I am currently in a section of my geometry book titled Applying Properties of Similar Triangles. This is a very easy section but there is on problem where I cannot figure out (forgot) the next step.

1. z-4 12
--- = ---
z/2 10

2.(z-4)10 = (z/2)12

3. 10z+40 = ?

Thank you for your time and your help would be appreciated a lot a lot a lot!!! :D please help

from (z-4)10 = (z/2)12

10z - 40 = 6z

take it from here.

To solve the equation (z - 4)/10 = (z/2)/12, you can cross-multiply.

1. Multiply the numerator of the first fraction (z - 4) by the denominator of the second fraction (12):

(z - 4) * 12 = 12z - 48

2. Multiply the numerator of the second fraction (z/2) by the denominator of the first fraction (10):

(z/2) * 10 = 5z

3. Now, set both results equal to each other:

12z - 48 = 5z

4. To isolate the variable z, you need to get rid of the term with 12z on one side of the equation. Do this by subtracting 5z from both sides:

12z - 5z - 48 = 5z - 5z
7z - 48 = 0

5. To solve for z, add 48 to both sides of the equation:

7z - 48 + 48 = 0 + 48
7z = 48

6. Finally, divide both sides of the equation by 7:

7z/7 = 48/7
z = 6.857 (rounded to three decimal places)

So, the value of z in the equation (z - 4)/10 = (z/2)/12 is approximately 6.857.