Answer:
g(x) = (-1/25)x + (203/25)
Step-by-step explanation:
The general equation for a line is slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
We know that perpendicular lines have opposite-signed, reciprocal slopes of the original line. Therefore, if the slope of f(x) is m = 25, the slope of g(x) must be m = (-1/25).
To find the y-intercept, we can use the newfound slope and the values from the given point to isolate "b".
g(x) = mx + b <----- General equation
g(x) = (-1/25)x + b <----- Plug (-1/25) in "m"
8 = (-1/25)(3) + b <----- Plug in "x" and "y" from point
8 = (-3/25) + b <----- Multiply (1/25) and 3
200/25 = (-3/25) + b <----- Covert 8 to a fraction
203/25 = b <----- Add (3/25) to both sides
Now that we know both the values of the slope and y-intercept, we can construct the equation of g(x).
g(x) = (-1/25)x + (203/25)
Inversely proportional: z = k/r
k = 32 * 1.5 = 48
Plug that into equation
8 = 48/r
Multiply both sides by r
8r = 48
Divide by 8
r = 6
Easy, showing work,
using the method FOIL (First,Outer,Inner, Last)
Take, (x+3)(x+5) and multiply,
First,
x*x=
Outer,
x*5=5x
Inner,
3*x=3x
Last,
3*5=15
Add the terms together,
+8x+15 (
+5x+3x+15)
Thus, your answer.
