Let's break down each question based on the provided math expressions:
a. ( 3x - 2 = 81 )
b. ( y = 4x )
c. ( 2^x \geq 32 )
1. What is the similarity of (a), (b), and (c)?
- All three expressions involve variables (x or y) and constants or numbers (2, 3, 4, 81, 32). They are all equations or inequalities involving algebraic expressions.
2. What is the similarity of (a) and (c)?
- Both (a) and (c) involve the variable ( x ) and require solving for ( x ). However, (a) is a linear equation and (c) is an exponential inequality.
3. How do (a) and (c) differ from (b)?
- (a) and (c) are equations or inequalities involving ( x ), while (b) is an equation defining ( y ) in terms of ( x ).
4. How are (a) and (b) similar to each other?
- Both (a) and (b) are equations where \( x \) is involved. In (a), ( x ) is directly solved for, and in (b), ( y ) is expressed as a function of ( x ).
5. How do (a) and (b) differ from (c)?
- (c) involves an exponential expression ( 2^x ), which does not directly appear in (a) and (b). (a) and (b) are linear in nature, while (c) is exponential.
6. Can you recall which among them is an exponential function?
- Expression (c), ( 2^x \geq 32 ), is the exponential function because it involves the variable ( x ) as an exponent.
7. Which among the three is/are exponential expression/s?
- Only (c), ( 2^x \geq 32 ), is the exponential expression.
To summarize:
- (a) and (b) both involve linear relationships with ( x ).
- (c) involves an exponential relationship with ( x ).
- (a) and (c) involve solving for ( x ), but (a) is linear and (c) is exponential.
- (b) defines ( y ) in terms of ( x ) without explicitly solving for ( x ).
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