How many 27 go into in 97

Suppose X and Y are non-empty sets. Which set contains more elements: X U Y or X ∩ Y? Explain.

katrin [286]

Answer:

The union of two sets is guaranteed to result in an equal or larger set than if they were intersected.

This only makes sense because intersecting sets is exceptional, only values that already exist in both sets are in the result. Whereas a union of two sets gives you all of the content of both.

The only time when an intersection is even equal to a union is when the two sets are identical. If they aren't then the intersection will be smaller.

4 0

3 years ago

Solve the system by finding the reduced row-echelon form of the augmented matrix.

Alex

Answer:

The reduced row-echelon form is

$\left[ \begin{array}{cccc} 1 & 0 & 6 & -10 \\\\ 0 & 1 & 2 & -3 \\\\ 0 & 0 & 0 & 0 \end{array} \right]$

The solutions to the system of equations are:

$y=-2z-3,\:x=-6z-10$

Step-by-step explanation:

To solve this system of linear equations,

$x-4y-2z=2\\2x-11y-10z=13\\-x+6y+6z=-8$

you must:

Step 1: Transform the augmented matrix to the reduced row echelon form.

In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.

This is the augmented matrix that represents the system.

$\left[ \begin{array}{cccc} 1 & -4 & -2 & 2 \\\\ 2 & -11 & -10 & 13 \\\\ -1 & 6 & 6 & -8 \end{array} \right]$

It can be transformed by a sequence of elementary row operations to the matrix.

There are three kinds of elementary matrix operations.

Interchange two rows (or columns).
Multiply each element in a row (or column) by a non-zero number.
Multiply a row (or column) by a non-zero number and add the result to another row (or column).

Using elementary matrix operations, we get that

Row Operation 1: add -2 times the 1st row to the 2nd row

Row Operation 2: add 1 times the 1st row to the 3rd row

Row Operation 3: multiply the 2nd row by -1/3

Row Operation 4: add -2 times the 2nd row to the 3rd row

Row Operation 5: add 4 times the 2nd row to the 1st row

$\left[ \begin{array}{cccc} 1 & 0 & 6 & -10 \\\\ 0 & 1 & 2 & -3 \\\\ 0 & 0 & 0 & 0 \end{array} \right]$

Step 2: Interpret the reduced row echelon form

The reduced row echelon form of the augmented matrix is

$\left[ \begin{array}{cccc} 1 & 0 & 6 & -10 \\\\ 0 & 1 & 2 & -3 \\\\ 0 & 0 & 0 & 0 \end{array} \right]$

which corresponds to the system

$x+6z=-10\\y+2z=-3\\0=0$

The system has infinitely many solutions.

$y=-2z-3,\:x=-6z-10$

4 0

4 years ago

A paralegal assistant processes 64 phone calls in 3 hours. what is the rate per hour?

mrs_skeptik [129]

64/3=x/1
easy, just divide
64/3=21 and 1/3 calls per hour

7 0

3 years ago

Use the line graph to solve. Between which two weeks did the water level decrease? A. week 0 and week 1 B. week 1 and week 2 C.

Vesna [10]

Answer:

C

Step-by-step explanation:

7 0

3 years ago

9. Consider the function, f(x) = x4 – 5x2 + 4. Select the statements that are true. In the box provided,

konstantin123 [22]

Answer:

the degree of the polynomial is 5

3 0

3 years ago