05-04-2010, 05:22 AM
Question # 1
Solve the inequality
Solution:
multipling by 2 two both sides
-10 < 4 - 3x < 4
Subtracting 4 from both sides
-14 < -3x < 0
Divide -3 from both sides
14 < x < 0
3
solution set is ( 0 , 14 / 3)
Question # 2
Show that (3,1), (6,3) and (2,9) are the vertices of a right triangle by using the Slopes form
Solution:
Given point= (x1,y1) = ( 3 , 1)
= (x2,y2) = ( 6 , 3)
= (x3, y3) = (2 , 9)
Slop formula is m = y2 – y1
x2 – x1
perpendicular lines = m1m2 = -1
then ,
m1 = ( 3- 1) / ( 6 - 3) = 2 / 3
m2 = ( 9 - 3) / (2 - 6) = 6 / - 4 = - 3 / 2
m3 = ( 9 - 1) / (2 - 3) = -8
m1 m2 = -1
( 2 / 3 ) ( -3 / 2 ) = -1
-1 = -1
Solve the inequality
Solution:
multipling by 2 two both sides
-10 < 4 - 3x < 4
Subtracting 4 from both sides
-14 < -3x < 0
Divide -3 from both sides
14 < x < 0
3
solution set is ( 0 , 14 / 3)
Question # 2
Show that (3,1), (6,3) and (2,9) are the vertices of a right triangle by using the Slopes form
Solution:
Given point= (x1,y1) = ( 3 , 1)
= (x2,y2) = ( 6 , 3)
= (x3, y3) = (2 , 9)
Slop formula is m = y2 – y1
x2 – x1
perpendicular lines = m1m2 = -1
then ,
m1 = ( 3- 1) / ( 6 - 3) = 2 / 3
m2 = ( 9 - 3) / (2 - 6) = 6 / - 4 = - 3 / 2
m3 = ( 9 - 1) / (2 - 3) = -8
m1 m2 = -1
( 2 / 3 ) ( -3 / 2 ) = -1
-1 = -1
