A ladder 13 m long when set against the wall of house just reaches a window at a height of 12 m from the ground. How far is the lower end of the ladder from the base of the wall?

Let the ladder be AB=13m

Let the vertical height reached be AC=12m

Let the distance between the foot of the ladder and wall be BC= x meters

By Pythagoras Theorem,

(AB)^2=(AC)^2+(BC)^2

(13)^2=(12)^2+(x)^2

x^2=169-144

x^2=25

x = 5 meters

Therefore,the foot of the ladder is 5 m away from the wall.

Step-by-step explanation:

Hope this helps!!!

:))

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