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 (represented as \(- 20\)), the decrease per week is \(5\) in (represented as \(-5\)). The formula \(\text{time}=\frac{\text{total change}}{\text{change per unit time}}\).

Step2: Interpret the result of the division

When we calculate \(-20\div(-5)\), we are finding out how many weeks (\(4\)) it takes for the lake's height to decrease by \(20\) in (since \(\frac{-20}{-5} = 4\), and the negative signs cancel out, representing the number of time - intervals).

Answer:

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