The variable z varies jointly with x and y. if z = 18 when x = 2 and y = 6, find the constant of variation, k, and then find the value of z when x = −4 and y = 5.

the constant of variation k is
the value of z is

The constant of variation k is 3/2.

The value of z is -30.

Step-by-step explanation:

As we know Function form is

Z=kxy1

So for k  

K = z/xy

So if z=18, x=2 y=6

k= 18/2 x6

k= 18/12

k=3/2

Now we have to find for z, now we know the value of x= -4  y =5 z =3/2

z= kxy

z= 3/2  (-4)(5)

z= -30

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.