which equation represents the line shown on the coordinates plane below? y= 4x, y= -4x, y=1/4 x, y= -1/4x

2(2x + 3) = -4 + 2(2x + 5)

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 6

4x - 6 + 6 = 4x - 6 + 6

4x = 4x

x = x

unlimited solutions.

answer-

the equation that models this pattern is

solution-

a researcher placed a petri dish with 32,000 bacterial cells. one hour after being placed in the vacuum chamber, the number of cells in the petri dish had halved. another hour later, the number of cells had again halved.

this can be represented as exponential decreasing function,

where,

putting the values,

y-intercept means, where x=0, so

the coordinate of this poin will be (0, 32000)

this means when x=0 or at the starting of the research, the number of bacteria cells was 32000.

after 3 hours, number of bacteria cells will be,

the   coordinate of this point will be (3, 4000)

we are given expression: and .

in order to find it's greatest common factor, let us break it into smaller parts.

let us find greatest common factor of 54 and 27 first.

54 = 27 × 2

27 = 27 × 1

now, let us find the greatest common factor of m and m^3.

now, let us find the greatest common factor of n^4 and n^2.

therefore, following expressions are part of the greatest common factor of 54mn^4 and 27m^3n^2.