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2 years ago

Which of the following is a solution to the following system of inequalities let the green region represents the answer region

Mathematics

1 answer:

Fofino [41]2 years ago

8 0

The given inequalities are

x+2y≤4, 3x-y>2

To plot the graph first convert it into slope intercept form in two coordinate system i.e To convert equation of the type Ax + By= C in Slope intercept form

x/C÷A + y/C÷B =1

So,the equation becomes

x/4 + y/2≤ 1,

x/2÷3 + y/-2>1,

We have to also consider x>0 and y>0.

Now The shaded area in green is shown in the graph.

x=8/7 and y=20/7 is the point of intersection of lines

A triangular region is formed having vertices (0,0) (4,0) and (8/7,20/7) is the required solution.

You might be interested in

Parallelogram ABCD is shown.<br>

hichkok12 [17]

Answer:

Step-by-step explanation:

#4 part A= D

#4 part B = 76

Your question only states parrallelogram ABCD is shown, so I assume you only wanted those answers, GL

3 0

1 year ago

Which explains whether or not the function represents a direct variation?

s2008m [1.1K]

Answer:

The function represents a direct variation

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a linear direct variation the line passes through the origin and the constant of proportionality k is equal to the slope m

Let

$A(0,0)$ ------> the line passes through the origin

$B(2,10)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=10/2=5$

$C(4,20)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=20/4=5$

$D(6,30)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=30/6=5$

$E(8,40)$

Find the value of k------> substitute the value of x and y

$y/x=k$ -----> $k=40/8=5$

The value of k is equal in all the points of the table and the line passes through the origin

therefore

The function represents a direct variation

the equation of the direct variation is equal to

$f(x)=5x$

4 0

2 years ago

Read 2 more answers

Maggie's brother is 4 years younger than three times her age. The sum of their ages is 16.

bearhunter [10]

Answer:

Maggie is 5 years old

Step-by-step explanation:

3M-4+M=16

add 4 to both sides

4M=20

Divide both sides by 4

20/4 = 5

M/Maggie is 5

7 0

3 years ago

Câu 99: Cho hàm số f x  xác định trên ℝ , bảng biến thiên của hàm số f x   như sau.

OLga [1]

Answer:

i doesn,t understand this language

4 0

2 years ago

Find all solutions of the given system of equations (If the system is infinite many solution, express your answer in terms of x)

lisov135 [29]

Answer:

(a) The system of the equations $\left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right.$ has no solution.

(b) The system of the equations $\left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right.$ has many solutions $y=\frac{2x}{3}-\frac{5}{3}$

Step-by-step explanation:

(a) To find the solutions of the following system of equations $\left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right.$ you must:

Multiply $2x-3y=3$ by 2:

$\begin{bmatrix}4x-6y=6\\ 4x-6y=3\end{bmatrix}$

Subtract the equations

$4x-6y=3\\-\\4x-6y=6\\------\\0=-3$

0 = -3 is false, therefore the system of the equations has no solution.

(b) To find the solutions of the system $\left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right.$ you must:

Isolate x for $4x-6y=10$

$x=\frac{5+3y}{2}$

Substitute $x=\frac{5+3y}{2}$ into the second equation

$16\cdot \frac{5+3y}{2}-24y=40\\8\left(3y+5\right)-24y=40\\24y+40-24y=40\\40=40$

The system has many solutions.

Isolate y for $4x-6y=10$

$y=\frac{2x}{3}-\frac{5}{3}$

3 0

2 years ago