If the triangles are similar, which must be true? -

RY

YS

RX _ XY

XT TS

1

RY

RS

RX

RT

XY

TS

2 회

RY

RS

III

RX

RT

RS

RY

RY

RX

RS

RT

=

TS

Since △RST and △RYX are similar triangles, the statement that must be true is:

B. RY/RS = RX/RT = XY/TS

Thus, △RST and △RYX  are similar triangles.

RY/RS = RX/RT = XY/TS

Therefore, since △RST and △RYX are similar triangles, the statement that must be true is:

B. RY/RS = RX/RT = XY/TS

Learn more about similar triangles on:

link

B. RY/RS=RX/RT=XY/TS

Step-by-step explanation:

In the picture attached, △RST and △RYX (which are similar) are shown

The options are:

Given that the triangles are similar, then their sides are proportional. Then, there is some constant k, which satisfies:

k*RS = RY

k*RT = RX

k*TS = XY

This can be rewritten as:

k = RY/RS = RX/RT = XY/TS

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