Answer:
see explanation
Step-by-step explanation:
Since x and y vary inversely then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k use the condion x = 10 when y = 12
k = yx = 12 × 10 = 120
y = [tex]\frac{120}{x}[/tex] ← equation of variation
Complete the table using this formula
when x = 8 then y = [tex]\frac{120}{8}[/tex] = 15
when x = 20 then y = [tex]\frac{120}{20}[/tex] = 6
when y = 30, then
30 = [tex]\frac{120}{x}[/tex]
Multiply both sides by x
30x = 120 ( divide both sides by 30 )
x = 4
The completed table is
x | 10, 5, 8, 4, 20
y | 12, 24, 15, 30, 6
