A regular pentagon with sides each measuring 6 inches is dilated by a scale factor of 3.1. What is the length of each side of the dilated pentagon?

18.6inches

Step-by-step explanation:

Given the length of a side of a pentagon to be 6 inches.

If this length is dilated by a factor of 3.1, the new length will be;

New length = Old length * dilation factor

New length = 6 * 3.1

New length = 18.6inches

Hence the length of each side of the dilated pentagon is 18.6inches

infinitely many solutions

step-by-step explanation:

we have been given the equation;

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

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

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

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions