What is the length of the diagonal of a square of the square has a perimeter of 60 inches

15 sqrt(2)

Step-by-step explanation:

The perimeter of a square is given by

P = 4s  where s is the side length

60 = 4s

Divide each side by 4

60/4 = 4s/4

15 =s

The diagonal is the hypotenuse of the right triangle where the legs are the sides of length 15

Using the Pythagorean theorem

a^2 + b^2 = c^2

15^2 + 15^2 = c^2

225+225 = c^2

450 = c^2

Taking the square root of each side

sqrt(450) = sqrt( c^2)

sqrt (2*225) = c

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(2) sqrt(225) =c

sqrt(2) 15 = c

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.