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NISA [10]
2 years ago
9

WILL GIVE BRAINLIEST(3x – 14) (2x + 10) Find the value of x.​

Mathematics
1 answer:
Brut [27]2 years ago
6 0

Answer:

(3x - 14) = (2x+ 10) { Because the angles are vertically opposite to each other}

3x-2x= 14+10

x=24

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Consider the transpose of Your matrix A, that is, the matrix whose first column is the first row of A, the second column is the
Zarrin [17]

Answer:The system could have no solution or n number of solution where n is the number of unknown in the n linear equations.

Step-by-step explanation:

To determine if solution exist or not, you test the equation for consistency.

A system is said to be consistent if the rank of a matrix (say B ) is equal to the rank of the matrix formed by adding the constant terms(in this case the zeros) as a third column to the matrix B.

Consider the following scenarios:

(1) For example:Given the matrix A=\left[\begin{array}{ccc}1&2\\3&4\end{array}\right], to transpose A, exchange rows with columns i.e take first column as first row and second column as second row as follows:

Let A transpose be B.

∵B=\left[\begin{array}{ccc}1&3\\2&4\end{array}\right]

the system Bx=0 can be represented in matrix form as:

\left[\begin{array}{ccc}1&3\\2&4\end{array}\right]\left[\begin{array}{ccc}x_{1} \\x_{2} \end{array}\right]=\left[\begin{array}{ccc}0\\0\end{array}\right] ................................eq(1)

Now, to determine the rank of B, we work the determinant of the maximum sub-square matrix of B. In this case, B is a 2 x 2 matrix, therefore, the maximum sub-square matrix of B is itself B. Hence,

|B|=(1*4)-(3*2)= 4-6 = -2 i.e, B is a non-singular matrix with rank of order (-2).

Again, adding the constant terms of equation 1(in this case zeros) as a third column to B, we have B_{0}:      

B_{0}=\left[\begin{array}{ccc}1&3&0\\4&2&0\end{array}\right]. The rank of B_{0} can be found by using the second column and third column pair as follows:

|B_{0}|=(3*0)-(0*2)=0 i.e, B_{0} is a singular matrix with rank of order 1.

Note: a matrix is singular if its determinant is = 0 and non-singular if it is \neq0.

Comparing the rank of both B and B_{0}, it is obvious that

Rank of B\neqRank of B_{0} since (-2)<1.

Therefore, we can conclude that equation(1) is <em>inconsistent and thus has no solution.     </em>

(2) If B=\left[\begin{array}{ccc}-4&5\\-8&10&\end{array}\right] is the transpose of matrix A=\left[\begin{array}{ccc}-4&-8\\5&10\end{array}\right], then

Then the equation Bx=0 is represented as:

\left[\begin{array}{ccc}-4&5\\-8&10&\end{array}\right]\left[\begin{array}{ccc}x_{1} \\x_{2} \end{array}\right]=\left[\begin{array}{ccc}0\\0\end{array}\right]..................................eq(2)

|B|= (-4*10)-(5*(-8))= -40+40 = 0  i.e B has a rank of order 1.

B_{0}=\left[\begin{array}{ccc}-4&5&0\\-8&10&0\end{array}\right],

|B_{0}|=(5*0)-(0*10)=0-0=0   i.e B_{0} has a rank of order 1.

we can therefor conclude that since

rank B=rank B_{0}=1,  equation(2) is <em>consistent</em> and has 2 solutions for the 2 unknown (X_{1} and X_{2}).

<u>Summary:</u>

  • Given an equation Bx=0, transform the set of linear equations into matrix form as shown in equations(1 and 2).
  • Determine the rank of both the coefficients matrix B and B_{0} which is formed by adding a column with the constant elements of the equation to the coefficient matrix.
  • If the rank of both matrix is same, then the equation is consistent and there exists n number of solutions(n is based on the number of unknown) but if they are not equal, then the equation is not consistent and there is no number of solution.
5 0
3 years ago
Which ordered pair is a solution of this equation? -6x + y = 35 Click on the correct answer. (-1,-7 (-6,-1) (-1,-6) (-7,-1)​
nikklg [1K]

Answer:

The ordered pair (-6, -1) is the only solution.

Step-by-step explanation:

-6x + y = 35

Let's plug in the points.

(-1, -7) --> -6(-1) - 7 = 6 - 7 = -1 which does not equal 35

(-6, -1) --> -6(-6) -1 = 35

(-1, -6) --> -6(-1) - 6 = 0 which does not equal 35

(-7, -1) --> -6(-7) - 1 = 41 which does not equal 35

8 0
2 years ago
I spent 3/4 of my money and then I spent 1/5 of what was left.
Kazeer [188]

(3/4)+(1/5(1/4)

As my thinking, this is the answer...

please click on the thanks button if this was helpful..

Have a great day!

4 0
3 years ago
How do i simplify -10x+10x
USPshnik [31]

Answer:

0

Step-by-step explanation:

when they have the same variable you can add them together. When adding 10x and --10x, the cancel out (negate) and you are left with 0

7 0
3 years ago
If SS= 162 from a sample of 15 data, find s^2
Genrish500 [490]

Answer:

11.57

Step-by-step explanation:

We have a simple formula to solve this:

s^2=\frac{SS}{n-1}

where

SS is sum of squares

s^2 is the variance, and

n is the number of data points

We are given all the info to find out s^2. Hence,

s^2=\frac{SS}{n-1}\\s^2=\frac{162}{15-1}\\s^2=\frac{162}{14}=11.57

8 0
3 years ago
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