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3 years ago

Choose the system of inequalities whose solution is represented by the graph.

Mathematics

1 answer:

Elena L [17]3 years ago

8 0

Answer:

-x + y > -4; x + y < 3 . . . . . last choice

Step-by-step explanation:

The boundary lines are both dashed, so there will be no "or equal to" as part of the inequality symbols (eliminates the second choice).

The downward sloping line has x- and y-intercepts that are both 3, so it will have the equation in intercept form ...

x/3 + y/3 = 1

Multiplying by 3 gives x+y=3. The shading is below it, so the inequality with that line as the boundary is ...

x + y < 3

This inequality is only part of the last choice.

The upward sloping line has x- and y- intercepts of 4 and -4, so its equation in intercept form is ...

x/4 + y/-4 = 1

Multiplying by -4 gives -x+y=-4. The shading is above it, so the inequality with that boundary line is ...

-x + y > -4

This inequality is included in the last choice.

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Identify the following sequences as arithmetic, geometric, or neither. For the arithmetic and geometric sequences, identify the

Lapatulllka [165]

Hence,

a. 12, 144, 1728,.. => Geometric

b. 0,5, 10, 15, 20, 25,... => Arithmetic

c. 0,4, 16, 36, 64,... => Neither arithmetic nor geometric

d. 1.5, 2.25, 3.375, 5.0625,... => Geometric

Step-by-step explanation:

In order to identify the sequence as geometric or arithmetic sequence, we find the common difference and common ratio of the sequence. If the common difference is same, it is an arithmetic sequence and if the common ratio is same the sequence is a geometric sequence

Common difference is the difference between consecutive terms of an arithmetic sequence and common ration is the ratio between two consecutive terms of a sequence

So,

a. 12, 144, 1728,..

Here,

$a_1=12\\a_2=144\\a_2=1728$

Common difference:

$d=a_2-a_1 = 144-12 = 132\\=a_3-a_2 = 1728-144=1584$

Common Ratio:

$r=\frac{a_2}{a_1} =\frac{144}{12} = 12\\=\frac{a_3}{a_2}=\frac{1728}{144} =12$

As the common ratio is same, the given sequence is a geometric sequence.

b. 0,5, 10, 15, 20, 25,...

Here,

$a_1 = 0\\a_2 =5\\a_3 =10$

Common difference:

$d=a_2-a_1 = 5-0 = 5\\d=a_3-a_2 = 10-5 = 5$

As the common difference is same, the given sequence is an arithmetic sequence

c. 0,4, 16, 36, 64,...

Here

$a_1 = 0\\a_2 =4\\a_3 = 16\\a_4 = 36$

Common Difference:

$d= a_2-a_1 = 4-0 = 4\\a_3-a_2 = 16-4 = 12$

Common Ratio:

$r=\frac{a_2}{a_1} = \frac{4}{0} = Doesn't\ exist$

Neither the common ratio nor common difference are same, so the given sequence is neither arithmetic nor geometric

d. 1.5, 2.25, 3.375, 5.0625,...

Here

$a_1 = 1.5\\a_2 = 2.25\\a_3 = 3.375$

Common Difference:

$d=a_2-a_1 = 2.25-1.5 = 0.75\\a_3-a_2 =3.375-2.25 = 1.125[/tex]Common Ratio: [tex]r=\frac{a_2}{a_1} = \frac{2.25}{1.5}=1.5\\=\frac{a_3}{a_2} =\frac{3.375}{2.25}=1.5$

As the common ratio is same, given sequence is geometric

Hence,

a. 12, 144, 1728,.. => Geometric

b. 0,5, 10, 15, 20, 25,... => Arithmetic

c. 0,4, 16, 36, 64,... => Neither arithmetic nor geometric

d. 1.5, 2.25, 3.375, 5.0625,... => Geometric

Keywords: Sequence, Ratio

Learn more about sequences at:

#LearnwithBrainly

4 0

3 years ago

Which of the following is a unit for area? ◦ m 3 ◦ inches ◦ feet ◦ cm 2

statuscvo [17]

Answer:

$\huge\boxed{Answer\hookleftarrow}$

⋆┈┈｡ﾟ❃ུ۪❀ུ۪❁ུ۪❃ུ۪❀ུ۪ﾟ｡┈┈⋆

6 0

3 years ago

Read 2 more answers

Multiply c by 9, then add 2 to the result

Novosadov [1.4K]

Answer:

9c+2

Step-by-step explanation:

6 0

3 years ago

Which ordered pair is a solution of the equation? 5x-2y=18

irakobra [83]

Answer:

(2, -4)

Step-by-step explanation:

I did some research.

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<Jayla>

3 0

3 years ago

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What fraction is equivalent to 30/360?

Firdavs [7]

Answer:

1/12

Step-by-step explanation:

Given that

30/360 to lowest fraction equivalent

Now, we can write 30 as 3×10

Also, we can write 360 as 36×10

Then, we have

(3×10)/(36×10)

Then, 10 cancel 10, we are left with

3/36

Also we can write 36 as 12×3

Then, we have

3/(12×3)

Also, 3 cancel 3, we are left with

1/12

Then the lowest fraction is 1 / 12

1/12

4 0

3 years ago

Read 2 more answers