Last night, julie's pet hamster zoe kept julie awake for at least an hour running on her exercise wheel and scratching at the corner of her cage. zoe ran on the wheel at lease twice as long as she scratched at the corners of her cage, and she spent more than 1/4 hour running on her wheel. which system of inequalities represents the time zoe kept juile awake last night if x is the number of hours zoe spent running on her wheel and y is the nu=umber of hours spent scratching her cage

, ,   and

Step-by-step explanation:

Here,  x represents the number of hours Zoe spent running on her wheel and y represents the number of hours spent scratching her cage.

Julie was awoke for at least an hour running on her exercise wheel and scratching the of her cage.

⇒

She ran on her wheel at least twice as long as she scratched at the corners of her cage.

⇒

Also, She spent more than 1/4 hour running on her wheel.

⇒

And, we know that number of hours can not be negative.

⇒  

Therefore, the complete system of inequality which shows the given situation is,

, and ,

Note: the feasible region ( covered by the given system) is shown in the below graph.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is