The equations of three lines are given below. Line 1: 2y = 3x+7
Line 2: 4x-6y=-2
3
Line 3: y==x-4
For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2:
O Parallel
O Perpendicular O Neither
Х
?
Line 1 and Line 3: O Parallel O Perpendicular ONeither
Line 2 and Line 3:
O Parallel Operpendicular ONeither

a) Neither

b) parallel

Two slopes are L₁  and L₃ is equal

∴ L₁  and L₃ are parallel lines

c) neither

Step-by-step explanation:

Step(i):-

Given that the Line 1

                         2 y = 3x+7

                              ...(i)

comparing       y = m x +c

               here  

Given that the Line 2

                     4x-6y =-2

                     4x +2 =6y

                      ...(ii)

                 m =

The two lines are not parallel or perpendicular

Step(ii):-

     Given that line 3    

                 ...(iii)

     here  

Two slopes are L₁  and L₃ is equal

∴ L₁  and L₃ are parallel lines

Step(iii):-

        ...(ii)

         ...(iii)

L₂  and L₃ arenot  parallel lines and not perpendicular

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)