Answer:
5x -7y = 21
Step-by-step explanation:
A sketch can convince you that BC is a transversal perpendicular to parallel lines AB and CD. The question asks for an equation for CD, so we just need to write the equation of a line through D that is parallel to AB.
One way to do this is to equate the slopes of the parallel lines:
∆y/∆x for AB = ∆y/∆x for CD
(y2 -y1)/(x2 -x1) = (y -2)/(x -7) . . . . . . where (x1, y1) = A; (x2, y2) = B; (7, 2) = D
(4 -(-1))/(1 -(-6)) = (y -2)/(x -7)
5(x -7) = 7(y -2) . . . . . . . . . . . . . cross multiply
5x -7y = 21 . . . . . . . . . . . . . . . . add 35 -7y, simplify
_____
Note that the graph shows the line CD is named "b", and its equation is shown at upper left. Multiplying that equation by -1 gives the one shown here.
Answer:
7
Step-by-step explanation:
5(x - 3) = 2(x + 3) Distribute
5x - 15 = 2x + 6
+ 15 + 15 Switch sides to the liked terms
5x = 2x + 6 + 15
-2x -2x Switch sides to the liked terms
5x - 2x = 6 + 15
<u>3x</u> = 21 Divide
3 3
x = 7
1 quarter note=2 eighth notes
1 eight note=2 sixteenth notes
so
1 quarter note=4 sixteenth note
so
times 3 both sides
3 quarter notes=12 sixteenth notes