A rectangular dog pen is constructed using a barn wall as one side and 60 meters of fencing for the other three sides. What is the maximum area of the dog pen?

450 m^2

Step-by-step explanation:

let the length be y m (the single side)

let the width be x m

so according to the question

2x + y = 60

or, y = 60 - 2x

now, Area = xy

= x(60-2x)

= -2x^2 + 60x

d(Area)/dx = -4x + 60

= 0 for a max of area

-4x + 60 = 0

x = 15

then y = 30

the width has to be 15 m, and the length has to be 30 m for a maximum area of 15(30) or 450 m^2.

180-142=38 for the acute angle next to the entry

90+38=128

180-128=52

a=52

step-by-step explanation:

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.