which of the ff. coordinates of points belong to the solution set of the inequality y<3x^2+3x-6?
a)(-1,2)
b)(1,-2)
c)(-2,7)
d)(-1,1)
just plug in the values and see. For example, take (1,-2). Is
3*1 + 3*1 - 6 < -2 ?
0 < -2 ?
No.
Now try the others.
To determine which of the coordinates belong to the solution set of the inequality y < 3x^2 + 3x - 6, we need to substitute the x and y values of each point into the inequality and see if the inequality holds true.
Let's go through each option:
a) (-1, 2):
Substituting x = -1 and y = 2 into the inequality:
2 < 3(-1)^2 + 3(-1) - 6
2 < 3(1) - 3 - 6
2 < 3 - 3 - 6
2 < -3 - 6
2 < -9
Since 2 is not less than -9, (-1, 2) does not belong to the solution set.
b) (1, -2):
Substituting x = 1 and y = -2 into the inequality:
-2 < 3(1)^2 + 3(1) - 6
-2 < 3(1) + 3 - 6
-2 < 3 + 3 - 6
-2 < 6 - 6
-2 < 0
Since -2 is less than 0, (1, -2) belongs to the solution set.
c) (-2, 7):
Substituting x = -2 and y = 7 into the inequality:
7 < 3(-2)^2 + 3(-2) - 6
7 < 3(4) - 6 - 6
7 < 12 - 6 - 6
7 < 6
Since 7 is not less than 6, (-2, 7) does not belong to the solution set.
d) (-1, 1):
Substituting x = -1 and y = 1 into the inequality:
1 < 3(-1)^2 + 3(-1) - 6
1 < 3(1) - 3 - 6
1 < 3 - 3 - 6
1 < 0 - 6
1 < -6
Since 1 is not less than -6, (-1, 1) does not belong to the solution set.
Therefore, the only coordinate that belongs to the solution set is (1, -2) from option b.
To determine which of the given coordinates belong to the solution set of the inequality y < 3x^2 + 3x - 6, we will substitute the x and y values into the inequality and check if the inequality is satisfied.
Let's go through each coordinate one by one:
a) (-1, 2):
Substituting x = -1 and y = 2 into the inequality:
2 < 3(-1)^2 + 3(-1) - 6
2 < 3 + (-3) - 6
2 < 0 - 6
2 < -6
Since 2 is NOT less than -6, this point does NOT belong to the solution set.
b) (1, -2):
Substituting x = 1 and y = -2 into the inequality:
-2 < 3(1)^2 + 3(1) - 6
-2 < 3 + 3 - 6
-2 < 6 - 6
-2 < 0
Since -2 is less than 0, this point DOES belong to the solution set.
c) (-2, 7):
Substituting x = -2 and y = 7 into the inequality:
7 < 3(-2)^2 + 3(-2) - 6
7 < 3(4) + (-6) - 6
7 < 12 - 6 - 6
7 < 12 - 12
7 < 0
Since 7 is NOT less than 0, this point does NOT belong to the solution set.
d) (-1, 1):
Substituting x = -1 and y = 1 into the inequality:
1 < 3(-1)^2 + 3(-1) - 6
1 < 3 + (-3) - 6
1 < 0 - 6
1 < -6
Since 1 is NOT less than -6, this point does NOT belong to the solution set.
So, the only coordinate that belongs to the solution set of the inequality y < 3x^2 + 3x - 6 is b) (1, -2).