The variable z is inversely proportional to x. when x is 16, z has the value 0.5625. what is the value of z when x= 25?

0.36

Step-by-step explanation:

z is inversely proportional to x:

z = k / x

When x is 16, z has the value 0.5625.

0.5625 = k / 16

k = 9

What is the value of z when x= 25?

z = 9 / 25

z = 0.36

The answer is 9/25 or .36 if you prefer it in decimal form.

Step-by-step explanation:

inversely proportional means there is a constant that we are going to divide by.

So z is inversely proportional to x means z=k/x where k is a constant.

We are given when x=16, z=0.5625.  This information will be used to find our constant value k.

0.5625=k/16

Multiply both sides by 16:

16(0.5625)=k

Simplify:

9=k.

This means no matter what (x,z) pair we have the constant k in z=k/x will always be 9.

The equation we have is z=9/x.

Now we want to find z when x=25.

z=9/25

z=.36

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."