The distance from the ground to where the ladder is touching the wall is 7 feet. The distance from the wall to the base of the ladder is 4 feet. What is
the length of the ladder?
wall
ladder

L=8.062 feet

Step-by-step explanation:

wall=7

distance=4

Pythagorean theorem

7^2+4^2=L^2

49+16=L^2

65=L^2

L=8.062 feet

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.