Answered

Join IDNLearn.com and become part of a knowledge-sharing community that thrives on curiosity. Ask your questions and get detailed, reliable answers from our community of knowledgeable experts.

Select the expressions that are equivalent to [tex]\( 5(5v + 8) + 8v \)[/tex].

[tex]\[
\begin{array}{c}
A. \ 5(8v + 5) + 8v \\
B. \ 33v + 8 \\
C. \ 8(5v + 5) + 8v \\
D. \ 33v + 40
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To determine which of these expressions are equivalent to [tex]\( 5(5v + 8) + 8v \)[/tex], we need to simplify each expression step by step and compare them with the original expression.

### Step-by-Step Simplification:

1. Simplify the original expression [tex]\( 5(5v + 8) + 8v \)[/tex]:

[tex]\( 5(5v + 8) = 25v + 40 \)[/tex]

[tex]\( 25v + 40 + 8v = 33v + 40 \)[/tex]

So, the simplified form of [tex]\( 5(5v + 8) + 8v \)[/tex] is [tex]\( 33v + 40 \)[/tex].

Now, let’s check each given expression to see if it simplifies to [tex]\( 33v + 40 \)[/tex].

2. Check [tex]\( 5(8v + 5) + 8v \)[/tex]:

[tex]\( 5(8v + 5) = 40v + 25 \)[/tex]

[tex]\( 40v + 25 + 8v = 48v + 25 \)[/tex]

This does not match [tex]\( 33v + 40 \)[/tex].

3. Check [tex]\( 33v + 8 \)[/tex]:

This is already simplified and does not match [tex]\( 33v + 40 \)[/tex].

4. Check [tex]\( 8(5v + 5) + 8v \)[/tex]:

[tex]\( 8(5v + 5) = 40v + 40 \)[/tex]

[tex]\( 40v + 40 + 8v = 48v + 40 \)[/tex]

This does not match [tex]\( 33v + 40 \)[/tex].

5. Check [tex]\( 33v + 40 \)[/tex]:

This is already simplified and it exactly matches [tex]\( 33v + 40 \)[/tex].

### Conclusion:

The expression that is equivalent to [tex]\( 5(5v + 8) + 8v \)[/tex] is:

[tex]\[ 33v + 40 \][/tex]

So, the correct selection is the fourth expression, [tex]\(\boxed{33v + 40}\)[/tex].
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.