|z - 1| = 7z - 13 solve this equation and check for extraneous solutions

Given:  |z-1| = 7z - 13

Due to the absolute value function, this equation yields two separate equations:

+(z-1) = 7z - 13, and

-(z-1) = 7z - 13.

Simplifying the first, we get z - 1 = 7z - 13, or

                                               -1 + 13 = 7z - z, or 12 = 6 z.  Then z = 2.

Doing the same to the 2nd equation:   -z + 1 = 7z - 13, or 14 = 8z, or z = 7/4.

We must check both results by subst. into  |z-1| = 7z - 13:

If z = 2, we get 2 - 1 = 14 - 13, or 1 = 1.  Thus, z = 2 is a solution.

If z = 7/4, we get 3/4 = 7(7/4) - 13, or   3/4 = 49/4 - 52.  This is clearly false.

The (single) solution is thus z = 2

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

is should be y = 5x

step-by-step explanation:

correct me if im wrong