Given that the two triangles are similar, solve for x if au = 20x + 108, ub = 273, bc = 703, uv = 444, av = 372 and ac = 589.

Given:

segment AU = 20x + 108, 
UB = 273, 
BC = 703,
UV = 444, 
AV = 372 and 
AC = 589. 

Point U lies on AB and V lies on AC.

UV is perpendicular to AC.

Therefore, the similar triangles are AUV and ABC

So the similarity is: segment AU / segment UV = segment AB / segment BC

20x + 108       20X + 381
      =
372                      589

(20x + 108)* 589 = (20X + 381)*372

11780 X + 63612 = 7440X + 141732

4340 X - 78120 = 0

4340 X = 78120

X = 78120/4340 = 18


x = 18

To check:

AU = 20*18 + 108 = 360 + 108 = 468

AB = 741

468/372 = 741/589

Which the two are equal ratios

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles