Answer: [tex]z = 4[/tex]
Step-by-step explanation:
Given:
[tex]x \alpha yz[/tex]
replacing the proportionality sign with a constant , we have :
[tex]x = kyz[/tex]
substituting : [tex]y = -2[/tex] , [tex]z = -3[/tex] and [tex]x = 30[/tex] into the equation , we have :
[tex]30 = k(-2)(-3)[/tex]
[tex]30 = 6k[/tex]
divide through by 6
[tex]k = 5[/tex]
substituting [tex]k = 5[/tex] into the equation , the equation becomes
[tex]x = 5yz[/tex]
To find the value of z , when y = 4 , x = 80 , we will substitute the values into the formula , we have :
[tex]80 = 5(4)(z)[/tex]
[tex]80 = 20z[/tex]
dividing through by 20 , we have :
[tex]z = 4[/tex]
