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Answer :
Let's solve these questions step by step:
### Question 1:
You are asked to find the value of [tex]\( a \)[/tex] if the expression is equivalent to 30. Unfortunately, without additional details about the expression involving [tex]\( a \)[/tex], it is difficult to determine which number satisfies the condition since none of the options (4, 10, 8, 2) directly appear to match or helpfully clarify what is needed with only the information that the result should be 30.
### Question 2:
You need to find the value of [tex]\( x \)[/tex] that makes the expression [tex]\( 2 \sqrt{51x} \)[/tex] equivalent to [tex]\( 10 \sqrt{51} \)[/tex].
We can set up the equation as follows:
[tex]\[
2 \sqrt{51x} = 10 \sqrt{51}
\][/tex]
Divide both sides by [tex]\(\sqrt{51}\)[/tex]:
[tex]\[
2 \sqrt{x} = 10
\][/tex]
Then, divide both sides by 2:
[tex]\[
\sqrt{x} = 5
\][/tex]
To solve for [tex]\( x \)[/tex], square both sides:
[tex]\[
x = 5^2 = 25
\][/tex]
Therefore, the value for [tex]\( x \)[/tex] that satisfies the equation is [tex]\( 25 \)[/tex].
In conclusion, for question 2, the correct answer is [tex]\( x = 25 \)[/tex].
### Question 1:
You are asked to find the value of [tex]\( a \)[/tex] if the expression is equivalent to 30. Unfortunately, without additional details about the expression involving [tex]\( a \)[/tex], it is difficult to determine which number satisfies the condition since none of the options (4, 10, 8, 2) directly appear to match or helpfully clarify what is needed with only the information that the result should be 30.
### Question 2:
You need to find the value of [tex]\( x \)[/tex] that makes the expression [tex]\( 2 \sqrt{51x} \)[/tex] equivalent to [tex]\( 10 \sqrt{51} \)[/tex].
We can set up the equation as follows:
[tex]\[
2 \sqrt{51x} = 10 \sqrt{51}
\][/tex]
Divide both sides by [tex]\(\sqrt{51}\)[/tex]:
[tex]\[
2 \sqrt{x} = 10
\][/tex]
Then, divide both sides by 2:
[tex]\[
\sqrt{x} = 5
\][/tex]
To solve for [tex]\( x \)[/tex], square both sides:
[tex]\[
x = 5^2 = 25
\][/tex]
Therefore, the value for [tex]\( x \)[/tex] that satisfies the equation is [tex]\( 25 \)[/tex].
In conclusion, for question 2, the correct answer is [tex]\( x = 25 \)[/tex].
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