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2 years ago

Which compound inequality represented by the graph below?

Mathematics

1 answer:

nekit [7.7K]2 years ago

6 0

Answer: x < -1 or x ≥ 3

Step-by-step explanation:

First we will look at the left part. The circle is open (not "equal to), arrow is pointing to the left (showing "less than" in this case), and the value is on -1;

x < -1

Second, we will look at the right part. The circle is closed (showing "equal to"), the arrow is pointing to the right (showing "greater than" in this case). and the value is on 3;

x ≥ 3

Lastly, we will write the final compound inequality. In this case, we use the word "or" because the solution value is either less than -1 or greater than and equal to 3.

<em>Note: The word "and" is only used when the "arrows point towards each other" creating a segment, so to say. In this case, they "point away" so we use the word or.</em>

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x = 120/6
x = 20 <== the scale factor

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# 1) 22 students are __% of 55 * Show Work *

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An investor bought an antique table for $6000. He paid 5% as a deposit and borrowed the remainder from a bank for two years at 1

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3 years ago

In the 7th grade, 132 students take Spanish as an elective. If there are 330 seventh graders, what percent of

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You are given the following sequence:

borishaifa [10]

<h2> Question No 1</h2>

Answer:

7.5 is the 4th term of the sequence $60, 30, 15, 7.5, ...$ .

In other words: $\boxed{a_4=7.5}$

Step-by-step explanation:

Considering the sequence

$60, 30, 15, 7.5, ...$

As we know that a sequence is said to be a list of numbers or objects in a special order.

$60, 30, 15, 7.5, ...$

is a sequence starting at 60 and decreasing by half each time. Here, 60 is the first term, 30 is the second term, 15 is the 3rd term and 7.5 is the fourth term.

In other words,

$a_1=60$ ,

$\:a_2=30$ ,

$a_3=15$ , and

$a_4=7.5$

Therefore, 7.5 is the 4th term of the sequence $60, 30, 15, 7.5, ...$ .

In other words: $\boxed{a_4=7.5}$

<h2> Question # 2</h2>

Answer:

The value of a subscript 5 is 16.

i.e. When n = 5, then h(5) = 16

Step-by-step explanation:

To determine:

What is the value of a subscript 5?

Information fetching and Solution Steps:

Chart with two rows.

The first row is labeled n.

The second row is labeled h of n. i.e. h(n)

The first row contains the numbers three, four, five, and six.

The second row contains the numbers four, nine, sixteen, and twenty-five.

Making the data chart

n 3 4 5 6

h(n) 4 9 16 25

As we can reference a specific term in the sequence by using the subscript. From the table, it is clear that 'n' row represents the input and and 'h(n)' represents the output.

So, when n = 5, the value of subscript 5 corresponds with 16. In other words: When n = 5, then h(5) = 16

Therefore, the value of a subscript 5 is 16.

<h2> Question # 3</h2>

Answer:

We determine that the sequence 33, 31, 28, 24, 19, … is neither arithmetic nor geometric.

Step-by-step explanation:

Considering the sequence

33, 31, 28, 24, 19, …

Lets calculate the common difference 'd' to determine if the sequence is Arithmetic or not.

$\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n$

$d = 31 - 33 = -2$

$d = 28 - 31 = -3$

$d = 24 - 28 = -4$

$d = 19 - 24 = -5$

As the common difference 'd' is not constant. It means the sequence is not Arithmetic.

Lets now calculate the common ratio 'r' to determine if the sequence is Geometric or not.

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_n}{a_{n-1}}$

$\frac{31}{33}=0.93939\dots ,\:\quad \frac{28}{31}=0.90322\dots ,\:\quad \frac{24}{28}=0.85714\dots ,\:\quad \frac{19}{24}=0.79166\dots$

The ratio is not constant. It means the sequence is not Geometric.

From the above analysis, we determine that the sequence 33, 31, 28, 24, 19, … is neither arithmetic nor geometric.

<h2> Question # 4</h2>

Answer:

We determine that the sequence -99, -96, -92, -87, -81... is neither arithmetic nor geometric.

Step-by-step explanation:

From the description statement:

''negative 99 comma negative 96 comma negative 92 comma negative 87 comma negative 81 comma dot dot dot''.

The statement can be translated algebraically as

-99, -96, -92, -87, -81...

Lets calculate the common difference 'd' to determine if the sequence is Arithmetic or not.

$\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n$

$-96-\left(-99\right)=3,\:\quad \:-92-\left(-96\right)=4,\:\quad \:-87-\left(-92\right)=5,\:\quad \:-81-\left(-87\right)=6$

As the common difference 'd' is not constant. It means the sequence is not Arithmetic.

Lets now calculate the common ratio 'r' to determine if the sequence is Geometric or not.

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_n}{a_{n-1}}$

$\frac{-96}{-99}=0.96969\dots ,\:\quad \frac{-92}{-96}=0.95833\dots ,\:\quad \frac{-87}{-92}=0.94565\dots ,\:\quad \frac{-81}{-87}=0.93103\dots$

The ratio is not constant. It means the sequence is not Geometric.

From the above analysis, we determine that the sequence -99, -96, -92, -87, -81... is neither arithmetic nor geometric.

<h2> Question # 5</h2>

Step-by-step explanation:

Considering the sequence

12, 22, 30, 36, 41, …

$\mathrm{Compute\:the\:differences\:of\:all\:the\:adjacent\:terms}:\quad \:d=a_{n+1}-a_n$

$22-12=10,\:\quad \:30-22=8,\:\quad \:36-30=6,\:\quad \:41-36=5$

As the common difference 'd' is not constant. It means the sequence is not Arithmetic.

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_n}{a_{n-1}}$

$\frac{22}{12}=1.83333\dots ,\:\quad \frac{30}{22}=1.36363\dots ,\:\quad \frac{36}{30}=1.2,\:\quad \frac{41}{36}=1.13888\dots$

The ratio is not constant. It means the sequence is not Geometric.

From the above analysis, we determine that the sequence 12, 22, 30, 36, 41, … is neither arithmetic nor geometric.

8 0

3 years ago