Answer:
The table B represent an inverse variation
The constant of variation k is 30
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
Verify table A
For x=3, y=8 ----> [tex]k=y*x[/tex] ----> [tex]k=8*3=24[/tex]
For x=4, y=6 ----> [tex]k=y*x[/tex] ----> [tex]k=6*4=24[/tex]
For x=5, y=4.8 ----> [tex]k=y*x[/tex] ----> [tex]k=4.8*5=24[/tex]
For x=5.5, y=4 ----> [tex]k=y*x[/tex] ----> [tex]k=5.5*4=22[/tex]
The values of k are different
therefore
The table A not represent an inverse variation
Verify table B
For x=0.1, y=300 ----> [tex]k=y*x[/tex] ----> [tex]k=300*0.1=30[/tex]
For x=0.5, y=60 ----> [tex]k=y*x[/tex] ----> [tex]k=60*0.5=30[/tex]
For x=75, y=0.4 ----> [tex]k=y*x[/tex] ----> [tex]k=75*0.4=30[/tex]
For x=100, y=0.3 ----> [tex]k=y*x[/tex] ----> [tex]k=100*0.30=30[/tex]
All the values of k are the same
therefore
The table B represent an inverse variation
The equation is equal to
[tex]y*x=30[/tex]
