Question

after spending the afternoon at the park, kathleen and her friend sadie each biked back to their houses. kathleens house is 7 miles away from the park. sadies house is farther away than kathleens house. let ( d ) represent the distance, in miles, that sadies house could be from the park. which inequality models the story? ( d > 7 ) ( d geq 7 ) ( d < 7 ) ( d leq 7 ) graph the inequality that models the story. to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.

Explanation:

Step1: Understand the problem

Kathleen's house is 7 miles from the park. Sadie's house is farther from the park than Kathleen's. So Sadie's distance \( d \) must be greater than 7.

Step2: Analyze the inequalities

• \( d > 7 \): means distance is greater than 7.
• \( d \geq 7 \): means distance is greater than or equal to 7, but we need farther (strictly greater), so \( d > 7 \) is correct.
• \( d < 7 \): less than 7, not farther.
• \( d \leq 7 \): less than or equal to 7, not farther.

Answer:

\( d > 7 \)

For graphing:

• The ray should start at 7 (open circle, since \( d > 7 \) not \( d \geq 7 \)) and point to the right (towards values greater than 7, like 8, 9, 10, etc.).