He variable z is directly proportional to x, and inversely proportional to y. when x is 5 and y is 19, z has the value 2.8947368421053. what is the value of z when x = 12, and y = 24

Given Z is directly proportional to X and inversely proportional to Y.

This means that

Z=kX/Y where k is a yet-unknown constant.

We are also given that, when X=5, y=19, Z=2.8947368421053, this means

2.8947368421053=k(5/19)

or

k=2.8947368421053*19/5

=11.0000000000001

=>

Z=11.000000000000*X/Y

If X=12, Y=24, then

Z=11.000000000000*X/Y

=11.000000000000*12/24

=5.500000000000

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions