Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Which of the following points is a solution of the inequality [tex]y \ \textless \ -|x|[/tex]?

A. [tex]\((1,0)\)[/tex]
B. [tex]\((1,-1)\)[/tex]
C. [tex]\((1,-2)\)[/tex]

Sagot :

GinnyAnswer
To determine which of the points is a solution to the inequality [tex]\( y < -|x| \)[/tex], we need to check each point against this inequality step-by-step.

### Check Point (1, 0)
1. For [tex]\( (1, 0) \)[/tex]:
- [tex]\( x = 1 \)[/tex]
- [tex]\( y = 0 \)[/tex]
- Calculate [tex]\( -|x| \)[/tex]: [tex]\( -|1| = -1 \)[/tex]
- Check if [tex]\( y < -|x| \)[/tex]: [tex]\( 0 < -1 \)[/tex]
- This is false.

### Check Point (1, -1)
2. For [tex]\( (1, -1) \)[/tex]:
- [tex]\( x = 1 \)[/tex]
- [tex]\( y = -1 \)[/tex]
- Calculate [tex]\( -|x| \)[/tex]: [tex]\( -|1| = -1 \)[/tex]
- Check if [tex]\( y < -|x| \)[/tex]: [tex]\( -1 < -1 \)[/tex]
- This is false.

### Check Point (1, -2)
3. For [tex]\( (1, -2) \)[/tex]:
- [tex]\( x = 1 \)[/tex]
- [tex]\( y = -2 \)[/tex]
- Calculate [tex]\( -|x| \)[/tex]: [tex]\( -|1| = -1 \)[/tex]
- Check if [tex]\( y < -|x| \)[/tex]: [tex]\( -2 < -1 \)[/tex]
- This is true.

After evaluating all the points, we see that the point [tex]\((1, -2)\)[/tex] satisfies the inequality [tex]\( y < -|x| \)[/tex].

Therefore, the point which is a solution of the inequality [tex]\( y < -|x| \)[/tex] is [tex]\((1, -2)\)[/tex].
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.