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A and B are constants such that the graphs of the lines 3x - 4y = 7 and 8x + Ay = B are perpendicular and intersect at (5,2). What is A+B?

 Apr 19, 2019
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A and B are constants such that the graphs of the lines 3x - 4y = 7 and 8x + Ay = B are perpendicular and intersect at (5,2). What is A+B?

 

 

Slope   of first line  =    3/4

Slope of second line = -4/3

 

Rearrange the second equation

Ay  = -8x+ B

y  =  (-8/A)x + B/A

Which implies that  -8/A =  -4/3   so    24 = 4A  ⇒  A = 6

 

And since (5,2) is on the both lines...then

 

(6) 2  = -8(5) + B

12 = -40 + B

52  = B

 

 

A + B  =   6 + 52  =  58

 

Here's a graph : https://www.desmos.com/calculator/4q0eh6wjme

 

 

cool cool cool

 Apr 19, 2019

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