Slightly harder triangle proportionality. Solve for X

Can somebody explain this to me please?

3) x = 14

4) x = 5

Step-by-step explanation:

First, let's separate the triangle into two separate triangles.

Let's start with number 3. Here, we have one triangle with the sides of 25, 15, and the parallel line. But, we also have another triangle that has sides of 25+(x+6), 27, and the other parallel line.

So, since the two lines in the triangle are parallel, we can say that the angles are equal of both triangles are equal

Since the angles are equal, that means that the triangles are similar.

The triangles being similar means that they don't exactly have the same size or area, but they're similar in proportion. One triangle just looks like the other but smaller.

Since they have the same proportions, that means that there must be some sort of scale to compare the triangles. That is known as the scale factor.

We can find the scale factor by comparing two corresponding sides of the two triangles we made. The side that is 15 long corresponds with the side that is 27 long.

If we want the scale factor, we see how much 15 needs to multiply by to be 27

let s be the scale factor

15s = 27

s = 9/5 or 1.8

That means that the larger triangle's sides are 9/5 times larger.

Knowing this, we can look at the other side. The side that is 25 long corresponds with the side that is 25+(x+6)

Since we know that larger is side is 9/5 times larger than the short side, we can write it like this

(9/5)(25) = 25+(x+6)

45 = x+31

14 = x

Now, let's move on to number 4, where we pretty much do the same thing.

The side that is 30 long corresponds with the side that is 50 long

30s = 50

s = 5/3

The side that is 9x-3 long corresponds with the side that is 9x-3+28 long

(5/3)(9x-3) = 9x-3+28

15x-5 = 9x+25

6x = 30

x = 5

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2