What is the radical expression that is equivalent to the expression (35) 1/4
2 answers:
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Answer:
4 units wide
Step-by-step explanation:
Let the width of the table be 'w'
Given:
Perimeter of the table is,
The perimeter of the rectangular table is given as the sum of all the sides of the rectangle. The sides include two lengths and two widths.
Length of the table is 8 times longer than its width. Therefore,
Now, perimeter is given as:
Now, plug in 72 for 'P' and solve for 'w'. This gives,
So, the table is 4 units wide.
Answer:
C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.
Step-by-step explanation:
The Invertible matrix Theorem is a Theorem which gives a list of equivalent conditions for an n X n matrix to have an inverse. For the sake of this question, we would look at only the conditions needed to answer the question.
- There is an n×n matrix C such that CA=
.
- There is an n×n matrix D such that AD=
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix
- For each column vector b in
, the equation Ax=b has a unique solution.
- The columns of A span
Therefore the statement:
If there is an n X n matrix D such that AD=I, then there is also an n X n matrix C such that CA = I is true by the conditions for invertibility of matrix:
- The equation Ax=0 has only the trivial solution x=0.
- A is row-equivalent to the n×n identity matrix
The correct option is C.