IDNLearn.com is designed to help you find the answers you need quickly and easily. Ask any question and receive comprehensive, well-informed responses from our dedicated team of experts.
Sagot :
To determine which ordered pairs [tex]\((x, y)\)[/tex] satisfy the inequality [tex]\(y > x^2 + 3x - 4\)[/tex], we need to check each pair by plugging the [tex]\(x\)[/tex] value into the quadratic expression [tex]\(x^2 + 3x - 4\)[/tex] and then comparing [tex]\(y\)[/tex] to the resulting value.
Let's check each pair step-by-step:
1. Pair [tex]\((0, 0)\)[/tex]:
[tex]\[ y = 0, \quad x = 0 \][/tex]
Substitute [tex]\(x = 0\)[/tex] into [tex]\(x^2 + 3x - 4\)[/tex]:
[tex]\[ 0^2 + 3 \cdot 0 - 4 = -4 \][/tex]
Now, compare [tex]\(y\)[/tex] with [tex]\(-4\)[/tex]:
[tex]\[ 0 > -4 \quad \text{(True)} \][/tex]
Therefore, [tex]\((0, 0)\)[/tex] satisfies the inequality.
2. Pair [tex]\((2, 1)\)[/tex]:
[tex]\[ y = 1, \quad x = 2 \][/tex]
Substitute [tex]\(x = 2\)[/tex] into [tex]\(x^2 + 3x - 4\)[/tex]:
[tex]\[ 2^2 + 3 \cdot 2 - 4 = 4 + 6 - 4 = 6 \][/tex]
Now, compare [tex]\(y\)[/tex] with 6:
[tex]\[ 1 > 6 \quad \text{(False)} \][/tex]
Therefore, [tex]\((2, 1)\)[/tex] does not satisfy the inequality.
3. Pair [tex]\((-2, -1)\)[/tex]:
[tex]\[ y = -1, \quad x = -2 \][/tex]
Substitute [tex]\(-2\)[/tex] into [tex]\(x^2 + 3x - 4\)[/tex]:
[tex]\[ (-2)^2 + 3 \cdot (-2) - 4 = 4 - 6 - 4 = -6 \][/tex]
Now, compare [tex]\(y\)[/tex] with [tex]\(-6\)[/tex]:
[tex]\[ -1 > -6 \quad \text{(True)} \][/tex]
Therefore, [tex]\((-2, -1)\)[/tex] satisfies the inequality.
4. Pair [tex]\((-5, -1)\)[/tex]:
[tex]\[ y = -1, \quad x = -5 \][/tex]
Substitute [tex]\(-5\)[/tex] into [tex]\(x^2 + 3x - 4\)[/tex]:
[tex]\[ (-5)^2 + 3 \cdot (-5) - 4 = 25 - 15 - 4 = 6 \][/tex]
Now, compare [tex]\(y\)[/tex] with 6:
[tex]\[ -1 > 6 \quad \text{(False)} \][/tex]
Therefore, [tex]\((-5, -1)\)[/tex] does not satisfy the inequality.
After evaluating each pair, the pairs that satisfy the inequality [tex]\(y > x^2 + 3x - 4\)[/tex] are:
[tex]\[ (0, 0) \quad \text{and} \quad (-2, -1) \][/tex]
Thus, the selected pairs are [tex]\((0, 0)\)[/tex] and [tex]\((-2, -1)\)[/tex].
Let's check each pair step-by-step:
1. Pair [tex]\((0, 0)\)[/tex]:
[tex]\[ y = 0, \quad x = 0 \][/tex]
Substitute [tex]\(x = 0\)[/tex] into [tex]\(x^2 + 3x - 4\)[/tex]:
[tex]\[ 0^2 + 3 \cdot 0 - 4 = -4 \][/tex]
Now, compare [tex]\(y\)[/tex] with [tex]\(-4\)[/tex]:
[tex]\[ 0 > -4 \quad \text{(True)} \][/tex]
Therefore, [tex]\((0, 0)\)[/tex] satisfies the inequality.
2. Pair [tex]\((2, 1)\)[/tex]:
[tex]\[ y = 1, \quad x = 2 \][/tex]
Substitute [tex]\(x = 2\)[/tex] into [tex]\(x^2 + 3x - 4\)[/tex]:
[tex]\[ 2^2 + 3 \cdot 2 - 4 = 4 + 6 - 4 = 6 \][/tex]
Now, compare [tex]\(y\)[/tex] with 6:
[tex]\[ 1 > 6 \quad \text{(False)} \][/tex]
Therefore, [tex]\((2, 1)\)[/tex] does not satisfy the inequality.
3. Pair [tex]\((-2, -1)\)[/tex]:
[tex]\[ y = -1, \quad x = -2 \][/tex]
Substitute [tex]\(-2\)[/tex] into [tex]\(x^2 + 3x - 4\)[/tex]:
[tex]\[ (-2)^2 + 3 \cdot (-2) - 4 = 4 - 6 - 4 = -6 \][/tex]
Now, compare [tex]\(y\)[/tex] with [tex]\(-6\)[/tex]:
[tex]\[ -1 > -6 \quad \text{(True)} \][/tex]
Therefore, [tex]\((-2, -1)\)[/tex] satisfies the inequality.
4. Pair [tex]\((-5, -1)\)[/tex]:
[tex]\[ y = -1, \quad x = -5 \][/tex]
Substitute [tex]\(-5\)[/tex] into [tex]\(x^2 + 3x - 4\)[/tex]:
[tex]\[ (-5)^2 + 3 \cdot (-5) - 4 = 25 - 15 - 4 = 6 \][/tex]
Now, compare [tex]\(y\)[/tex] with 6:
[tex]\[ -1 > 6 \quad \text{(False)} \][/tex]
Therefore, [tex]\((-5, -1)\)[/tex] does not satisfy the inequality.
After evaluating each pair, the pairs that satisfy the inequality [tex]\(y > x^2 + 3x - 4\)[/tex] are:
[tex]\[ (0, 0) \quad \text{and} \quad (-2, -1) \][/tex]
Thus, the selected pairs are [tex]\((0, 0)\)[/tex] and [tex]\((-2, -1)\)[/tex].
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com is your source for precise answers. Thank you for visiting, and we look forward to helping you again soon.
The Campers In Cabin A Walked 1/4 Of The Way To Otter Ridge (13 Miles) How Many Miles Did They Walk?