In the expression \(2v^2 + 2v\), the terms are:
- \(2v^2\)
- \(2v\)
Each term consists of a coefficient (the number in front) and a variable raised to a power (in this case, \(v\) raised to either 2 or 1).
11 answers
In the expression \(2v^2 + 2v\), the terms are:
Each term consists of a coefficient (the number in front) and a variable raised to a power (in this case, \(v\) raised to either 2 or 1).
The terms in the expression \(2v^2 + 2v\) are:
These are the individual components that make up the expression.
The commutative property of multiplication states that the order of the factors does not change the product.
In your expression \((2 \cdot 3n) + 11\), we can rearrange the multiplication using the commutative property:
\[ (3 \cdot 2n) + 11 \]
This rewritten expression maintains the same value but changes the order of the factors in the multiplication.
To determine which expressions are equivalent to \((4 + 17v) + 4v\), we can simplify the original expression first:
\[ (4 + 17v) + 4v = 4 + 17v + 4v = 4 + (17v + 4v) = 4 + 21v \]
Now let's evaluate each provided answer choice:
A. \(21v^2 + 4\)
This is not equivalent because the original expression simplifies to \(4 + 21v\), and \(21v^2\) does not match \(21v\).
B. \((17v + 4) + 4v\)
This is equivalent. Reordering does not change the sum, and it can be simplified to \(4 + 17v + 4v = 4 + 21v\).
C. \(4 + (17v + 4v)\)
This is also equivalent. This expression simplifies directly to \(4 + 21v\).
So, the equivalent expressions are B and C.
I apologize for the confusion. Let's analyze the expressions again.
The original expression is:
\[ (4 + 17v) + 4v \]
We already simplified it to:
\[ 4 + 17v + 4v = 4 + 21v \]
Now let's check each option again for equivalence:
A. \(21v^2 + 4\)
This is not equivalent because it involves \(v^2\) instead of \(v\), and does not match \(4 + 21v\).
B. \((17v + 4) + 4v\)
This can be simplified to:
\[
(17v + 4) + 4v = 17v + 4 + 4v = 4 + 21v
\]
This is equivalent to the original expression.
C. \(4 + (17v + 4v)\)
This simplifies to:
\[
4 + (17v + 4v) = 4 + 21v
\]
This is also equivalent to the original expression.
Since you mention that there is only one answer, let’s clarify:
If you are looking for strictly one equivalent expression, it would be best to recognize that both B and C are equivalent to the original expression.
However, if you must choose only one based on the question format, it is common to take the first equivalent found in the order given.
Thus, the correct single answer under standard conventions would be B. Thank you for your patience!
To determine if the two expressions \((3b + 1) + 10b + 9\) and \(13b + 9\) are equivalent, we can simplify the first expression:
\[ 3b + 10b + 1 + 9 = (3b + 10b) + (1 + 9) = 13b + 10 \]
Now we compare this result to the second expression:
Since \(13b + 10\) is not equal to \(13b + 9\), the two expressions are not equivalent.