PLEASE HELPPP.

Mathematics

1 answer:

Lelechka [254]3 years ago

4 0

Answer:In the graph you need to use quradrant 4

Step-by-step explanation:

no need

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Is ( 0,0) a solution to this system? y<=x^2-4 y>2x-1?

Xelga [282]

Answer:

The point $(0,0)$ is not a solution of the system of inequalities

Step-by-step explanation:

we have

$y\leq x^{2} -4$ -----> inequality A

$y> 2x-1$ -----> inequality B

we know that

If a ordered pair is a solution of the system of inequalities

then

the ordered pair must be satisfy the inequalities of the system

Verify

For $x=0, y=0$

substitute the value of x and the value of y in the inequalkity A and in the inequality B

Inequality A

$0\leq 0^{2} -4$

$0\leq -4$ -------> is not true

therefore

The point $(0,0)$ is not a solution of the system of inequalities

3 0

3 years ago

Read 2 more answers

Create a matrix for this system of linear equations, The determinant of the coefficient matrix is

marin [14]

Answer: The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.

Step-by-step explanation: The given system of linear equations is :

$2x+y+3z=13~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+2y=11~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\3x+z=10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.

The determinant of the co-efficient matrix is given by

$D=\begin{vmatrix}2 & 1 & 3\\ 1 & 2 & 0\\ 3 & 0 & 1\end{vmatrix}=2(2-0)+1(0-1)+3(0-6)=4-1-18=-15.$

Now, from equations (ii) and (iii), we have

$x+2y=11~~~~~\Rightarrow y=\dfrac{11-x}{2}~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\\\\\\3x+z=10~~~~~~\Rightarrow z=10-3x~~~~~~~~~~~~~~~~~~~~~~~~~(v)$

Substituting the value of y and z from equations (iv) and (v) in equation (i), we get

$2x+y+3z=13\\\\\Rightarrow 2x+\dfrac{11-x}{2}+3(10-3x)=13\\\\\Rightarrow 4x+11-x+60-18x=26\\\\\Rightarrow -15x+71=26\\\\\Rightarrow -15x=26-71\\\\\Rightarrow -15x=-45\\\\\Rightarrow x=3.$