Solve 5x2 = −30x − 65. x = −3 ± 2i x = −3 ± 4i x = −6 ± 2i x = −6 ± 4i

x = -3 + 2 i or x = -3 - 2 i

Step-by-step explanation:

Solve for x:

5 x^2 = -5 (6 x + 13)

Expand out terms of the right hand side:

5 x^2 = -30 x - 65

Add 30 x + 65 to both sides:

5 x^2 + 30 x + 65 = 0

Divide both sides by 5:

x^2 + 6 x + 13 = 0

Subtract 13 from both sides:

x^2 + 6 x = -13

Add 9 to both sides:

x^2 + 6 x + 9 = -4

Write the left hand side as a square:

(x + 3)^2 = -4

Take the square root of both sides:

x + 3 = 2 i or x + 3 = -2 i

Subtract 3 from both sides:

x = -3 + 2 i or x + 3 = -2 i

Subtract 3 from both sides:

x = -3 + 2 i or x = -3 - 2 i

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.