Question

before baseball practice, jaxon spends at least 90 minutes on homework but no more than 100 minutes. which graph represents the scenario? graphs with number lines labeled 85, 90, 95, 100, 105, 110, and options with circles (closed/open) and colored segments are shown

Explanation:

Step1: Analyze the inequality

Let \( t \) be the time Jaxon spends on homework (in minutes). The problem states he spends at least 90 minutes (so \( t \geq 90 \)) and no more than 100 minutes (so \( t \leq 100 \)). This can be written as the compound inequality \( 90 \leq t \leq 100 \).

Step2: Interpret the number line

• A closed circle (filled dot) on a number line represents that the point is included in the solution set. For \( t \geq 90 \), we use a closed circle at 90. For \( t \leq 100 \), we use a closed circle at 100.
• The line segment between the two closed circles (from 90 to 100) represents all the values of \( t \) that satisfy both inequalities.

Now, let's analyze each option:

• First option: The circles at 90 and 100 are closed, but the line is extending beyond 100 in the positive direction and beyond 90 in the negative direction, which does not match \( 90 \leq t \leq 100 \).
• Second option: The circles at 90 and 100 are open (not filled), but we need closed circles because 90 and 100 are included (at least 90, no more than 100 means 90 and 100 are allowed).
• Third option: The circles at 90 and 100 are open, and the line is between them but in the wrong direction (the shaded part is not between 90 and 100 as we need).
• Fourth option: Closed circles at 90 and 100, with the line segment between them (shaded from 90 to 100), which matches \( 90 \leq t \leq 100 \).

Answer:

The fourth number line (with closed circles at 90 and 100, and the segment between them shaded) represents the scenario.