Question

Use the properties of operations to add 9(k+13)+10(12k−1)
9
(
𝑘
+
1
3
)
+
10
(
1
2
𝑘
−
1
)
.(1 point)
Responses

14k−23
14
𝑘
−
2
3
14 k minus Start Fraction 2 over 3 End Fraction

1912k−23
19
1
2
𝑘
−
2
3
19 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction

14k+13
14
𝑘
+
13
14 k plus 13

14k−7 ..

Answer 1

pick from the options ...

Answer 2

To simplify the expression \( 9(k + 13) + 10(12k - 1) \), we can follow these steps:

1. Distribute the coefficients (9 and 10) to the terms inside the parentheses.

\[
9(k + 13) = 9k + 117
\]
\[
10(12k - 1) = 120k - 10
\]

2. Now, we can combine these results:

\[
9k + 117 + 120k - 10
\]

3. Combine like terms:

- For the \( k \) terms: \( 9k + 120k = 129k \)
- For the constant terms: \( 117 - 10 = 107 \)

Thus, we have:

\[
129k + 107
\]

Now let's check the possible response options you provided:

- **14k − 23**
- **19(1/2)k − 2/3**
- **14k + 13**
- **14k − 7**

None of these options match our simplified expression of \( 129k + 107 \), indicating that there may be an error in the transcription or in the response options given.

However, based on the original expression you provided, the correctly simplified result is:

\[
129k + 107
\]

Answer 3

I apologize for the confusion. Based on the calculations, let's evaluate the options you provided:

1. **14k − 23**
2. **19(1/2)k − 2/3**
3. **14k + 13**
4. **14k − 7**

Since none of these options match \( 129k + 107 \), let's check the options to find the one that might come closest when simplified.

Starting by comparing the terms of the options:

1. **14k - 23**: This cannot be correct as it is far off.
2. **19(1/2)k - 2/3**: This simplifies to \( (19/2)k - 2/3 \), which is approximately \( 9.5k - 0.67 \), still not close.
3. **14k + 13**: This is too low for \( k \) terms.
4. **14k − 7**: This is also too low.

Since the exact simplified version we got isn't present among the options, I made an incorrect analysis assuming exact equality.

Given that we have to choose the closest possible response based on the calculation pattern:

If forced to choose one, the best option seems to be:

**14k − 7**

due to it having the \( k \) term prevalent. However, be mindful that none of the options provided are equivalent to the calculated expression \( 129k + 107 \).