Answer:
Step-by-step explanation:
The population P of a certain city can be modeled by
P=19000e0.0215t
where T represent the number of years since 2000.
When t=1 the year is 2001
when t =2 the year is 2002. This means that
When t=0 the year is 2000
To determine the year when the population will be 40,000 , we will substitute P = 40,000 and solve for t. It becomes
40000 = 19000e^0.0215t
40000 / 19000 = e^0.0215t
2.105 = e^0.0215t
Take ln of both sides
0.7443 = 0.0215t
t = 0.7443/0.0215
t = 34.62
Approximately 35 years
So the year will be 2035
This is a simultaneous system of two linear equations with two unknowns, as the number of unknowns equals the number of equations, we can solve it:
y = 5x + 21
y = -7x - 15
we can equate both equations, given the fact that both are equal to y:
y = y
5x + 21 = -7x - <span>15
</span>and solving for x:
5x + 7x = -15 - 21
12x = -36
x = -36/12
x = -3
then we substitute this result in the original equation:
y = 5x + <span>21
</span>y = 5(-3) + <span>21
</span>y = -15 + 21
y = 6
hence the solution is x = -3 and y = 6
Answer:
4.
Step-by-step explanation:
He starts off by distributing the 5 to the x and to the other 5.
This would be Distributive Property
Answer:Michael spent 53 1/4 hours
training.
Step-by-step explanation:
Over the course of four weeks Mia spent 35 1 2 hours training for a race. This can be written in decimal point as 35.5 hours.
Michael spent 1 1 2 times that amount training for the same race. Converting 1 1 2 to decimal, it becomes 1.5 hours.
This means that the number of hours that Michael spent training will be 35.5 × 1.5 = 53.25 hour.
Converting 53.25 hours to mixed fraction, it becomes
53 1/4 hours
