Question

plot an inequality by dragging the correct circle to the number line. a movie club charges $10 per month, plus $1.50 per rental. diego spends no more than $25 per month on movies. describe the graph representing the number of diegos rentals. check all that apply. the graph has an open circle at 2.5. the graph has a closed circle at 2.5. the graph has an open circle at 10. the graph has a closed circle at 10. the arrow points left.

Explanation:

Step1: Set up the inequality

Let \(x\) be the number of rentals. The cost function is \(C = 10+1.5x\). Since Diego spends no more than \(25\), we have the inequality \(10 + 1.5x\leq25\).

Step2: Solve the inequality

Subtract \(10\) from both sides: \(1.5x\leq25 - 10\), so \(1.5x\leq15\).
Divide both sides by \(1.5\): \(x\leq\frac{15}{1.5}=10\).

Step3: Analyze the graph of the inequality

When \(x = 10\), the inequality \(x\leq10\) includes \(x = 10\) (because of the "\(\leq\)" sign), so there is a closed - circle at \(x = 10\). The values of \(x\) that satisfy the inequality are less than or equal to \(10\), so the arrow points to the left.

Answer:

The graph has a closed circle at \(10\). The arrow points left.