Question

Pls show work! questions on pic

Answer 1

a.(10,23)

b.(7,30)

e.(20,20)

Explanation:

We are given that

x=Width of garden

y=Length of garden

According to question

`x\geq 5`

`y\geq 20`

Perimeter of rectangle=
`2(x+y)`

Where x=Width of rectangle

y=Length of rectangle

Fencing used =
`2(x+y)`

`2(x+y)\leq 80`

First we change inequality into equality

`x=5`...(1)

`y=20`...(2)

`2(x+y)=80`

`x+y=40`...(3)

Substitute x=0 in equation (3)

`y=40`

Substitute y=0 in equation (3)

`x=40`

Substitute x=0 and y=0 in equation (3)

`2(x+y)\leq 80`

`0\leq 80`

It is true. Therefore, the shaded region below the line.

`0\geq 5`

`0\geq 20`

These are false equation .Therefore, the shaded region above the line.

Substitute x=5 in equation (3)

`5+y=40`

`y=40-5=35`

Substitute y=20 in equation (3)

`x+20=40`

`x=40-20=20`

Intersection point of equation (1) and (3) is (5,35) and intersect point of equation (2) and (3) is (20,20).

Now,

a.(10,23)

Substitute in

`2(x+y)\leq 80`

`2(10+23)\leq 80`

`66\geq 80`

10>5 and 23>20

it satisfied all inequality.

Hence, it is a solution.

b.(7,30)

7>5

30>20

`2(7+30)=74<80`

it satisfied all inequality.

Hence, it is a solution.

c.(18,25)

18>5

25>20

`2(18+25)=86>80`

It does not satisfied third inequality

Hence, it is not a solution.

d.(8,35)

8>5

35>20

`2(8+35)=86>80`

It does not satisfied third inequality

Hence, it is not a solution.

e.(20,20)

`2(20+20)=80`

20>5

20=20

it satisfied all inequality.

Hence, it is a solution.