Mary is thinking of three consecutive even integers, x, y, and z. three times the value of z exceeds half the value of x by 37. what is the value of x?

  x = 10

Step-by-step explanation:

You know z = x+4, so ...

  3z -x/2 = 37 . . . . . . . . the given relation

  3(x +4) -x/2 = 37 . . . . substituting for z

  5/2x +12 = 37 . . . . . . .eliminate parentheses and simplify

  5/2x = 25 . . . . . . . . . . subtract 12

  x = 10 . . . . . . . . . . . . . multiply by 2/5

Check

3z = 3·14 = 42

x/2 = 10/2 = 5

42 exceeds 5 by 37 . . . . true

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft