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Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended. The variable [tex]\( c \)[/tex] represents Central's score before the three-pointer.

Express the total points scored in the game as a variable expression. Check all that apply.

A. [tex]\(2c + c\)[/tex]

B. [tex]\(3c + 3\)[/tex]

C. [tex]\(2c + 3\)[/tex]

D. [tex]\(2c + c - 3\)[/tex]

E. [tex]\(2c - c + 3\)[/tex]

F. [tex]\(2c + c + 3\)[/tex]

Sagot :

GinnyAnsweridn
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].
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