In inequality system, for the zoo keeper fencing, the greater than sign used for at least word of habitat length and less then sign used for no more than word.
- a) The system of inequalities for the given problem is,
- [tex]x\geq80[/tex]
- [tex]y\leq-x+150[/tex]
- The graph which shows the inequalities of is attached below.
- b) The dimensions for two possible solution are 90 ft by 20 ft and 110 ft by 30 ft.
What is linear inequality system?
Inequality equation is the equation in which the two expressions are compared with greater than, less than or other inequality signs. The system having linear inequality equations is called the linear inequality system.
Given information-
The length of the habitat should be at least 80 feet.
The perimeter of the habitat should be no more than 300 feet.
Suppose [tex]x[/tex] is the length of the rectangular habitat and [tex]y[/tex] is the width of the rectangular habitat.
As the length of the habitat should be at least 80 feet. Thus the value of [tex]x[/tex] should be more than or equal to the 80 feet. Therefore,
[tex]x\geq80[/tex]
Perimeter of the rectangle is twice the sum of length and width. As the perimeter of the habitat should be no more than 300 feet. Thus,
[tex]2(x+y)\leq300\\2x+2y\leq300\\y\leq-x+150[/tex]
Hence, the system of inequalities for the given problem is,
[tex]x\geq80[/tex]
[tex]y\leq-x+150[/tex]
The graph which shows the inequalities of is attached below.
As in the graph attached below shown the area which can be gives the solution for the given system. We take two points as, (90,20)and (110,30).
Thus the dimensions for two possible solution are 90 ft by 20 ft and 110 ft by 30 ft.
Hence,
- a) The system of inequalities for the given problem is,
- [tex]x\geq80[/tex]
- [tex]y\leq-x+150[/tex]
- The graph which shows the inequalities of is attached below.
- b) The dimensions for two possible solution are 90 ft by 20 ft and 110 ft by 30 ft.
Learn more about the linear inequality system here;
https://brainly.com/question/17724536
