20 points in what direction and by how many units is the graph of f(x) = −3 cos(2x − π) + 2 vertically and horizontally shifted? (1 point) down 2, left pi over 2 down 2, right pi over 2 up 2, left pi over 2 up 2, right pi over 2

Step-by-step explanation:

We are given a trigonometric function f(x) = −3 cos(2x − π) + 2.

We need to explain the transformations in the given function being applied.

We can see that 2 is being added to −3 cos(2x − π) in th given function.

According to rules of transformations, y=f(x)+D, shifts D units up if D is a positive number.

Therefore, for adding 2 in −3 cos(2x − π), it would shift 2 units up.

Let us see other transformation being applied there.

We can see that π is being subtracted in parenthesis from 2x.

According to rules of transformations, y=f(x-C), shifts C units right if C is a positive value.

Therefore, on subtracting π from 2x in −3 cos(2x) inside parenthesis, the function shifts π units right.

Therefore, correct option for transformations would be :

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950