A flagpole 12 meters tall casts a 24-meter shadow. Nearby, luke stands and is 4 meters tall. Determine the length of luka's shadow. Include all labels.

8 meters

Step-by-step explanation:

This is a question that deals with Proportion

Height of flagpole/Shadow of flagpole = Height of Luke/Shadow of Luke

Length of the shadow of Luke = x

= 12/24 = 4/x

We cross Multiply

12 × x = 24 × 4

x = 24 × 4/12

x = 8 meters

Hence, the length of the shadow of Luke = 8 meters

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c