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

Step2: Interpret the division result

When we calculate \(-20\div(-5)\), using the rule \(\frac{a}{b}=c\) (where \(a\) is total change, \(b\) is rate of change per unit time), \(c\) gives the number of units of time. Here, it 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.