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3 years ago

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Whats the definition of quadratic expression

1 answer:

pantera1 [17]3 years ago

8 0

A quadratic expression<span> is any mathematical </span>expression<span> whose power or degree is two. In other words, any </span>expression<span> that uses variables where the highest exponent or the </span>expression's<span> degree is two is a </span>quadratic expression<span>. The </span>expression<span> must have a power of two, no higher nor lower.</span>

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Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 3y 6212 3x + (x, y. z)

Gekata [30.6K]

Answer:

The solution of the system of linear equations is $x=3, y=4, z=1$

Step-by-step explanation:

We have the system of linear equations:

$2x+3y-6z=12\\x-2y+3z=-2\\3x+y=13$

Gauss-Jordan elimination method is the process of performing row operations to transform any matrix into reduced row-echelon form.

The first step is to transform the system of linear equations into the matrix form. A system of linear equations can be represented in matrix form (Ax=b) using a coefficient matrix (A), a variable matrix (x), and a constant matrix(b).

From the system of linear equations that we have, the coefficient matrix is

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

the variable matrix is

$\left[\begin{array}{c}x&y&z\end{array}\right]$

and the constant matrix is

$\left[\begin{array}{c}12&-2&13\end{array}\right]$

We also need the augmented matrix, this matrix is the result of joining the columns of the coefficient matrix and the constant matrix divided by a vertical bar, so

$\left[\begin{array}{ccc|c}2&3&-6&12\\1&-2&3&-2\\3&1&0&13\end{array}\right]$

To transform the augmented matrix to reduced row-echelon form we need to follow these row operations:

multiply the 1st row by 1/2

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\1&-2&3&-2\\3&1&0&13\end{array}\right]$

add -1 times the 1st row to the 2nd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\3&1&0&13\end{array}\right]$

add -3 times the 1st row to the 3rd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\0&-7/2&9&-5\end{array}\right]$

multiply the 2nd row by -2/7

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&-7/2&9&-5\end{array}\right]$

add 7/2 times the 2nd row to the 3rd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&3&3\end{array}\right]$

multiply the 3rd row by 1/3

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&1&1\end{array}\right]$

add 12/7 times the 3rd row to the 2nd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&0&4\\0&0&1&1\end{array}\right]$

add 3 times the 3rd row to the 1st row

$\left[\begin{array}{ccc|c}1&3/2&0&9\\0&1&0&4\\0&0&1&1\end{array}\right]$

add -3/2 times the 2nd row to the 1st row

$\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&4\\0&0&1&1\end{array}\right]$

From the reduced row echelon form we have that

$x=3\\y=4\\z=1$

Since every column in the coefficient part of the matrix has a leading entry that means our system has a unique solution.

7 0

3 years ago

Simplify the expression:<br> -1 + -1 + -3h + -8h

ValentinkaMS [17]

Answer:

-2 + 11h

Step-by-step explanation:

To simplify this equation, you can first combine like terms:

( -1 + -1 ) + ( -3h + -8h )

-2 + -11h

3 0

3 years ago

The measure of ZPQS is 180°. The measure of ZRQS is 30°.

Ray Of Light [21]

The measure of ZPQR is C. 150°

4 0

3 years ago

The ratio of red to green marbles is 3 to 2 there is 36 red marbles how many green marbles are there

nasty-shy [4]

Answer:

There are 24 green marbles.

Step-by-step explanation:

Let x be the number of green marbles, then:

3/2 = 36/x

3x = 2*36

3x = 72

x = 24.

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3 years ago

Solve this problem: 3(6 - 8)^2 + 8÷2<br><br> a- 8<br><br> b- 16<br><br> c- 28

zaharov [31]

The answer for 3(6-8)^2 + 8÷2 = 16 ☺

6 0

3 years ago