4.06 Question 9
Choose the graph that represents the following system of inequalities:

y ≤ −3x + 1
y ≤ 1 over 2x + 3

In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.

Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line.

Graph of two lines intersecting lines. Both lines are solid. One line g of x passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded above the line.

Graph of two intersecting lines. Both lines are solid. One line passes g of x through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded below the line.

Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded below the line.

Question

02-11-2021
Mathematics

Answered

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4.06 Question 9
Choose the graph that represents the following system of inequalities:

y ≤ −3x + 1
y ≤ 1 over 2x + 3

In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.

Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line.

Graph of two lines intersecting lines. Both lines are solid. One line g of x passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded above the line.

Graph of two intersecting lines. Both lines are solid. One line passes g of x through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded below the line.

Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded below the line.

Sagot :

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IIitzAryanII IIitzAryanII · Answer 1 · 2021-11-02T21:35:48-04:00

Answer:

we have

[tex]\begin{gathered} y \geq -3x + 1 \\ \\ y \leq \frac{1}{2} x+3 \end{gathered}[/tex]

using a graph tool

see the attached figure

The solution of the system is the shaded area

we know that

The line is solid

The line passes through points (0,1) and is shaded above the line.

[tex]y \leq \frac{1}{2} x+3[/tex]

The line is solid

The line passes through points (-2,2) and (0,3)and is shaded below the line

The two lines intersect at one point

therefore the answer is the option

B) Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.

[tex]{\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt}{\red{\rule{100pt}{5pt}{\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt} }}}}}}}}}}[/tex][tex]{\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt}{\red{\rule{100pt}{5pt}{\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt} }}}}}}}}}}[/tex][tex]{\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt}{\red{\rule{100pt}{5pt}{\blue{\rule{25pt}{1pt}{\pink{\rule{30pt}{3pt} }}}}}}}}}}[/tex]

Sagot :

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