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2 years ago

5

How many three-letter "words" can Bob make using just these letters?

1 answer:

alekssr [168]2 years ago

4 0

Answer:

two

Step-by-step explanation:

the two "words" Bob can make using the three letters t, o, and a are;

oat and tao

hope this helps

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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

For what x-value(s) does sin(x) = -1?

poizon [28]

sin (x) = -1

arcsin (-1) = x

x = -90

and multiples of 360

x =-90, 270,....

x =-90 + 360n where n is an integer

or in radians

-pi/2 + 2*pi *n where n is an integer

6 0

3 years ago

Find the missing side of this right

Delvig [45]

Answer:

19is the answer I think so please check it iam sorry

6 0

3 years ago

Read 2 more answers

Assume that lines that appear to be tangent are tangent. O is the center of the circle. In degrees, what is the value of x?

Nastasia [14]

9514 1404 393

Answer:

145

Step-by-step explanation:

In this geometry, the central angle (x°) and the external angle (35°) are supplementary.

x° = 180° -35°

x = 145

4 0

3 years ago

Let f(x) = x^3-3x^2+2 and g(x) = x^2 -6x+11 Enter the value of x such that f(x)=g(x)

Licemer1 [7]

The value of x such that f(x) = g(x) is x = 3

<h3>Quadratic equation</h3>

Given the following expressions as shown

f(x) = x^3-3x^2+2 and;

g(x) = x^2 -6x+11

Equate the expressions

x^3-3x^2+2 = x^2 -6x+11

Equate to zero

x^3-3x^2-x^2+2-11 = 0

x^3-3x^2-x^2 + 6x - 9 = 0

x^3-4x^2+6x-9 = 0

Factorize

On factorizing the value of x = 3

Hence the value of x such that f(x) = g(x) is x = 3

Learn more on polynomial here: brainly.com/question/2833285

#SPJ1

7 0

2 years ago