Final answer:
To determine the length of the rectangle with an area of −7x+10 and a width of x−5, divide the area by the width. None of the provided answer options accurately represent the length, which simplifies to −7 + (10 ÷ (x − 5)).
Step-by-step explanation:
To find the expression that represents the length of a rectangle, you need to divide the area of the rectangle by its width. Given that the area of the rectangle is −7x+10 square meters and the width is x−5 meters, you can calculate the length by dividing the area by the width.
Length = Area ÷ Width
Length = (−7x + 10) ÷ (x − 5)
When we divide −7x + 10 by x − 5, we get:
Length = −7 + (10 ÷ (x − 5))
The division of the constant term 10 by the linear term x − 5 does not simplify to an algebraic term without x, thus leaving us with only the −7 from the −7x term. Therefore, the correct answer is not provided in the options since none equals −7 or −7 + (10 ÷ (x − 5)). If this is a typo in the options, and it is meant to represent −7x + 10 in terms of x − 5, then it could be rewritten as −7 + (10 ÷ (x − 5)), meaning none of the provided options, A) x−5 B) a^2−7x+10 C) −7x+10 D) a^2−5x+10, are correct as they stand.