Apoint of the form 25 +bi is 37 units from 13 – 31i. what is the value of b?

                        The value of b is: 4 and -66

We are given distance between two points i.e. 25+bi and 13-31i as: 37 units.

We know that the point 25+bi is given in coordinate plane as: (25,b)

and 13-31i is given in coordinate plane as: (13,-31)

Since, any complex number is expressed in the form z=x+iy

Now we know that the distance between two points (a,b) and (c,d) is given by:

Here we have:

Distance=37 units.

(a,b)=(25,b) and (c,d)=(13,-31)

Hence, we have:

Now on squaring both side we obtain:

on taking square root both side we obtain:

                    Hence, the value of b is:  4 and -66

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.

h * s * a

h = history teacher

s = science teacher

a =   art teacher.

i see no data table, but just multiply the number of history teachers, science teachers, and art teachers.