Paul is locked out of his house. An 18-ft ladder is outside and an upstairs window is open. Paul read the safety warning on the ladder recommending it be placed six feet away from the wall. He placed the ladder according to the warning and it reached the base of the window. How high is the base of the window off the ground?

17.0 ft

Step-by-step explanation:

Let h be the height of the base of the window from the ground, L be the length of the ladder = 18 ft and d be the distance of the ladder from the wall = 6 ft. Now, these three lengths form a right-angled triangle with the length of the ladder, L as the hypotenuse side.

So, using Pythagoras' theorem,

L² = h² + d²

So, h = √(L² - d²)

Substituting the values of L = 18 ft and d = 6 ft, we have

h = √((18 ft)² - (6 ft)²)

= √(324 ft² - 36 ft²)

= √288 ft²

= 16.97 ft

≅ 17.0 ft

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.