Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Let's analyze the problem step by step.
1. Define the Variables:
- Let [tex]\( c \)[/tex] represent Central's score before they scored a three-pointer.
- Eastern's score before the three-pointer is then [tex]\( 2c \)[/tex] since they had double the score of Central.
2. Calculate Central's Final Score:
- Central scored a three-pointer just as the game ended. Therefore, their final score is [tex]\( c + 3 \)[/tex].
3. Calculate the Total Score in the Game:
- The total score in the game is the sum of Central's score after the three-pointer and Eastern's score.
- Central's final score is [tex]\( c + 3 \)[/tex].
- Eastern's score is [tex]\( 2c \)[/tex].
- Therefore, the total score in the game can be expressed as:
[tex]\[ (c + 3) + 2c = 3c + 3 \][/tex]
4. Verify which Expressions Match the Total Score:
Now, we will compare the total score expression [tex]\( 3c + 3 \)[/tex] with the given expressions to find the matching ones.
- The first given expression is [tex]\( 2c + c \)[/tex]:
[tex]\[ 2c + c = 3c \][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The second given expression is [tex]\( 3c + 3 \)[/tex]:
[tex]\[ 3c + 3 \][/tex]
This matches our total score expression [tex]\( 3c + 3 \)[/tex].
- The third given expression is [tex]\( 2c + 3 \)[/tex]:
[tex]\[ 2c + 3 \][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The fourth given expression is [tex]\( 2c + c - 3 \)[/tex]:
[tex]\[ 2c + c - 3 = 3c - 3 \][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The fifth given expression is [tex]\( 2c - c + 3 \)[/tex]:
[tex]\[ 2c - c + 3 = c + 3 \][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The sixth given expression is [tex]\( 2c + c + 3 \)[/tex]:
[tex]\[ 2c + c + 3 = 3c + 3 \][/tex]
This matches our total score expression [tex]\( 3c + 3 \)[/tex].
Therefore, the matching expressions for the total score are [tex]\( 3c + 3 \)[/tex] and [tex]\( 2c + c + 3 \)[/tex].
To summarize:
- The total points scored in the game is expressed as [tex]\( 3c + 3 \)[/tex].
- The matching expressions are [tex]\( 3c + 3 \)[/tex] and [tex]\( 2c + c + 3 \)[/tex].
1. Define the Variables:
- Let [tex]\( c \)[/tex] represent Central's score before they scored a three-pointer.
- Eastern's score before the three-pointer is then [tex]\( 2c \)[/tex] since they had double the score of Central.
2. Calculate Central's Final Score:
- Central scored a three-pointer just as the game ended. Therefore, their final score is [tex]\( c + 3 \)[/tex].
3. Calculate the Total Score in the Game:
- The total score in the game is the sum of Central's score after the three-pointer and Eastern's score.
- Central's final score is [tex]\( c + 3 \)[/tex].
- Eastern's score is [tex]\( 2c \)[/tex].
- Therefore, the total score in the game can be expressed as:
[tex]\[ (c + 3) + 2c = 3c + 3 \][/tex]
4. Verify which Expressions Match the Total Score:
Now, we will compare the total score expression [tex]\( 3c + 3 \)[/tex] with the given expressions to find the matching ones.
- The first given expression is [tex]\( 2c + c \)[/tex]:
[tex]\[ 2c + c = 3c \][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The second given expression is [tex]\( 3c + 3 \)[/tex]:
[tex]\[ 3c + 3 \][/tex]
This matches our total score expression [tex]\( 3c + 3 \)[/tex].
- The third given expression is [tex]\( 2c + 3 \)[/tex]:
[tex]\[ 2c + 3 \][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The fourth given expression is [tex]\( 2c + c - 3 \)[/tex]:
[tex]\[ 2c + c - 3 = 3c - 3 \][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The fifth given expression is [tex]\( 2c - c + 3 \)[/tex]:
[tex]\[ 2c - c + 3 = c + 3 \][/tex]
Does not match [tex]\( 3c + 3 \)[/tex].
- The sixth given expression is [tex]\( 2c + c + 3 \)[/tex]:
[tex]\[ 2c + c + 3 = 3c + 3 \][/tex]
This matches our total score expression [tex]\( 3c + 3 \)[/tex].
Therefore, the matching expressions for the total score are [tex]\( 3c + 3 \)[/tex] and [tex]\( 2c + c + 3 \)[/tex].
To summarize:
- The total points scored in the game is expressed as [tex]\( 3c + 3 \)[/tex].
- The matching expressions are [tex]\( 3c + 3 \)[/tex] and [tex]\( 2c + c + 3 \)[/tex].
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
