Answer:
Step-by-step explanation:
Given two points are (-1,7) and (7,7).
We are told to find a point which is in between them at a ratio of 6:5.
Formula for calculating a point at distance of ratio m:n is given by
where are the inital and final points.
also m:n=6:5 ,
by substituting all the values we get,
Problem #2
We must find the solution to the following system of inequalities:
(1) We solve for y the first inequality:
Now, we multiply both sides of the inequality by (-1), this changes the signs on both sides and inverts the inequality symbol:
The solution to this inequality is the set of all the points (x, y) over the line:
This line has:
• slope m = 3/2,
,• y-intercept b = -2.
(2) We solve for y the second inequality:
The solution to this inequality is the set of all the points (x, y) below the line:
This line has:
• slope m = -1/3,
,• y-intercept b = 2.
(3) Plotting the lines of points (1) and (2), and painting the region:
• over the line from point (1),
,• and below the line from point (2),
we get the following graph:
AnswerThe points that satisfy both inequalities are given by the intersection of the blue and red regions:
