Hi there!

The two trapezoids are similar, so we can determine a common scale factor:
OL/UR = NM/TS
9/3 = 6/2
3 = 3
Trapezoid ONML is 3x larger than UTSR, so:
RS = 4, LM = y
3RS = LM
3 · 4 = y = 12.
Find x using the same method:
3UT = ON
3(2x+1) = 4x + 9
6x + 3 = 4x + 9
2x = 6
x = 3.
Answer:
Step-by-step explanation:

Answer: option d
Step-by-step explanation:
Remember the identity:

The inverse of the tangent function is arctangent. You need to use this to calculate the angle "S":
Knowing that: you need to find the measure of the angle "S" ,
(which is the adjacent side) and
(which is the opposite side), you can sustitute values into 
Then, you get that the measure of "S" rounded to the nearest tenth is:

First you differentiate to find the gradient
dy/dx = (6 - - 8) / (-4 - 7)
= 14 / -11
= - 14/11
Then you use this formula
y - y1 = m (x - x1)
y1 being the y coordinate
x1 being the x coordinate
m being the gradient (or slope)
y - 6 = -14/11 (x - - 4)
y - 6 = -14/11x - 56/11
y = -14/11x + 10/11