How do you solve 4x+1+7x=13+8x
1 answer:
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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
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
<u>The slope of line 1</u>
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
<u>The slope of line 2</u>
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.
The value of constant a is -5
Further explanation:
We will use the comparison of co-efficient method for finding the value of a
So,
Given
As it is given that
(x^2 - 3x + 4)(2x^2 +ax + 7) = 2x^4 -11x^3 +30x^2 -41x +28
In this case, co-efficient of variables will be equal, so we can compare the coefficients of x^3, x^2 or x
Comparing coefficient of x^3
So the value of constant a is -5
Keywords: Polynomials, factorization
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