Which graph shows the solution to this system of inequalities? y< 1/2 x - 2 y≤ - 2x + 4
2 answers:
Answer:
The graph that shows the solution is A.
Step-by-step explanation:
The solution to a system of inequalities in two variables is often shown as a shaded graph on the coordinate plane. Shaded regions show the areas that contain points in the solution.
The following process works by isolating the y variable in each inequality. Since greater y values are higher up in the coordinate plane, a > or ≥ symbol means that the solution exists above the line of the inequality. Likewise, a < or ≤ symbol means that the solution exists below the line of the inequality.
We have the following system of inequalities
Graph the line that bounds each inequality. If the symbol is ≤ or ≥, then the line should be solid to show that the points on the line are included in the solution. If the symbol is <, >, then the line should be dashed to show that the points on the line are not included in the solution.
The shaded region is the intersection of the inequalities. Every point in the shaded region and on the solid ray is part of the solution. The dashed lines and rays are not part of the solution.
Using Desmos as a tool for making the graphs of the inequalities we get that the graph that shows the solution is A.
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The <span>given the piecewise function is :
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![f(x) = \[ \begin{cases} 2x & x \ \textless \ 1 \\ 5 & x=1 \\ x^2 & x\ \textgreater \ 1 \end{cases} \]](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5C%5B%20%5Cbegin%7Bcases%7D%20%0A%20%20%20%20%20%202x%20%26%20x%20%5C%20%5Ctextless%20%5C%20%201%20%5C%5C%0A%20%20%20%20%20%205%20%26%20x%3D1%20%5C%5C%0A%20%20%20%20%20%20x%5E2%20%26%20x%5C%20%5Ctextgreater%20%5C%201%20%0A%20%20%20%5Cend%7Bcases%7D%0A%5C%5D)
To find f(5) ⇒ substitute with x = 5 in the function → x²
∴ f(5) = 5² = 25
To find f(2) ⇒ substitute with x = 5 in the function → x²
∴ f(2) = 2² = 4
To find f(-2) ⇒ substitute with x = 5 in the function → 2x
∴ f(-2) = 2 * (-2) = -4
To find f(1) ⇒ substitute with x = 1 in the function → 5
∴ f(1) = 5
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So, the statements which are true:<span>
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To find f(5) ⇒ substitute with x = 5 in the function → x²
∴ f(5) = 5² = 25
To find f(2) ⇒ substitute with x = 5 in the function → x²
∴ f(2) = 2² = 4
To find f(-2) ⇒ substitute with x = 5 in the function → 2x
∴ f(-2) = 2 * (-2) = -4
To find f(1) ⇒ substitute with x = 1 in the function → 5
∴ f(1) = 5
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So, the statements which are true:<span>