Answer:
You selected the correct answer: {x | x <<em> </em>-4 or x > 2}
Step-by-step explanation:
5(x - 2)(x + 4) > 0
Use FOIL method to expand (x - 2)(x + 4):
> 0
Distribute 5 into
> 0
Divide all terms by 5 from both sides of the inequality:
Factor the trinomial:
(x + 4) ( x - 2) > 0
x < -4 or x > -2
Therefore, the solution set to the inequality is {x | x < -4 or x > 2}
<em>Interval notation: </em>(-∞, -4) ∪ (2, ∞)
Answer:
q = 2
Step-by-step explanation:
0.5-0.125q=(q-1)/4
At first, we have to multiply both the sides by 4.
4 × (0.5 - 0.125q) = q - 1
or, 2 - 0.5q = q - 1
now, we change the side by taking constant into the right side and the number into the left side.
2 + 1 = q + 0.5q
or, 3 = q (1 + 0.5)
or, 3 = 1.5 q
or, 1.5 q = 3
or, = (3 ÷ 1.5) [Dividing both the sides by 1.5]
or, q = 2
Therefore, q = 2
Answer:
The population is of 500 after 10.22 hours.
Step-by-step explanation:
The rate of change of the population of a certain organism is proportional to the population at time t, in hours.
This means that the population can be modeled by the following differential equation:
In which r is the growth rate.
Solving by separation of variables, then integrating both sides, we have that:
Applying the exponential to both sides:
In which K is the initial population.
At time t = 0 hours, the population is 300.
This means that K = 300. So
At time t = 24 hours, the population is 1000.
This means that P(24) = 1000. We use this to find the growth rate. So
So
At what time t is the population 500?
This is t for which P(t) = 500. So
The population is of 500 after 10.22 hours.