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3 years ago

Which graph represents the solution set of the system of inequalities? {y≤2x+1y>−2x−3

Mathematics

1 answer:

d1i1m1o1n [39]3 years ago

3 0

we have

------> inequality A

The solution of the inequality A is the shaded area below the solid red line

see the attached figure N

------> inequality B

The solution of the inequality B is the shaded area above the dotted blue line

see the attached figure N

therefore

The solution of the system of inequalities is the shaded area between the solid red line and the dotted blue line

see the attached figure N

therefore

the answer in the attached figure N

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Can you tell me how to calculate R for below Matrix ?

scoray [572]

Answer:

The rank of the matrix is 3.

Step-by-step explanation:

Consider the prided information.

$x=\begin{bmatrix}x_1\\ x_2\\ x_3\end{bmatrix}=\begin{bmatrix}9&2&6&5&8\\ 12&8&6&4&10\\ 3&4&0&2&1\end{bmatrix}$

Reduce the matrix in row echelon form as shown:

$R_1\:\leftrightarrow \:R_2\begin{bmatrix}12&8&6&4&10\\ 9&2&6&5&8\\ 3&4&0&2&1\end{bmatrix}\\$

$R_2\:\leftarrow \:R_2-\frac{3}{4}\cdot \:R_1\ and\ R_3\:\leftarrow \:R_3-\frac{1}{4}\cdot \:R_1\\\\\begin{bmatrix}12&8&6&4&10\\ 0&-4&\frac{3}{2}&2&\frac{1}{2}\\ 0&2&-\frac{3}{2}&1&-\frac{3}{2}\end{bmatrix}$

$R_3\:\leftarrow \:R_3+\frac{1}{2}\cdot \:R_2\\\begin{bmatrix}12&8&6&4&10\\ 0&-4&\frac{3}{2}&2&\frac{1}{2}\\ 0&0&-\frac{3}{4}&2&-\frac{5}{4}\end{bmatrix}$

$R_2\:\leftarrow \:R_2-\frac{3}{2}\cdot \:R_3\ and\ R_1\:\leftarrow \:R_1-6\cdot \:R_3\\\begin{bmatrix}12&8&0&20&0\\ 0&-4&0&6&-2\\ 0&0&1&-\frac{8}{3}&\frac{5}{3}\end{bmatrix}\\R_2\:\leftarrow \:-\frac{1}{4}\cdot \:R_2\ , \ R_1\:\leftarrow \:R_1-8\cdot \:R_2\ and\ \:R_1\:\leftarrow \frac{1}{12}\cdot \:R_1\\\begin{bmatrix}1&0&0&\frac{8}{3}&-\frac{1}{3}\\ 0&1&0&-\frac{3}{2}&\frac{1}{2}\\ 0&0&1&-\frac{8}{3}&\frac{5}{3}\end{bmatrix}$

The rank of a matrix is the number of non zeros rows.

Thus, the rank of the matrix is 3.

6 0

3 years ago

Answer it plssss........

AleksandrR [38]

Answer:

Step-by-step explanation:

Because x has the degree one and it’s figure at the numerator

4 0

3 years ago

Can you guys help?<br> Need to find x, BA, DA

7nadin3 [17]

Answer:

x=2,BA=DA which is7

Step-by-step explanation:

5x-3=3x+1

both sides share an angle and B=D right angles

5x-3x=1+3

2x=4

x=4÷2

x=2

BA=5x-3

BA=5(2)-3

BA=10-3

BA=7

DA=3x+1

DA=3(2)+1

DA=6+1

DA=7

4 0

3 years ago

For a quantitative variable in a particular population, how many different sample means are there?.

gladu [14]

A quantitative variable is a variable that can be measured i.e. quantified

There can be many sample means as possible

<h3>How to determine the number of samples</h3>

From the question, we understand that the variable is a quantitative variable

This means that the variable can be measured.

When a variable can be measured, there can be many sample means

Hence, the number of sample means is many