SAT Exam > SAT Questions > y≤ -15x + 3000y ≤ 5xIn the xyplane, if ...
Start Learning for Free
y ≤ -15x + 3000
y ≤ 5x
y ≤ 5x
In the xy‑plane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?
Correct answer is '750'. Can you explain this answer?
Most Upvoted Answer
y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates ...
The correct answer is 750. The inequalities y ≤ −15x + 3000 and y ≤ 5x can be graphed in the xy-plane.
They are represented by the half-planes below and include the boundary lines y = −15x + 3000 and y = 5x, respectively.
The solution set of the system of inequalities will be the intersection of these half-planes, including the boundary lines, and the solution (a, b) with the greatest possible value of b will be the point of intersection of the boundary lines.
The intersection of boundary lines of these inequalities can be found by setting them equal to each other: 5x = −15x + 3000, which has solution x = 150.
Thus, the x-coordinate of the point of intersection is 150.
Therefore, the y-coordinate of the point of intersection of the boundary lines is 5(150) = −15(150) + 3000 = 750.
This is the maximum possible value of b for a point (α, b) that is in the solution set of the system of inequalities.
They are represented by the half-planes below and include the boundary lines y = −15x + 3000 and y = 5x, respectively.
The solution set of the system of inequalities will be the intersection of these half-planes, including the boundary lines, and the solution (a, b) with the greatest possible value of b will be the point of intersection of the boundary lines.
The intersection of boundary lines of these inequalities can be found by setting them equal to each other: 5x = −15x + 3000, which has solution x = 150.
Thus, the x-coordinate of the point of intersection is 150.
Therefore, the y-coordinate of the point of intersection of the boundary lines is 5(150) = −15(150) + 3000 = 750.
This is the maximum possible value of b for a point (α, b) that is in the solution set of the system of inequalities.
|
Explore Courses for SAT exam
|
|
Similar SAT Doubts
Top Courses for SATView all
y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer?
Question Description
y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer?.
y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer?.
Solutions for y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer? in English & in Hindi are available as part of our courses for SAT.
Download more important topics, notes, lectures and mock test series for SAT Exam by signing up for free.
Here you can find the meaning of y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer?, a detailed solution for y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer? has been provided alongside types of y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice y≤ -15x + 3000y ≤ 5xIn the xyplane, if a point with coordinates (α,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b ?Correct answer is '750'. Can you explain this answer? tests, examples and also practice SAT tests.
|
|
Explore Courses for SAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup