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2 answers:
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We have that
A(-2,-4) B(8,1) <span>
let
M-------> </span><span>the coordinate that divides the directed line segment from A to B in the ratio of 2 to 3
we know that
A--------------M----------------------B
2 3
distance AM is equal to (2/5) AB
</span>distance MB is equal to (3/5) AB
<span>so
step 1
find the x coordinate of point M
Mx=Ax+(2/5)*dABx
where
Mx is the x coordinate of point M
Ax is the x coordinate of point A
dABx is the distance AB in the x coordinate
Ax=-2
dABx=(8+2)=10
</span>Mx=-2+(2/5)*10-----> Mx=2
step 2
find the y coordinate of point M
My=Ay+(2/5)*dABy
where
My is the y coordinate of point M
Ay is the y coordinate of point A
dABy is the distance AB in the y coordinate
Ay=-4
dABy=(1+4)=5
Mx=-4+(2/5)*5-----> My=-2
the coordinates of point M is (2,-2)
see the attached figure
A(-2,-4) B(8,1) <span>
let
M-------> </span><span>the coordinate that divides the directed line segment from A to B in the ratio of 2 to 3
we know that
A--------------M----------------------B
2 3
distance AM is equal to (2/5) AB
</span>distance MB is equal to (3/5) AB
<span>so
step 1
find the x coordinate of point M
Mx=Ax+(2/5)*dABx
where
Mx is the x coordinate of point M
Ax is the x coordinate of point A
dABx is the distance AB in the x coordinate
Ax=-2
dABx=(8+2)=10
</span>Mx=-2+(2/5)*10-----> Mx=2
step 2
find the y coordinate of point M
My=Ay+(2/5)*dABy
where
My is the y coordinate of point M
Ay is the y coordinate of point A
dABy is the distance AB in the y coordinate
Ay=-4
dABy=(1+4)=5
Mx=-4+(2/5)*5-----> My=-2
the coordinates of point M is (2,-2)
see the attached figure
<span>Let C denote the number of candidates they interview and E the number of employees they train.
</span>
<span>If it takes 20 hours and $400 to interview a candidate, then it takes 20C hours and $400C to interview C candidates.
</span>
If <span>it takes 120 hours and $3600 to train an employee, then it takes 120E hours and $3600E to train E employees.
</span>
Company has less than <span>$95000, then 400C+3600E<95000.
</span>
Company <span>wants to spend at most 470 hours, then
.
</span>
<span>You obtain the system of two inequalities:
</span>
Then you can solve this system according to your demands.
</span>
<span>If it takes 20 hours and $400 to interview a candidate, then it takes 20C hours and $400C to interview C candidates.
</span>
If <span>it takes 120 hours and $3600 to train an employee, then it takes 120E hours and $3600E to train E employees.
</span>
Company has less than <span>$95000, then 400C+3600E<95000.
</span>
Company <span>wants to spend at most 470 hours, then
</span>
<span>You obtain the system of two inequalities:
</span>
Then you can solve this system according to your demands.