X=width of a coccer pitch
2x-20=length of a soccer pitch
Area (rectangule)=length x width
We suggest this equation:
x(2x-20)=6000
2x²-20x=6000
2x²-20x-6000=0
x²-10x-3000=0
We solve this quadratic equation:
x=[10⁺₋√(100-4*1*-3000)]/2=[10⁺₋√(100+12000)]/2=
=(10⁺₋110)/2
we have two solutions:
x₁=(10-110)/2=-50, invalid solution.
x₂=(10+110)/2=60
x=60
2x-20=2(60)-20=120-20=100
Solution: the length is 100 m, and the width is 60 m.
To check:
Area=100 m*60 m=6000 m²
The twice of width is =2(60 m)=120 m,
20 m less than twice its width is: 120 m-20 m=100 m=the length.
If we look at the rest of the input and output, we also realize that:
output = input + 5
Thus if the input is 'n' then the output is 'n+5'
Hope that helps!
For an arithmetic sequence, the nth term is the first term plus (n-1)×the differece
the first term is 28, the difference between each adjacent number is 8
so -36=(28)+8(n-1)
8(n-1)=64
n-1=8
n=9
the 9th term is -36
