Two different bacteria colonies begin with the same number of bacteria. The colony populations, P_(1) and P_(2), are modeled by the equations P_(1) = 100(2)^t and P_(2) = 100(5)^t where t is the time in hours. What describes the relation between P_(1) and P_(2) after 3 hours? PLEASE HELP ASAP!! I attached a picture of the original problem.

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4

using pemdas, (order of operations) you'll see the answer is 24.