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Find the area of the region bounded by the line y=3x−6 and line y=−2x+8.

b) the x-axis.
pls help

1 Answer

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B = 12/5 units

We can find the intersection point between these two lines:

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5

Set both equations equal to 0.

(I) 0 = 3x - 6

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

Divide both sides of the equation by 2.

x = 4

Formula for the Area of a Triangle:

B = 1/2bh

Substitute 2 for b and 14/5 for h.

B = (1/2) · (2) · (12/5)

Multiply and simplify.

B = 12/5

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

I hope this helps! o(〃^▽^〃)o

User Ravi Bhatt
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