Δabc with vertices a(-3, 0), b(-2, 3), c(-1, 1) is rotated 180° clockwise about the origin. it is then reflected across the line y = -x. what are the coordinates of the vertices of the image?

A(0, -3) ;  B(3, -2) and C(1, -1).

Step-by-step explanation:

Given  : ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin.

To find : What are the coordinates of the vertices of the image.

Solution : We have given

Vertices A(-3, 0), B(-2, 3), C(-1, 1)  is rotated 180° clockwise.

By the rotation rule of 180° clockwise : (x ,y) →→ ( -x ,-y).

Then vertices would be

A(-3, 0) →→ A(3, 0)

B(-2, 3) →→ B(2, -3)

C(-1, 1) →→ C(1, -1).

Reflection y = -x then

A(0, -3) ;  B(3, -2) and C(-1, 1).

Therefore, A(0, -3) ;  B(3, -2) and C(1, -1).

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.