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borishaifa [10]
3 years ago
10

Write the next five numbers in each sequence,

Mathematics
1 answer:
DIA [1.3K]3 years ago
3 0

Answer:

SOLUTION

First, we write the augmented matrix.

⎡

⎢

⎣

1

−

1

1

2

3

−

1

3

−

2

−

9

 

|

 

8

−

2

9

⎤

⎥

⎦

Next, we perform row operations to obtain row-echelon form.

−

2

R

1

+

R

2

=

R

2

→

⎡

⎢

⎣

1

−

1

1

0

5

−

3

3

−

2

−

9

|

8

−

18

9

⎤

⎥

⎦

−

3

R

1

+

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

5

−

3

0

1

−

12

|

8

−

18

−

15

⎤

⎥

⎦

The easiest way to obtain a 1 in row 2 of column 1 is to interchange \displaystyle {R}_{2}R

​2

​​  and \displaystyle {R}_{3}R

​3

​​ .

Interchange

R

2

and

R

3

→

⎡

⎢

⎣

1

−

1

1

8

0

1

−

12

−

15

0

5

−

3

−

18

⎤

⎥

⎦

Then

−

5

R

2

+

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

1

−

12

0

0

57

|

8

−

15

57

⎤

⎥

⎦

−

1

57

R

3

=

R

3

→

⎡

⎢

⎣

1

−

1

1

0

1

−

12

0

0

1

|

8

−

15

1

⎤

⎥

⎦

The last matrix represents the equivalent system.

 

x

−

y

+

z

=

8

 

y

−

12

z

=

−

15

 

z

=

1

Using back-substitution, we obtain the solution as \displaystyle \left(4,-3,1\right)(4,−3,1).

Step-by-step explanation:

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nikdorinn [45]

Answer:

The two numbers are -365 and -1825.

Step-by-step explanation:

5x=y

x-y=1460

--------------

x-5x=1460

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x=1460/-4

x=-365

-365-y=1460

y=-365-1460=-1825

8 0
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Katie wants to collect over 100100100 seashells. She already has 343434 seashells in her collection. Each day, she finds 121212
Elden [556K]

Katie wants to collect over 100 seashells. She already has 34 seashells in her collection. Each day, she finds 12 more seashells on the beach. Katie can use fractions of days to find seashells.

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<em><u>Answer:</u></em>

Kathie needs more than 5 days to get over 100 shells

The required inequality is 34 + 12d > 100

<em><u>Solution:</u></em>

Given that,

Katie wants to collect over 100 seashells.

She already has 34 seashells in her collection.

Each day, she finds 12 more seashells on the beach

Let "d" be the number of days she takes to cover 100 sea shells

From given statement,

She finds 12 seashells each day

Then for "d" days, the number of sea shells she collected is 12d

She already had = 34

So, the equation can be framed as:

34 + 12d > 100

Here we used "greater than" symbol, since she wants to collect over 100 seashells

Solve the inequality

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8 0
3 years ago
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What is the common factor of each term in the expression 2b+5b?
S_A_V [24]
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5 0
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If f(1) = 160 and f(n+ 1) = -2f(n), what is f(4)?
sertanlavr [38]
F(1) = 160 is given to us. We'll use it to find f(2)
f(n+1) = -2*f(n)
f(1+1) = -2*f(1) ... replace every n with 1
f(1+1) = -2*160 ... replace f(1) with 160
f(2) = -320

Now use f(2) to find f(3)
f(n+1) = -2*f(n)
f(2+1) = -2*f(2) ... replace every n with 2
f(3) = -2*(-320) ... replace f(2) with -320
f(3) = 640

Finally, use f(3) to find f(4)
f(n+1) = -2*f(n)
f(3+1) = -2*f(3) ... replace every n with 3
f(4) = -2*640 ... replace f(3) with 640
f(4) = -1280

Final Answer: -1280

7 0
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