Find the perimeter of the triangle with vertices  d(3, 4),  e(8, 7), and  f(5, 9). do not round before calculating the perimeter. after calculating the perimeter, round your answer to the nearest tenth.  

14.6 to the nearest tenth.

Step-by-step explanation:

Length of DE = √([ 7-4)^2 + (8-3(^2] = √(34)

Length of EF = √([ 9-7)^2 + (5-8)^2] = √(13)

Length of FD = √([ 9-4)^2 + (5-3)^2] = √(27)

So the perimeter = √(34) +√(13) +  √(27)

= 14.63

= 14.6 to the nearest tenth.

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