(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.

ok

step-by-step explanation:

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.