A 10 footTall ladder is placed against the wall so that the top of the latter is 9 feet above the ground how far is the base of the latter from the base of the wall along the ground explain or show your reasoning

The base of the ladder to the base of the wall is 4.4 ft

Step-by-step explanation: Please refer to the attached diagram.

If the ladder which measures ten feet is placed against the wall, it's going to tilt at a diagonal. This means the foot of the ladder would lie some distance away from the foot of the wall.

The wall is at a perpendicular with the ground. This also means that we have a right angled triangle. Two sides are known, according to the diagram. One is the hypotenuse (the side which is facing the right angle) which is ten feet, and the other is one of the remaining two sides which is nine feet.

To measure the distance from the foot of the ladder to the base of the wall, we apply the Pythagoras theorem which states that

AC² = AB² + BC²

Where AC is the hypotenuse and AB and BC are the other two sides

Therefore

10² = 9² + X²

100 = 81 + X²

Subtract 81 from both sides of the equation

19 = X²

Add the square root sign to both sides of the equation

√19 = X

X = 4.3589

Approximately, X = 4.4 ft

d

step-by-step explanation:

d

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4