Question

the height of a lake decreases by 20 in over a period of time. the height decreases by 5 in each week. the equation below is written to represent the situation: -20 ÷ (-5) = 4 which description best explains the meaning of 4 in the equation? a the new height of the water in the lake is 4 in. b the change in the height of the lake is 4 in. c the time it takes for the lake to decrease in height by 5 in is 4 weeks. d the time it takes for the lake to decrease in height by 20 in is 4 weeks.

Explanation:

Step1: Analyze the equation components

The total decrease is - 20 in (negative as it's a decrease), and the rate of decrease is - 5 in per week (negative as it's a decrease).

Step2: Use the division formula meaning

In the formula \(a\div b = c\), \(a\) is the total amount, \(b\) is the rate per unit time, and \(c\) is the time. Here, \(-20\div(-5)=4\) means the time taken for a 20 - in decrease (since \(\vert - 20\vert=20\)) at a rate of 5 - in per week (since \(\vert - 5\vert = 5\)) is 4 weeks.

Answer:

D. The time it takes for the lake to decrease in height by 20 in is 4 weeks.