Geoffrey and amara's teacher gave them a system of linear equations to solve. they each took a few steps that led to the systems shown in the table below.
teacher
6x-5y=16x−5y=16, x, minus, 5, y, equals, 1
-2x+2y=-1−2x+2y=−1minus, 2, x, plus, 2, y, equals, minus, 1
geoffrey amara
6x-5y=16x−5y=16, x, minus, 5, y, equals, 1 4x-3x=04x−3x=04, x, minus, 3, x, equals, 0
14x-14y=714x−14y=714, x, minus, 14, y, equals, 7 -2x+2y=1−2x+2y=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.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

there are infinitely many solutions.

answer: two angles are called supplementary if they add up to 180°. example: the two angles (140° and 40°) are supplementary because they add up to 180°.

step-by-step explanation: