First, we need to get the slope of the equation of the train tracks. We can transform the given equation into the slope-intercept form.
4x +2y = 16
y = -2x +8
The slope of the equation is -2.
A perpendicular line will have the same slope but the opposite sign.
So, the slope of the line of the train crossing is 2. Since, it will pass through the point (8,15), the slope-intercept form can also be used to solve for the equation.
y = mx + b
The slope is 2, so m=2. We solve b by substituting the coordinates.
15 = 2(8) +b
b = -11
The equation is now,
y = -2x - 11
Or it can also be expresses as:
2x - y = 11
The only factoring you need to do is already done for you:
<em>x</em>² + <em>x</em> - 12 = (<em>x</em> + 4) (<em>x</em> - 3)
What you're asked to do is decompose
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12)
into partial fractions, i.e. find <em>a</em> and <em>b</em> such that
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12) = <em>a</em> / (<em>x</em> + 4) + <em>b</em> / (<em>x</em> - 3)
Multiply both sides by <em>x</em>² + <em>x</em> - 12 :
3<em>x</em> - 4 = <em>a</em> (<em>x</em> - 3) + <em>b</em> (<em>x</em> + 4)
3<em>x</em> - 4 = (<em>a</em> + <em>b</em>) <em>x</em> + (-3<em>a</em> + 4<em>b</em>)
So we have
<em>a</em> + <em>b</em> = 3
-3<em>a</em> + 4<em>b</em> = -4
and solving this system gives
<em>a</em> = 16/7 and <em>b</em> = 5/7
so you should submit the numbers in bold:
(3<em>x</em> - 4) / (<em>x</em>² + <em>x</em> - 12) = 16 / (7 (<em>x</em> + 4)) + 5 / (7 (<em>x</em> - 3))
Answer:
x=−2y+6
Step-by-step explanation:
Step 1: Add -12 to both sides.
−2x+12+−12=4y+−12
−2x=4y−12
Step 2: Divide both sides by -2.
−2x /−2 = 4y−12/−2
x=−2y+6
You at the photos and what you see put it down and what you know put it down
