Answer :
To determine which expression is equivalent to [tex]\(2.5^2 - 3y\)[/tex], let's go through each option step by step.
1. Simplify the expression [tex]\(2.5^2 - 3y\)[/tex]:
- [tex]\(2.5^2 = 6.25\)[/tex].
- Therefore, the expression simplifies to [tex]\(6.25 - 3y\)[/tex].
Let's compare the simplified expression with each option:
2. Option (a): [tex]\(\frac{6.25}{(15,625)^{-y}}\)[/tex]
- This can be expressed as [tex]\(6.25 \times (15,625)^y\)[/tex].
- This does not match the form [tex]\(6.25 - 3y\)[/tex].
3. Option (b): [tex]\(6.25(2.5)^{3y}\)[/tex]
- This can be written as [tex]\(6.25 \times (2.5^3)^y\)[/tex].
- This is not comparable to [tex]\(6.25 - 3y\)[/tex].
4. Option (c): [tex]\(6.25 - (2.5)^{3y}\)[/tex]
- This subtracts the expression [tex]\((2.5)^{3y}\)[/tex] from 6.25.
- This form does not match [tex]\(6.25 - 3y\)[/tex].
5. Option (d): [tex]\(6.25(15,625)^{-y}\)[/tex]
- This is equivalent to [tex]\(6.25 / (15,625)^y\)[/tex].
- This form does not align with [tex]\(6.25 - 3y\)[/tex].
6. Option (e): [tex]\(\frac{6.25}{(15,625) - y}\)[/tex]
- This expression can be seen as [tex]\(\frac{6.25}{15,625} - y\)[/tex].
- It does not match the form of [tex]\(6.25 - 3y\)[/tex].
Upon reviewing all options, none of them is equivalent to [tex]\(6.25 - 3y\)[/tex]. Therefore, the answer is that none of the given options is equivalent to the expression [tex]\(2.5^2 - 3y\)[/tex].
1. Simplify the expression [tex]\(2.5^2 - 3y\)[/tex]:
- [tex]\(2.5^2 = 6.25\)[/tex].
- Therefore, the expression simplifies to [tex]\(6.25 - 3y\)[/tex].
Let's compare the simplified expression with each option:
2. Option (a): [tex]\(\frac{6.25}{(15,625)^{-y}}\)[/tex]
- This can be expressed as [tex]\(6.25 \times (15,625)^y\)[/tex].
- This does not match the form [tex]\(6.25 - 3y\)[/tex].
3. Option (b): [tex]\(6.25(2.5)^{3y}\)[/tex]
- This can be written as [tex]\(6.25 \times (2.5^3)^y\)[/tex].
- This is not comparable to [tex]\(6.25 - 3y\)[/tex].
4. Option (c): [tex]\(6.25 - (2.5)^{3y}\)[/tex]
- This subtracts the expression [tex]\((2.5)^{3y}\)[/tex] from 6.25.
- This form does not match [tex]\(6.25 - 3y\)[/tex].
5. Option (d): [tex]\(6.25(15,625)^{-y}\)[/tex]
- This is equivalent to [tex]\(6.25 / (15,625)^y\)[/tex].
- This form does not align with [tex]\(6.25 - 3y\)[/tex].
6. Option (e): [tex]\(\frac{6.25}{(15,625) - y}\)[/tex]
- This expression can be seen as [tex]\(\frac{6.25}{15,625} - y\)[/tex].
- It does not match the form of [tex]\(6.25 - 3y\)[/tex].
Upon reviewing all options, none of them is equivalent to [tex]\(6.25 - 3y\)[/tex]. Therefore, the answer is that none of the given options is equivalent to the expression [tex]\(2.5^2 - 3y\)[/tex].
