Which description matches the transformations y=cosx undergoes to produce y= -2cos3x

a. horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis
b. reflection through the y-axis, vertical shift of 2 units, horizontal shift right by 3 units
c. horizontal shift 2 units, then vertical shift up by 3 units
d. horizontal stretch by factor 2, reflection through the x-axis, then the vertical stretch by factor 3

 A. Horizontal compression by factor 1/3, vertical stretch by factor 2, then a reflection through the x-axis

Step-by-step explanation:

Since, If there is a function, y= a cos bx

Then a shows vertical stretch while b shows horizontal compression.

Here, Given function, y= cos x

After transformation, It is giving y = -2 cos 3x

therefore here is a horizontal compression occurs with factor 1/3.

Also Negative sign shows there also did reflection through x-axis.

And, It also, stretched vertically by factor 2. ( also shown in the below graph)

Thus, Option A) is correct.      

i wish i could u

step-by-step explanation:

i wish i could u

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.