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2 years ago

9,-81, 729,-6561... What is the common ratio? Help which is the correct answer?

Mathematics

1 answer:

GrogVix [38]2 years ago

7 0

Answer:

$r = -9$

Step-by-step explanation:

Given

$Sequence: 9,-81, 729,-6561...$

Required

Determine the common ratio

The common ratio r is calculated using:

$r = \frac{T_n}{T_{n-1}}$

Let $n = 2$

So, we have:

$r = \frac{T_2}{T_{2-1}}$

$r = \frac{T_2}{T_1}$

From the sequence:

$T_2 = -81$

$T_1=9$

So, the equation becomes

$r = \frac{-81}{9}$

$r = -9$

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A party is thrown where 25 tables are used. Each table either sits 4 people or 6 people. A total of 116 people can be sat at the

Soloha48 [4]

Answer:

(a) 4 y + 6 s = 116 represents the given situation.

(b)There are 8 six- person tables at the party.

Step-by-step explanation:

Here, the total number of tables = 25

Let y : Represent the number of four person tables.

s : Represents the number of six person tables.

Total people seated at all tables = 116

Now, the number of people seated at table of 4 = y x 4 = 4 y

the number of people seated at table of 6 = s x 6 = 6 s

(a) Total People Seated = People seated at { 4- table + 6 table}

⇒ 116 = 4 y + 6 s

Hence, 4 y + 6 s = 116 represents the given situation.

(b) Total tables are 25. ⇒ s + y = 25

Hence, the givens system of equations are:

4 y + 6 s = 116 ........ (1)

s + y = 25 ............ (2)

Solving the above system, we get, substitute y = 25 - s in (1)

4 y + 6 s = 116 ⇒ 4(25-s) + 6s = 116

or, 100 - 4s + 6s = 116

or. 2s = 16

or, s = 16 / 2 = 8 ⇒ s = 8

Hence, there are 8 six- person tables at the party.

3 0

2 years ago

Please Help Will Mark Brainly.

Free_Kalibri [48]

Answer:

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3 years ago

Read 2 more answers

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:

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

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True. If they never intersect then they must have the same slope and are parallel

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Is 4 a solution to the compound inequality “x < 0 and c < 7”

tester [92]

Answer:

Step-by-step explanation:

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