Question

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 \(10 + 1.5x\). Since Diego spends no more than \(25\), we have \(10+1.5x\leq25\).

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 \(x\leq10\)

For the inequality \(x\leq10\), when graphing on a number - line:

• If the inequality is \(x\leq a\) (where \(a = 10\) in our case), we use a closed circle at \(a\) (because \(x = 10\) is included in the solution set, since \(10+1.5\times10=10 + 15=25\) which satisfies \(10 + 1.5x\leq25\)).
• The arrow points to the left (towards the smaller numbers) because \(x\) can be any number less than or equal to \(10\).

Answer:

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