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 formula meaning

The formula \(-20\div(-5) = 4\) represents the relationship between the total decrease in height (\(-20\) in, negative because it's a decrease) and the rate of decrease per week (\(-5\) in per week, negative for the same reason).

Step2: Interpret the result

In the formula \(\text{time}=\frac{\text{total change in height}}{\text{change in height per week}}\). Here, \(\frac{- 20}{-5}=4\), which means the time taken for a \(20\) - inch decrease (since \(\vert-20\vert = 20\)) at a rate of \(5\) inches 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.