A = first piece, b = second piece, c = third piece

a + b + c = 47
b = 3a
c = 5a + 2

a + (3a) + (5a + 2) = 47.....combine like terms
9a + 2 = 47
9a = 47 - 2
9a = 45
a = 45/9
a = 5 ft

b = 3a.....b = 3(5)....b = 15 ft
c = 5a + 2....c = 5(5) + 2.....c = 25 + 2....c = 27 ft

longest piece (c) = 27 ft

7 0

2 years ago

Y = 2/3 x -3 y = -3/2 x +2 what statement about the lines are true

Hoochie [10]

Answer:

The product of the slopes of lines is -1.

i.e. m₁ × m₂ = -1

Thus, the lines are perpendicular.

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

m is the slope

b is the y-intercept

Given the lines

y = 2/3 x -3 --- Line 1

y = -3/2x +2 --- Line 2

The slope of line 1

y = 2/3 x -3 --- Line 1

By comparing with the slope-intercept form of the line equation

The slope of line 1 is: m₁ = 2/3

The slope of line 2

y = -3/2x +2 --- Line 2

By comparing with the slope-intercept y = mx+b form of the line equation

The slope of line 2 is: m₂ = -3/2

We know that when two lines are perpendicular, the product of their slopes is -1.

Let us check the product of two slopes m₁ and m₂

m₁ × m₂ = (2/3)(-3/2 )

m₁ × m₂ = -1

Thus, the product of the slopes of lines is -1.

i.e. m₁ × m₂ = -1

Thus, the lines are perpendicular.

7 0

2 years ago