Answer:
The equation of the line is
Step-by-step explanation:
Equation of a line is
Where m is the slope
c is the y intercept
y = 2x + 3
Comparing with the above formula
m is 2
Since the lines are perpendicular the slope of the other line is the negative inverse of the original line .
That's
m = - 1/2
Equation of the line using point (1,2) and slope - 1/2 is
y - 2 = -1/2(x - 1)
y - 2 = -1/2x + 1/2
y = -1/2x + 1/2 + 2
The final answer is
Hope this helps you.
I'm guessing the % of syrup refers to the % of sugar it has, therefore:
50% = 50 / 100 = 0.5
0.5 * x = 0.5
x = 0.5/0.5
x = 1
She will have 1 lbs of syrup
Right side:
(1/27)^(2x+10)
=(3^-3)^(2x+10)
= 3^(-6x - 30)
Re-write both sides:
3^(4x-5) = 3^(-6x - 30)
from here, you can solve x
4x - 5 = -6x - 30
4x + 6x = -30 + 5
10x = -25
x = -2.5
Domain: x≤5 (notice the closed dot on the right and the arrow on the left)
Range: y≤2 (notice the closed dot on the right and the arrow on the left)
The arrow means it keeps going infinitely. The closed dot means it stops there but is inclusive of that value.
The solution depends on the value of
. To make things simple, assume
. The homogeneous part of the equation is
and has characteristic equation
which admits the characteristic solution
.
For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be
. Then
So you have
This means
and so the general solution would be
