3d - 6 + 96 = 180
3d + 90 = 180
3d = 90
d = 30
So
<A = 4d - 20
<A = 4(30) - 20
<A = 120 - 20
<A = 100
Answer
<A = 100°
Step-by-step explanation:
9 (3y2 + 15y + 2y + 10)
9 ( 3y2 + 17y + 10)
27y2 + 153y + 90
If the two linear equations have the same slope (and different y-intercepts), the lines will be parallel. Since parallel lines never intersect, a system composed of two parallel lines will have NO solution (no intersection of the lines.
If we want to find when the population of species A will be equal to the population of species B, we need to see when the two equations for the population of each species are equal, ie. equate them and solve for t. Thus:
2000e^(0.05t) = 5000e^(0.02t)
(2/5)e^(0.05t) = e^(0.02t) (Divide each side by 5000)
2/5 = e^(0.02t) / e^(0.05t) (Divide each side by e^(0.05t))
2/5 = e^(-0.03t) (use: e^a / e^b = e^(a - b))
ln(2/5) = -0.03t (use: if b = a^c, then loga(b) = c )
t = ln(2/5) / -0.03 (Divide each side by -0.03)
= 30.54 (to two decimal places)
Therefor, the population of species A will be equal to the population of species B after 30.54 years.
I wasn't entirely sure about the rounding requirements so I've left it rounded to two decimal places.