MATH SOLVE

3 months ago

Q:
# A system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped. Which constraint could be part of the scenario?PLEASE ANSWER ASAP TIMED QUIZ

Accepted Solution

A:

Answer:The correct option is 1.Step-by-step explanation:It is given that a system of inequalities can be used to determine the depth of a toy, in meters, in a pool depending on the time, in seconds, since it was dropped.Let y be the depth of a toy and x is time, in seconds.In the given graph a solid horizontal line passes through the point (0,-1) and shaded region is above the line. So, the inequality of red line is[tex]y\geq -1[/tex]The depth of a toy can be less than -1. It means the pool is 1 meter deep.The blue line is a dashed line which passes through (0,0) and (2,-1).So the slope of line is[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-0}{2-0}=-\frac{1}{2}[/tex]The equation of blue line is[tex]y=mx+b[/tex]where, m is slope and b is y-intercept.[tex]y=-\frac{1}{2}x+0[/tex][tex]y=-\frac{1}{2}x[/tex]The shaded region is below the line so the required inequality is[tex]y< -\frac{1}{2}x[/tex]it means the toy sinks at a rate of less than 1/2 meter per second.Therefore the correct option is 1.