Respuesta :

altavistard

Answer:

        15·9

z = --------- = 135/4

         4

Step-by-step explanation:

The general formula here is as follows:

        ky

z = ---------

         x

We must find the value of the constant of proportionality.  To do this, subst. 6 for x, 2 for y and 5 for z and compute k:

        k·2

5 = ---------

         6

Multiplying both sides by 6 results in 30 = 2k.

Thus, k = 30/2, or k = 15.

Our formula becomes:

        15y

z = ---------

         x

if x = 4 and y = 9, we get:

        15·9

z = --------- = 135/4

         4

lublana

Answer:

[tex]z=33.75[/tex]

Step-by-step explanation:

We are given that z varies inversely with x and directly with y when x=6 and y=2 then z=5

We have to find the value of z when x=4 and y=9

According to question

[tex]z\propto\frac{1}{x}[/tex]

and [tex]z\proptoy[/tex]

Therefore, we have [tex]z\propto\frac{y}{x}[/tex]

[tex]z=k\frac{y}{x}[/tex]

k=proportionality constant

Substitute x=6 , y=2 and z=5 then we get

[tex]5=k\times \frac{2}{6}[/tex]

[tex]5=\frac{k}{3}[/tex]

[tex]k=5\times3[/tex]

By division  poperty of equality

k=15

Now, substitute the value x=4,y=9 and k=15 then the value of z

[tex]z=15\times \frac{9}{4}[/tex]

[tex]z=\frac{135}{4}[/tex]

[tex]z==33.75[/tex]

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