What type of number is 90.65i?

If y varies directly as x, and y is 18 when x is 5, which expression can be used to find the value of y when x is 11?

Leokris [45]

Answer: The value of y is 39.6 when x = 11 and the required expression is y(11) = 39.6

Step-by-step explanation:

Since we have given that

y varies directly as x.

If y = 18, when x = 5.

So, we need to find the value of y when x is 11.

According to question, we get that

$\dfrac{y}{x}=\dfrac{18}{5}=\dfrac{y}{11}\\\\18\times 11=5y\\\\198=5y\\\\\dfrac{198}{5}=y\\\\y=39.6$

Hence, the value of y is 39.6 when x = 11 and the required expression is y(11) = 39.6

5 0

3 years ago

Use Gaussian elimination to write each system in triangular form

Feliz [49]

Answer:

To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is $x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

Step-by-step explanation:

Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:

Swapping two rows
Multiplying a row by a nonzero number
Adding a multiple of one row to another row

To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:

$\left[\begin{array}{cccc|c}1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & -1 & -1 \\-1 & 1 & 1 & 2 & 2 \\1 & 2 & -1 & 1 & 0\end{array}\right]$

For this matrix we need to perform the following row operations:

$R_2 - 1 R_1 \rightarrow R_2$ (multiply 1 row by 1 and subtract it from 2 row)
$R_3 + 1 R_1 \rightarrow R_3$ (multiply 1 row by 1 and add it to 3 row)
$R_4 - 1 R_1 \rightarrow R_4$ (multiply 1 row by 1 and subtract it from 4 row)

$R_2 \leftrightarrow R_3$ (interchange the 2 and 3 rows)

$R_2 / 2 \rightarrow R_2$ (divide the 2 row by 2)
$R_1 - 1 R_2 \rightarrow R_1$ (multiply 2 row by 1 and subtract it from 1 row)
$R_4 - 1 R_2 \rightarrow R_4$ (multiply 2 row by 1 and subtract it from 4 row)
$R_3 \cdot ( -1) \rightarrow R_3$ (multiply the 3 row by -1)
$R_2 - 1 R_3 \rightarrow R_2$ (multiply 3 row by 1 and subtract it from 2 row)
$R_4 + 3 R_3 \rightarrow R_4$ (multiply 3 row by 3 and add it to 4 row)
$R_4 / 4.5 \rightarrow R_4$ (divide the 4 row by 4.5)

After this step, the system has an upper triangular form

The triangular matrix looks like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & -0.5 & -0.5 \\0 & 1 & 0 & -0.5 & -0.5\\0 & 0 & 1 & 2 & 2 \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

If you later perform the following operations you can find the solution to the system.

$R_1 + 0.5 R_4 \rightarrow R_1$ (multiply 4 row by 0.5 and add it to 1 row)
$R_2 + 0.5 R_4 \rightarrow R_2$ (multiply 4 row by 0.5 and add it to 2 row)
$R_3 - 2 R_4 \rightarrow R_3$ (multiply 4 row by 2 and subtract it from 3 row)

After this operations, the matrix should look like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & 0 & -\frac{1}{9} \\0 & 1 & 0 & 0 & -\frac{1}{9}\\0 & 0 & 1 & 0 & \frac{4}{9} \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

Thus, the solution is:

$x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

7 0

3 years ago

What is the range of the function in the graph?

Verdich [7]

The range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.

<h3>What is the Range and Domain of a Function?</h3>

All the possible set of x-values that are plotted on the horizontal axis (x-axis) are the domain of a function. In order words, they are the inputs of the function.

On the other hand, all the corresponding set of x-values that are plotted on the vertical axis (y-axis) are the range of a function. In order words, they are the outputs of the function.

In the graph given below that shows a function, s is plotted on the vertical axis (y-axis), and its values starts from 20, up to 100. The range can be said to be all values of s that are from 20 to 100.

Therefore, the range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.

Learn more about functions on:

brainly.com/question/15602982

#SPJ1

3 0

2 years ago

22broccy-here you go g-<br> what is the sum of negative two squared plus one?

yaroslaw [1]

Answer:

The sum is equal to 5

Step-by-step explanation:

we know that