he variable z is directly proportional to x, and inversely proportional to y. When x is 7 and y is 7, z has the value 2. What is the value of z when x=10, and y=12?

Respuesta :


[tex]z \alpha \frac{x}{y} [/tex]
[tex]z = \frac{kx}{y} [/tex]
Case 1:
But, x=7, y=7 and z=2
From;
[tex]z = \frac{kx}{y} [/tex]
[tex]2 = \frac{k7}{7} [/tex]
[tex]2 \times 7 = 7k[/tex]
[tex]14 = 7k[/tex]
[tex]k = \frac{14}{7} [/tex]
[tex]k = 2[/tex]
Therefore;
From;
[tex]z = \frac{kx}{y} [/tex]
[tex]z = \frac{2x}{y} [/tex]
Case 2:
z=?, x=10, y=12
From;
[tex]z = \frac{2x}{y} [/tex]
[tex]z = \frac{2(10)}{12} [/tex]
[tex]z = \frac{20}{12} [/tex]
Therefore;
[tex]z = \frac{5}{3} [/tex]