She wants to finish reading her book before the movie comes

alexandr402 [8]

Start at the beginning. 17 pages times 120 sentences is the first thing.
17 x 120 = 2040. So she has to read 2,040 sentences. If we now divide 2.040 by 14 pages/minute, we shoud get

2,040 divided by 14 = 145.7

The last thing to do, is changes those minutes into hours by dividing by 60.
2.42 hours.

8 0

3 years ago