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Airida [17]
3 years ago
6

Which of these rational numbers is also an integer? A. 2/4 B. 0.24 C. 4/2 D. 2.4

Mathematics
2 answers:
AnnyKZ [126]3 years ago
8 0
Answer is C. bottom left

4/2 : rational
4/2 = 2 : integer
Kryger [21]3 years ago
6 0
When you simplify 4/2 you get 2, 2 is an integer.
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Which transformation shows a translation of 3 units to the right?<br> A)A<br> B)С<br> C)B<br> D)D
Citrus2011 [14]

Answer:

Step-by-step explanation: It`s option  C

4 0
3 years ago
45-2x(15-3) I need help finding out the answer to this problem because the answer I got I think it is wrong
gizmo_the_mogwai [7]
45 - 2*(12)
45 - 24
21

Hope this helps!
6 0
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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 proportion could be used to solve
Brums [2.3K]

Answer:

Cups of carrot needed for 9 servings = 4.5 cups

Step-by-step explanation:

A recipe for sesame chicken calls for cup of chopped carrots

recipe 2 is for 4 servings

That is

2 cups of carrot = 4 servings

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Let x= number of carrot needed for 9 servings

1 : 2 = x : 9

1 /2 = x/ 9

Cross product

1*9 = 2*x

9=2x

Divide both sides by 2

9/2 = x

x= 4.5 Or 4 1/2

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3 years ago
Find the indicated term of the given arithmetic sequence. a1 = 115, d = 8, n = 14
olya-2409 [2.1K]
I took the same test and I put the answer D. 1487 and I got it wrong. The correct answer was 
A.3
3 0
2 years ago
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