Kate and Jean paint a house together in 6 days. If they work alone, Kate takes 5 fewer days than Jean would take to do the same job. Which equation represents the time it takes Kate to paint the house by herself? A. X^2-7x-30=0 B. X^2-5x-6=0 C. 2x-1=0 D. X^2-5x/6=0

Step-by-step explanation:

Let x = Time taken (in days) by Jean to do the job.

Then, Time taken by Kate to do the job = x-5

Then, together they will take time (t) as

 

.

Since it is given that Kate and Jean paint a house together in 6 days.

i.e.

So, the equation represents the time it takes Kate to paint the house by herself is .

We know that
point A( -2,4)
point B(0,-4)
point Z(0,2)

step 1
find the slope line AB
m=(y2-y1)/(x2-x1)> m=(-4-4)/(0+2)> m=-8/2---> m=-4

step 2
find the slope of the line perpendicular to AB

if two lines are perpendicular 
so
m1*m2=-1
m1=-4
m2=1/4

step 3
find the equation of the line perpendicular to AB that passes through point Z
m2=1/4  point z (0,2)
y-y1=m*(x-x1)> y-2=(1/4)*(x-0)---> y=0.25*x+2

step 4
analyze each point

case a) (-4,1)
for x=-4
y=0.25*-4+2> y=1
1 is equal to 1> this point is on the line

case b) (1,-2)
for x=1
y=0.25*1+2> y=2.25
2.25 is not -2> this point is not on the line

case c) (2,0)
for x=2
y=0.25*2+2> y=2.5
2.5 is not 0> this point is not on the line

case d)(4,4)
for x=4
y=0.25*4+2> y=3
3 is not 4> this point is not on the line
 

the answer is
the point (-4,1)