(04.07) two separate bacteria populations grow each month and are represented by the functions f(x) = 3x and g(x) = 7x + 6. in what month is the f(x) population greater than the g(x) population? (2 points)

3x> 7x+6

subtract 7x from each side

-4x > 6

divide by -4  which causes the inequality sign to flip

x < -6/4

x < 2/3

The f(x) population stops being larger in the first month

Hello there!

Here we have two functions:

f(x) = 3x

g(x) = 7x + 6

We want to see in what month f(x) is bigger than g(x)

or

f(x) > g(x)

3x > 7x + 6

we can subtract 7x in both sides:

3x  - 7x > 7x + 6 - 7x

-4x > 6

Now, this means that x should be a negative number, this has no sense because if we are measuring if we put a negative number there, then we will end up with a negative number of population.

Then there is no month where f(x) is greater than g(x)

This also can be seen because g(x) has a positive intercept when g(x) has an intercept equal to zero, and because g(x) has a bigger slope, which means that grows faster than f(x) as the months passes.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.