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2 years ago

State whether the system is consistent and independent, consistent and dependent or inconsistent.

Mathematics

2 answers:

user100 [1]2 years ago

7 0

Answer:

The correct option is 1.

Step-by-step explanation:

Inconsistent system: If the given system has no solutions, then it is an inconsistent system.

Consistent and independent system: If the given system has only one solutions, then it is an consistent and independent system.

Consistent and dependent system: If the given system has many solutions, then it is an consistent and dependent system.

The given equations are

$x+3y=18$ .... (1)

$-x+2y=7$ ..... (2)

Add both equations.

$x+3y-x+2y=18+7$

$5y=25$

$y=5$

Substitute this value in equation (1).

$x+3(5)=18$

$x+15=18$

$x=3$

The system of equations has only one solution, i.e.,(3,5).

Therefore the given system is consistent and independent. Option 1 is correct.

Archy [21]2 years ago

4 0

Answer:

Given system is consistent and independent.

Step-by-step explanation:

We have given two equations.

x+3y = 18 eq(1)

-x+2y = 7 eq(2)

We have to find whether the system is consistent, inconsistent and dependent or independent.

Consistent system has at least one solution.

Inconsistent system has no solution.

Dependent solution has identical lines.

Independent systems has different lines.

We use method of elimination to solve this.

Adding -3y to both sides of eq(1), we have

x+3y-3y = 18-3y

x = 18-3y eq(3)

put eq(3) into eq(2), we have

-(18-3y)+2y = 7

-18+3y+2y = 7

adding 18 to both sides of above equation , we have

18-18+3y+2y = 18+7

Adding like terms , we have

5y = 25

y = 5

Putting the value of y in eq(3), we have

x = 18-3(5)

x = 18-15

x = 3

Hence , the solution set is (3,5).

So, given system is consistent .

Their graphs are not same.so , their are independent.

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Answer:

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Step-by-step explanation:

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2 years ago

Factor the expression 2^2 +4-12

alekssr [168]

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2 years ago

(a) By inspection, find a particular solution of y'' + 2y = 14. yp(x) = (b) By inspection, find a particular solution of y'' + 2

SOVA2 [1]

Answer:

(a) The particular solution, y_p is 7

(b) y_p is -4x

(d) y_p is 8x + (7/2)

Step-by-step explanation:

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the nonhomogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the nonhomogeneus part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

y''_p = 0

Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

Therefore, the particular solution, y_p = A is 7

(b) y'' + 2y = −8x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x

2Ax + 2B = -8x

By inspection,

2B = 0 => B = 0

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x + 14

2Ax + 2B = -8x + 14

By inspection,

2B = 14 => B = 14/2 = 7

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x + 7

(d) Find a particular solution of y'' + 2y = 16x + 7

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

is 8x + (7/2)

8 0

2 years ago

Find the number that makes the ratio equivalent to 1:6.<br> 9:__

Anarel [89]

Answer: 54

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

Explanation:

The first ratio is 1:6. The jump from 1 to 6 has us multiplying the 1 by 6 to get 6.
1*6 = 6
So we follow the same rule of "multiply by 6" to go from 9 to 54 (9*6 = 54)

Or you can use a proportion to get
1/6 = 9/x
1*x = 6*9 ... cross multiply
x = 54
and we get the same answer

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2 years ago

These dot plots show the ages in years for sample of sea turtles and sample of koi fish

sineoko [7]

Answer:

B. Centers: the sea turtles have a greater median age than the koi

D. Spreads: the ages of the koi are more spread out

Step-by-step explanation:

The difference between the center and spread of the data distribution of koi and sea turtles as shown in the dot plots are as follows:

==>Median:

For Koi, the median value is the 14th value represented by the 14th dot on the plot, which is 30.

The median value for koi is between the 7th and the 8th value represented by dots on the plot. The average of both values will give us 55 as the median value for koi.

Therefore, the median age of sea turtle is greater than that of koi.

==>Spread:

Koi has a range of 45 (60-15), while sea turtles have a range of 20 (65-45). Invariably, mere looking at the dot plot, we can conclude that ages of the koi are more spread out.

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