Where P represents the total cost on Parabola skate and h the numbr of hours
[tex]A=5.25h+25[/tex]Where A represents the total cost on Arc o Hawka nd h the number of hours
h=2 for the second equation
[tex]\begin{gathered} A=(5.25\times2)+25 \\ A=10.50+25 \\ A=35.50 \end{gathered}[/tex]To know when the first store is cheaper than the second we compare the two equations using less than, so
[tex]Pso[tex]4.50h+35<5.25h+25[/tex]and solve for h
[tex]\begin{gathered} 35-25<5.25h-4.50h \\ 10<0.75h \\ h>\frac{10}{0.75} \\ \\ h>\frac{40}{3}\approx13.3 \end{gathered}[/tex]the first store will be cheaper when the skateboard is used for more than 13.3 hours
to know when they would cost the same we equal the equations
[tex]\begin{gathered} P=A \\ 4.50h+35=5.25h+25 \end{gathered}[/tex][tex]h=\frac{40}{3}=13.3[/tex]and if you need the coordinates, you can replace 40/3 on any equation to know the cost
so we can replace 40/3 on any equation, i will use the first
[tex]\begin{gathered} P=4.50h+35 \\ P=4.50(\frac{40}{3})+35 \\ P=60+35 \\ P=95 \end{gathered}[/tex]the cost is $95 and the coordinates ( 40/3 , 95 )
