Let's evaluate the given expressions to determine which one has a value of 35 for a specific value of [tex]\( p \)[/tex].
1. Expression: [tex]\(\frac{49}{p}\)[/tex]
[tex]\[
\frac{49}{p} = 35
\][/tex]
Solving for [tex]\( p \)[/tex]:
[tex]\[
49 = 35p \implies p = \frac{49}{35} \implies p = 1.4
\][/tex]
So, when [tex]\( p = 1.4 \)[/tex], [tex]\(\frac{49}{p} = 35\)[/tex].
2. Expression: [tex]\(5p\)[/tex]
[tex]\[
5p = 35
\][/tex]
Solving for [tex]\( p \)[/tex]:
[tex]\[
p = \frac{35}{5} \implies p = 7
\][/tex]
So, when [tex]\( p = 7 \)[/tex], [tex]\(5p = 35\)[/tex].
3. Expression: [tex]\(45 - p\)[/tex]
[tex]\[
45 - p = 35
\][/tex]
Solving for [tex]\( p \)[/tex]:
[tex]\[
p = 45 - 35 \implies p = 10
\][/tex]
So, when [tex]\( p = 10 \)[/tex], [tex]\(45 - p = 35\)[/tex].
4. Expression: [tex]\(25 + p\)[/tex]
[tex]\[
25 + p = 35
\][/tex]
Solving for [tex]\( p \)[/tex]:
[tex]\[
p = 35 - 25 \implies p = 10
\][/tex]
So, when [tex]\( p = 10 \)[/tex], [tex]\(25 + p = 35\)[/tex].
Therefore, each of the given expressions can have a value of 35 for specific values of [tex]\( p \)[/tex]:
- For [tex]\(\frac{49}{p}\)[/tex], [tex]\( p = 1.4 \)[/tex]
- For [tex]\(5p\)[/tex], [tex]\( p = 7 \)[/tex]
- For [tex]\(45 - p\)[/tex], [tex]\( p = 10 \)[/tex]
- For [tex]\(25 + p\)[/tex], [tex]\( p = 10 \)[/tex]
All expressions can result in the value 35 when the appropriate value for [tex]\( p \)[/tex] is used.
