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castortr0y [4]
3 years ago
15

100 Points! What are the classifications of each system?

Mathematics
1 answer:
alexdok [17]3 years ago
4 0

Answer:

Part 1) Is a inconsistent system

Part 2) Is a consistent independent system

Part 3) Is a consistent dependent system

see the attached figure

Step-by-step explanation:

we know that

If a system has at least one solution, it is said to be consistent .  

If a consistent system has exactly one solution, it is independent .  

If a consistent system has an infinite number of solutions, it is dependent

If a system not have solution, it is said to be inconsistent

Part 1) we have

x+5y=-2\\x+5y=4

This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept

so

The lines don't intersect

The system has no solution

therefore

Is a inconsistent system

Part 2) we have

y=3x+4\\-2x+y=4

we know that

If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution

In this problem, the lines have different slopes (m=3 and m=2)

so

The lines intersect at one point

The system has one solution

therefore

Is a consistent independent system

Part 3) we have

3x+y=4 ----> equation A

-6x-2y=-8 ----> equation B

Multiply equation A by -2 both sides

-2(3x+y)=-2(4)

-6x-2y=-8 ----> equation C

Compare equation B and equation C

Are identical lines

so

The system has infinity solutions

therefore

Is a consistent dependent system

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Given: △ABC; AB=BC, m∠BDA = 60°, BD=4 cm, BD ⊥ BA . Find: DC, AC.
vekshin1

Answer:

DC = 10.93 cm ,  AC = 9.8 cm

Step-by-step explanation:

From trigonometry;

⇒ Tan 60 = AB/BD

⇒AB = BD Tan 60 ( where BD = 4 cm )

⇒ AB = 6.93 cm

Also, AB=BC , therefore;

⇒ BC = 6.93 cm

⇒ Cos 60 = BD/AD

⇒ AD = BD/ Cos 60 = 4/Cos 60

⇒ AD = 8 cm

From Pythagoras theorem;

⇒ AC^{2} = AB^{2} + BC^{2} = (6.93)^{2} + (6.93)^{2}

⇒ AC = \sqrt{96.05} = 9.80 cm

⇒ DC = BD + BC = 4 + 6.93

⇒ DC = 10.93 cm

8 0
3 years ago
During science class,jimmy heated a substance and recorded the temperature of the substance over several minutes. He used the da
Elenna [48]

It’s -18 that’s the answer

8 0
2 years ago
Value of x for 12(x-2)+3x=1/2(x+6)+2​
Damm [24]

Answer:

The value of x = 2

Step-by-step explanation:

Given the equation

12\left(x-2\right)+3x=\frac{1}{2}\left(x+6\right)+2

  • Expand 12(x-2) = 12x - 24
  • Expand 1/2(x+6) = 1/2x + 3

so the equation becomes

12x-24+3x=\frac{1}{2}x+3+2

simplifying

15x-24=\frac{1}{2}x+5

15x=\frac{1}{2}x+29

multiplying both sides by 2

30x = x + 58

subtracting x from both sides

30x - x = 58 - x

29x = 58

divide both sides by 29

\frac{29x}{29}=\frac{58}{29}

simplifying

x = 2

Therefore, the value of x = 2

4 0
2 years ago
Drag each sequence to show whether it is a linear function, an exponential function, or
Sergeu [11.5K]

Answer:

Step-by-step explanation:

From the picture attached,

Option A

From the given table,

Ratio of the 2nd value and 1st value = \frac{8}{4}=2

Ratio of 3rd value and 2nd value = \frac{16}{8}=2

There is a common ratio of 2.

Therefore, the given table will represent an exponential function.

Option B

Given recursive formula of the sequence is,

A_1=3

A_n=5.A_{n-1}

From this recursive formula sequence will be,

3, 15, 75, 375,.......

Therefore, it's an exponential function.

Option C

F_n=3n+17

Given function is in the form of a linear function (y = mx + b),

Therefore, it's a linear function.

Option D

From the given table,

Difference between 2nd value to the 1st value = 8 - 4 = 4

Difference between 3rd value to the 2nd value = 12 - 8 = 4

Therefore, there is a common difference of 4 in each successive term to the previous term.

Hence, the given table represents a linear function.

7 0
3 years ago
Read 2 more answers
Sofia is saving fan an Iphone. She starts off with $50 that her parents gave her. She plans to deposit $30 per month from her pa
Klio2033 [76]
Y=30x+50
y is the total amount saved
x is the amount of months she deposited 30 dollars
30 is the amount she’s depositing
50 is the initial amount or the constant
8 0
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