Identify the terms in the expression 2v2 +2v

The expression given is \(2v^2 + 2v\).

The terms in this expression are:

1. \(2v^2\)
2. \(2v\)

Now, let's identify which of the provided responses correspond to the terms in the expression:

- **2v^2** (This is the first term.)
- **2 v squared** (This is another way of writing the first term.)
- **2v** (This is the second term.)

The remaining options, "2" and "v", do not represent complete terms on their own in the context of this expression, although "v" is part of the term "2v".

Therefore, the correct responses from the options provided are:

- **2v^2**
- **2 v squared**
- **2v**

Select all that apply.

Simplify the expression using the order of operations.

(18−2)+((16)√)6−22
(
18
−
2
)
+
(
(
16
)
)
6
−
2
2


(1 point)
Responses

6
6

5
5

10
10

9

Let's simplify the expression step-by-step using the order of operations (PEMDAS/BODMAS):

The expression provided is:

\[
(18 - 2) + (16) \sqrt{6} - 22
\]

1. **Calculate inside the parentheses**:
\[
18 - 2 = 16
\]
So, the expression now becomes:
\[
16 + 16\sqrt{6} - 22
\]

2. **Now compute the remaining addition and subtraction**:
\[
16 - 22 = -6
\]
Therefore, the expression is now:
\[
-6 + 16\sqrt{6}
\]

At this stage, \(16\sqrt{6}\) is a term and cannot be further simplified without a numeric approximation for \(\sqrt{6}\). However, based on the options provided (which seem to be single-digit numbers), we should find the approximate value of the expression:

Since \(\sqrt{6} \approx 2.45\):
\[
16\sqrt{6} \approx 16 \times 2.45 = 39.2
\]

So we calculate:
\[
-6 + 39.2 \approx 33.2
\]

Given the potential answer choices you've provided (6, 5, 10, 9), it appears there may be an error in the expression or answer choices. Based on the simplified evaluation, none of the options directly correspond to the resultant value.

Would you like to verify the expression? Let me know if there’s anything specific you need!

whats the answer

Let's simplify the expression step-by-step again clearly without confusion.

The expression you provided is:

\[
(18 - 2) + (16) \sqrt{6} - 22
\]

1. **Calculate inside the parentheses**:
\[
18 - 2 = 16
\]
So the expression becomes:
\[
16 + 16\sqrt{6} - 22
\]

2. **Combine the constants**:
\[
16 - 22 = -6
\]
Now, the expression looks like:
\[
-6 + 16\sqrt{6}
\]

Given the nature of the expression, it represents a combination of a constant (-6) and a term involving \(\sqrt{6}\). However, this might not yield a single answer among 6, 5, 10, or 9.

If you would like me to choose from the options based on how they might relate to components of the expression, here’s a final analysis:

1. The term \(16\sqrt{6}\) is the dominant component and is approximately 39.2, so it does not yield an option close to 5, 6, 9, or 10.
2. Hence, it seems the original expression might need to be clearer, as neither constant \(-6\) nor \(16\sqrt{6}\) evaluates to any of the options provided.

If the expression needed was different or if you were looking for a specific calculation or context, please clarify! As it stands, an exact match does not exist among the options.

Using the Associative Property, which of the following expressions is equivalent to (4+17v)+4v ?(1 point)

Responses

21v2 +4
21
𝑣
2

+
4
21v2 +4
21
𝑣
2

+
4

(17v+4)+4v
(17v+4)+4v

4 + (17v + 4v)

To determine which of the given expressions is equivalent to \( (4 + 17v) + 4v \) using the Associative Property, we need to understand the Associative Property of addition, which states that the way in which numbers are grouped does not change their sum. In other words, \( (a + b) + c = a + (b + c) \).

Starting with the expression:

\[
(4 + 17v) + 4v
\]

We can regroup the terms using the Associative Property:

1. **First option:** \( 21v^2 + 4 \)

- This is not equivalent as it suggests a different operation.

2. **Second option:** \( (17v + 4) + 4v \)

- This simply rearranges the terms in a different grouping, which is valid under the Associative Property:
\[
(4 + 17v) + 4v = (17v + 4) + 4v
\]
This option stays true to the Associative Property.

3. **Third option:** \( 4 + (17v + 4v) \)

- This also reorders the terms correctly. According to the Associative Property:
\[
(4 + 17v) + 4v = 4 + (17v + 4v)
\]
This expression is indeed equivalent.

### Summary:
Both the second option \( (17v + 4) + 4v \) and the third option \( 4 + (17v + 4v) \) are equivalent to the original expression by the Associative Property.

So, the correct responses are:

- **(17v + 4) + 4v**
- **4 + (17v + 4v)**

If you have to select only one or one set, confirm the instruction whether it’s asking for all valid options or more specifically, just one!

Using both the Commutative and Associate Properties, determine whether the following two expressions are equivalent:

Expression 1: (3b+1)+10b+9
(
3
𝑏
+
1
)
+
10
𝑏
+
9


Expression 2: 13b +9
13
𝑏

+
9


(1 point)
Responses

The expressions are equivalent
The expressions are equivalent

The expressions are NOT equivalent

To determine whether the two expressions are equivalent using the Commutative and Associative properties, let's simplify both expressions step by step.

#### Expression 1:
\[
(3b + 1) + 10b + 9
\]

1. **Using the Associative Property** to group the terms:
\[
(3b + 10b + 1 + 9)
\]

2. **Simplify \(3b + 10b\)**:
\[
3b + 10b = 13b
\]

3. **Combine the constants \(1 + 9\)**:
\[
1 + 9 = 10
\]

So, Expression 1 simplifies to:
\[
13b + 10
\]

#### Expression 2:
\[
13b + 9
\]

#### Comparison:
Now, let's compare the simplified expressions:
- Expression 1 simplifies to: \(13b + 10\)
- Expression 2 is: \(13b + 9\)

Since \(13b + 10 \neq 13b + 9\), the two expressions are **not equivalent**.

### Final Answer:
The expressions are **NOT equivalent**.

Use the FOIL method to multiply the following binomials: (x+2)(x−1)

(
𝑥
+
2
)
(
𝑥
−
1
)
(1 point)
Responses

2x2+x+2
2
𝑥
2
+
𝑥
+
2
2 x squared plus x plus 2

x2+x−2
𝑥
2
+
𝑥
−
2
x squared plus x minus 2

x2−x−2
𝑥
2
−
𝑥
−
2
x squared minus x minus 2

x2+2x+2

To multiply the binomials \((x + 2)(x - 1)\) using the FOIL method (First, Outside, Inside, Last), we proceed as follows:

1. **First**: Multiply the first terms in each binomial:
\[
x \cdot x = x^2
\]

2. **Outside**: Multiply the outer terms:
\[
x \cdot (-1) = -x
\]

3. **Inside**: Multiply the inner terms:
\[
2 \cdot x = 2x
\]

4. **Last**: Multiply the last terms in each binomial:
\[
2 \cdot (-1) = -2
\]

Now, combine all these results:
\[
x^2 - x + 2x - 2
\]

Combine the like terms:
\[
x^2 + (-x + 2x) - 2 = x^2 + x - 2
\]

Thus, the product of \((x + 2)(x - 1)\) is:
\[
x^2 + x - 2
\]

Based on your options, the correct response is:

**x² + x − 2**.