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Elis [28]
3 years ago
6

Which number completes the system of linear inequalities represented by the graph?

Mathematics
2 answers:
madam [21]3 years ago
6 0

we have

y \geq2x-2 ------> inequality A

The inequality A is the solid red line in the graph

the solution of the inequality A is the shaded area above the solid red line

x+4y \geq ? ------> inequality B

The inequality B is the solid blue line in the graph

the solution of the inequality B is the shaded area above the solid blue line

we know that

the point (0,-3) lie on the line of the inequality B

substitute the values of x and y in the equation of the line

x+4y = c

0+4*(-3) =c

c=-12

so

the equation of the line B is

x+4y =-12

the equation of the inequality B is

x+4y \geq -12

therefore

<u>the answer is</u>

The number is -12

Mekhanik [1.2K]3 years ago
4 0

The number is \boxed{-12} in the inequality \boxed{x+4y\geqslant -12}.

Further explanation:

The linear equation with slope m and intercept c is given as follows.

\boxed{y=mx+c}

The formula for slope of line with points \left({{x_1},{y_1}}\right) and \left({{x_2},{y_2}}\right) can be expressed as,

\boxed{m=\frac{{{y_2}-{y_1}}}{{{x_2}-{x_1}}}}

Explanation:

The orange line intersects y-axis at \left({0,-2}\right), therefore the y-intercept is -2.

The orange line intersect the points that are \left({1,0}\right) and \left({0,-2}\right).

The slope of the line can be obtained as follows.

\begin{aligned}m&=\frac{{-2-0}}{{0-\left(1\right)}}\\&=\frac{{-2}}{{-1}}\\&=2\\\end{aligned}

The slope of the line is m = 2.

Therefore, the orange line is y\geqslant 2x-2.

The blue line intersects y-axis at \left({0,-3}\right), therefore the y-intercept is -3.

The blue line intersect the points that are \left({-4,-2}\right) and \left({0,-3}\right).

The slope of the line can be obtained as follows.

\begin{aligned}m&=\frac{{-3-\left({-2}\right)}}{{0-\left({-4}\right)}}\\&=\frac{{-3+2}}{4}\\&=-\frac{1}{4}\\\end{aligned}

The slope of the line is m=-\frac{1}{4}.

The inequalities is x+4y\geqslant b passes through the point \left({0,-3}\right).

\begin{aligned}\left(0\right)+4\left({-3}\right)&=b\\-12&=b\\\end{aligned}

The number is – 12.

The number is \boxed{-12} in the inequality \boxed{x+4y\geqslant -12}.

Learn more:

1. Learn more about inverse of the function <u>brainly.com/question/1632445. </u>

2. Learn more about equation of circle <u>brainly.com/question/1506955. </u>

3. Learn more about range and domain of the function <u>brainly.com/question/3412497 </u>

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequalities

Keywords: numbers, slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.

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