the area of a square is 4x^2+12x+9. Write an expression to represent the length of the side of the square.

An expression to represent the length of the side of the square with an area of 4x^2+12x+9 in terms of x is 2x + 3

Step-by-step explanation:

all sides of a square are equal in length.

area of a square is the side length squared.

area a, side s, variable x.

a = 4x^2 + 12x + 9.   s = ?   x = ?

a = s^2.

a = 4x^2 + 12x + 9.

4x^2 + 12x + 9 = s^2.

x^2 + 3x + 9/4 = (s^2)/4.

factor x^2 + 3x + 9/4 = (s^2)/4.

(x + 3/2)(x + 3/2) = (s^2)/4.

(x + 3/2)^2 = (s^2)/4.

√((x + 3/2)^2) = √((s^2)/4).

take positive root.

x + 3/2 = s/2

solve for side s.

s/2 = x + 3/2

s = 2x + 3

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)