For each point listed below, circle every inequality for wwhich it is a solution. (0,0). Y<=3/2x+3 2x+y<10 Y>-1 Explain
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write244 answers
starTop subjects are Math, Science, and Literature
Substitute 0 in for x and y into all inequalties. Simplify and determine if the inequality is true or false. If the inequality is true, then (0, 0) is part of the solution. If the inequality is false, then (0, 0) is not part of the solution.
y `<=` 3/2 x + 3
0 `<=` 3/2 * 0 + 3
0 `<=` 0 + 3
0 `<=` 0 true (0, 0) is part of the solution
3x + y < 10
3 * 0 + 0 < 10
0 + 0 < 10
0 < 10 true (0, 0) is part of the solution
y > -1
0 > -1 true (0, 0) is part of the solution
Answer:
The point (0, 0) is part of the solution to all three given inequalities because when substituted in for x and y, the resulting inequalities were all true.
Related Questions
- What is the limit of `(x^3+y^3)/(x^2+y^2)` as (x,y)-->(0,0)? I'm supposed to use polar...
- 1 Educator Answer
- Limit as (x,y) --> (0,0) for sin(x^2+y^2)/(x^2+y^2)
- 1 Educator Answer
- Solve the inequality (2x-1)(x+2)<0
- 1 Educator Answer
- InequalitySolve the inequality x^2 - 2x>0.
- 1 Educator Answer
- Solve the inequality : 2x+3 =< 13
- 2 Educator Answers
calendarEducator since 2011
write5,349 answers
starTop subjects are Math, Science, and Business
The request of the problem is vague, hence, supposing that you need to check if the coordinates `(0,0)` verify the given inequalities, you should substitute 0 for x and 0 for y such that:
`0 <= (3/2)*0 + 3 => 0 <= 3`
Notice that this inequality is invalid since 0`< 3 ` but `0 != 3` .
Substituting 0 for x and y in `2x+y<10` yields:
`2*0 + 0 < 10 => 0 < 10`
Hence, the inequality holds for `(0,0).`
Substituting 0 for y in `y>-1` yields:
`0>-1`
Hence, the inequality holds for `y=0` and it not depends on x, hence, x can have all real values.
Hence, checking if the coordinates of the point `(0,0)` verify the given inequalities yields that the inequality `2x+y<10 ` holds for `(0,0).`