Get detailed and reliable answers to your questions on IDNLearn.com. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.
Sagot :
To determine which points are solutions to the linear inequality [tex]\( y < 0.5x + 275 \)[/tex], we need to evaluate each point separately and see if it satisfies the inequality.
Let's go through each point:
1. Point [tex]\((-3, -2)\)[/tex]:
[tex]\[ y = -2 \quad \text{and} \quad 0.5x + 275 = 0.5(-3) + 275 = -1.5 + 275 = 273.5 \][/tex]
Check if [tex]\( -2 < 273.5 \)[/tex]:
[tex]\[ -2 \text{ is indeed less than } 273.5 \quad \text{(True)} \][/tex]
So, [tex]\((-3, -2)\)[/tex] satisfies the inequality.
2. Point [tex]\((-2, 1)\)[/tex]:
[tex]\[ y = 1 \quad \text{and} \quad 0.5x + 275 = 0.5(-2) + 275 = -1 + 275 = 274 \][/tex]
Check if [tex]\( 1 < 274 \)[/tex]:
[tex]\[ 1 \text{ is indeed less than } 274 \quad \text{(True)} \][/tex]
So, [tex]\((-2, 1)\)[/tex] satisfies the inequality.
3. Point [tex]\((-1, -2)\)[/tex]:
[tex]\[ y = -2 \quad \text{and} \quad 0.5x + 275 = 0.5(-1) + 275 = -0.5 + 275 = 274.5 \][/tex]
Check if [tex]\( -2 < 274.5 \)[/tex]:
[tex]\[ -2 \text{ is indeed less than } 274.5 \quad \text{(True)} \][/tex]
So, [tex]\((-1, -2)\)[/tex] satisfies the inequality.
4. Point [tex]\((-1, 2)\)[/tex]:
[tex]\[ y = 2 \quad \text{and} \quad 0.5x + 275 = 0.5(-1) + 275 = -0.5 + 275 = 274.5 \][/tex]
Check if [tex]\( 2 < 274.5 \)[/tex]:
[tex]\[ 2 \text{ is indeed less than } 274.5 \quad \text{(True)} \][/tex]
So, [tex]\((-1, 2)\)[/tex] satisfies the inequality.
5. Point [tex]\((1, -2)\)[/tex]:
[tex]\[ y = -2 \quad \text{and} \quad 0.5x + 275 = 0.5(1) + 275 = 0.5 + 275 = 275.5 \][/tex]
Check if [tex]\( -2 < 275.5 \)[/tex]:
[tex]\[ -2 \text{ is indeed less than } 275.5 \quad \text{(True)} \][/tex]
So, [tex]\((1, -2)\)[/tex] satisfies the inequality.
Based on this evaluation, all the given points satisfy the inequality [tex]\( y < 0.5x + 275 \)[/tex]. Therefore, any three of these points can be selected as solutions to the inequality:
Three valid options could be:
1. [tex]\((-3, -2)\)[/tex]
2. [tex]\((-2, 1)\)[/tex]
3. [tex]\((-1, 2)\)[/tex]
Let's go through each point:
1. Point [tex]\((-3, -2)\)[/tex]:
[tex]\[ y = -2 \quad \text{and} \quad 0.5x + 275 = 0.5(-3) + 275 = -1.5 + 275 = 273.5 \][/tex]
Check if [tex]\( -2 < 273.5 \)[/tex]:
[tex]\[ -2 \text{ is indeed less than } 273.5 \quad \text{(True)} \][/tex]
So, [tex]\((-3, -2)\)[/tex] satisfies the inequality.
2. Point [tex]\((-2, 1)\)[/tex]:
[tex]\[ y = 1 \quad \text{and} \quad 0.5x + 275 = 0.5(-2) + 275 = -1 + 275 = 274 \][/tex]
Check if [tex]\( 1 < 274 \)[/tex]:
[tex]\[ 1 \text{ is indeed less than } 274 \quad \text{(True)} \][/tex]
So, [tex]\((-2, 1)\)[/tex] satisfies the inequality.
3. Point [tex]\((-1, -2)\)[/tex]:
[tex]\[ y = -2 \quad \text{and} \quad 0.5x + 275 = 0.5(-1) + 275 = -0.5 + 275 = 274.5 \][/tex]
Check if [tex]\( -2 < 274.5 \)[/tex]:
[tex]\[ -2 \text{ is indeed less than } 274.5 \quad \text{(True)} \][/tex]
So, [tex]\((-1, -2)\)[/tex] satisfies the inequality.
4. Point [tex]\((-1, 2)\)[/tex]:
[tex]\[ y = 2 \quad \text{and} \quad 0.5x + 275 = 0.5(-1) + 275 = -0.5 + 275 = 274.5 \][/tex]
Check if [tex]\( 2 < 274.5 \)[/tex]:
[tex]\[ 2 \text{ is indeed less than } 274.5 \quad \text{(True)} \][/tex]
So, [tex]\((-1, 2)\)[/tex] satisfies the inequality.
5. Point [tex]\((1, -2)\)[/tex]:
[tex]\[ y = -2 \quad \text{and} \quad 0.5x + 275 = 0.5(1) + 275 = 0.5 + 275 = 275.5 \][/tex]
Check if [tex]\( -2 < 275.5 \)[/tex]:
[tex]\[ -2 \text{ is indeed less than } 275.5 \quad \text{(True)} \][/tex]
So, [tex]\((1, -2)\)[/tex] satisfies the inequality.
Based on this evaluation, all the given points satisfy the inequality [tex]\( y < 0.5x + 275 \)[/tex]. Therefore, any three of these points can be selected as solutions to the inequality:
Three valid options could be:
1. [tex]\((-3, -2)\)[/tex]
2. [tex]\((-2, 1)\)[/tex]
3. [tex]\((-1, 2)\)[/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. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.
