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labwork [276]
3 years ago
5

Solve the system, please show each step.

Mathematics
2 answers:
Alekssandra [29.7K]3 years ago
8 0

Answer:

The given equations are

x + y + z = -4


-x + 2 y + 3 z = 3


x - 4 y - 2 z = -15

Writing in matrix form

A=   1     1      1             X=   x       B=   -4

     -1     2     3                    y               3            ⇒A,X,B are in matrix form.

       1     -4    -2                   z              -15

i.e  Ax=B

x =A^{-1}B

but ,A^{-1}=Adj.(A)/Determinant A

Determinant of A= 1(-4+12) -1(2-3)+1(4-2)=8+1+2=11

To find Adjoint of matrix A, we will find the cofactor of A and then it's transpose.

a_{11}=-4+12=8, a_{12}=-[2-3]=1,

,a_{13}=4-2=2,\\,a_{21}=-[-2+4]=-2\\,a_{22}=-2-1=-3,\\a_{23}=-[-4-1]=5,\\a_{31}=[3-2]=1\\,a_{32}=-[3+1]=-4\\,a_{33}=2+1=3

Now taking cofactor, and getting the adjoint

Adjoint (A)= 8     -2       1

                     1      - 3       -4

                     2       5         3

Adjoint(A). B=  -53

                        47

                         -38


\frac{Adjoint (A)\times B}{Determinant A} =   -53/11

                                                                                        47/11

                                                                                         -38/11

So, solution set is , x=-53/11, y=47/11, z=-38/11



Arlecino [84]3 years ago
3 0

Answer: The solution of the system of equations is x=\frac{-53}{11}, y=\frac{47}{11} and z=\frac{-38}{11}.

Explanation:

The given equations are,

x+y+z=-4            ..... (1)

-x+2y+3z=3         ..... (2)

x-4y-2z=-15        ...... (3)

From equation we get,

x=-4-y-z

Put this value in equation (4) and (5).

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

3y+4z=-1     .... (4)

(-4-y-z)-4y-2z=-15

-5y-3z=-11  .....(5)

Use elimination method to solve the equations (4) and (5).

Multiply equation (4) by 3 and equation (5) by 4, then add both equations as shown in figure,

-11y=-47

y=\frac{47}{11}

Put this value in equation (4).

3(\frac{47}{11})+4z=-1

4z=-1-\frac{141}{11}

4z=\frac{-11-141}{11}

z=\frac{-152}{11\times 4}

z=\frac{-38}{11}

Put y=\frac{47}{11} and z=\frac{-38}{11} in equation (1).

x+\frac{47}{11}+\frac{-38}{11}=-4

x+\frac{9}{11}=-4

x=\frac{-44-9}{11}

x=\frac{-53}{11}

Therefore, the The solution of the system of equations is x=\frac{-53}{11}, y=\frac{47}{11} and z=\frac{-38}{11}.

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VMariaS [17]

The <em>correct answer</em> is:

16√13.

Explanation:

The perimeter of a figure is found by adding together the lengths of all of the sides. The side lengths of this garden are: √13, √13, 7√13 and 7√13. This is because opposite sides in a rectangle are congruent.

Adding these together we have:

√13+√13+7√13+7√13 = (1+1+7+7)√13 = 16√13

7 0
3 years ago
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HELP
Brut [27]

Answer:

1) m<1 = 25

2) m<4 = 155

3) m< 5 = 25

4) m<7 = 25

5) 110

6) 30.5

7) 74

Step-by-step explanation:

1)

x + 155 = 180

x = 25

2)

<4 = 155 because of vertical angle thm

3)

<5 = 25 (congruent to <1) b/c of corresponding angles thm

4)

<7 = <5 (25) because of vertical angles thm

5)

5x + 15 = 8x - 42

-3x = -57

x = 19

5(x) + 15

5(19) + 15 = 110

6)

180 - 110 = 70

3x + x + 4 + 70 = 180

4x + 74 = 180

4x = 106

x = 26.5

x+ 4 = 30.5

7)

180 - 115 = 65

x + 4 + 2x + 65 = 180

3x + 69 = 180

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4 0
2 years ago
Choose the symbol that correctly compares the fractions below . 1/5 ? 4/5
icang [17]

Answer:

c

Step-by-step explanation:

4/5 is greater than 1/5

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Need help with this asap!
Brums [2.3K]

Answer:

The answer to your question is   b = 8.06 cm

Step-by-step explanation:

Data

hypotenuse = c = 9 cm

long leg = b = ?

short leg = a = 4 cm

Process

This is a right triangle so we must use the Pythagorean theorem to find the length of the long leg (b)

                      c² = a² + b²

-Solve for b²

                      b² = c² - a²

-Substitution

                      b² = 9² - 4²

-Simplification

                       b² = 81 - 16

                       b² = 65

-Result

                      b = 8.06 cm

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A large school district in southern California asked all of its eighth-graders to measure the length of their right foot at the
Ber [7]

Answer:

The probability of the sample mean foot length less than 23 cm is 0.120

Step-by-step explanation:

* Lets explain the information in the problem

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- The foot length is approximately Normally distributed, with a mean of

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- The rule to find σx is σx = σ/√n

∵ σ = 1.7 and n = 25

∴ σx = 1.7/√25 = 1.7/5 = 0.34

- Now lets find the z-score using the rule z-score = (x - μ)/σx

∵ x = 23 , μ = 23.4 , σx = 0.34

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- Use the table of the normal distribution to find P(x < 23)

- We will search in the raw of -1.1 and look to the column of 0.08

∴ P(X < 23) = 0.119 ≅ 0.120

* The probability of the sample mean foot length less than 23 cm is 0.120

4 0
3 years ago
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