Asked by Unknown no more
Use the properties of operations to add 9(k+13)+10(12k−1).(1 point)
Responses
14k−7
14k+13
19 1/2k−2/3
14k−2/3
Responses
14k−7
14k+13
19 1/2k−2/3
14k−2/3
Answers
Answered by
Unknown no more
sorry i meant "
Use the properties of operations to add 9(k+1/.3)+10(1/2k−1).
Use the properties of operations to add 9(k+1/.3)+10(1/2k−1).
Answered by
Unknown no more
Use the properties of operations to add 4(g−2)+(g+2).(1 point)
Responses
5g−6
5g+10
5g−10
5g
Responses
5g−6
5g+10
5g−10
5g
Answered by
Unknown no more
Use the properties of operations to subtract (h+k)−(2k−h).(1 point)
Responses
−k
2h−k
−2h−k
2h+k
Responses
−k
2h−k
−2h−k
2h+k
Answered by
Unknown no more
Use the properties of operations to subtract (p−3)−(2.4+2p).(1 point)
Responses
−p−5.4
3p−5.4
p−5.4
−p+5.4
Responses
−p−5.4
3p−5.4
p−5.4
−p+5.4
Answered by
Unknown no more
Subtract: 2(k−4)−3(2k−1).(1 point)
Responses
8k−11
−6k−18
−4k−11
−4k−5
Responses
8k−11
−6k−18
−4k−11
−4k−5
Answered by
GPT-4o mini
To simplify the expression \(9(k+13)+10(12k−1)\), we can use the properties of operations, specifically the distributive property.
1. Distribute \(9\) and \(10\):
\[
= 9k + 9 \cdot 13 + 10 \cdot 12k - 10 \cdot 1
\]
This results in:
\[
= 9k + 117 + 120k - 10
\]
2. Combine like terms:
Combine \(9k\) and \(120k\):
\[
9k + 120k = 129k
\]
Now combine the constant terms \(117\) and \(-10\):
\[
117 - 10 = 107
\]
3. Put it all together:
\[
= 129k + 107
\]
Thus, the final simplified expression is:
\[
129k + 107
\]
None of the responses you provided match the final result. Please check the options again or let me know if there are additional constraints or errors in the provided choices.
1. Distribute \(9\) and \(10\):
\[
= 9k + 9 \cdot 13 + 10 \cdot 12k - 10 \cdot 1
\]
This results in:
\[
= 9k + 117 + 120k - 10
\]
2. Combine like terms:
Combine \(9k\) and \(120k\):
\[
9k + 120k = 129k
\]
Now combine the constant terms \(117\) and \(-10\):
\[
117 - 10 = 107
\]
3. Put it all together:
\[
= 129k + 107
\]
Thus, the final simplified expression is:
\[
129k + 107
\]
None of the responses you provided match the final result. Please check the options again or let me know if there are additional constraints or errors in the provided choices.
Answered by
GPT-4o mini
Let's simplify the expression \(9(k + \frac{1}{3}) + 10(\frac{1}{2}k - 1)\) using the properties of operations, specifically the distributive property.
1. **Distribute \(9\) and \(10\):**
\[
9(k + \frac{1}{3}) = 9k + 9 \cdot \frac{1}{3} = 9k + 3
\]
\[
10(\frac{1}{2}k - 1) = 10 \cdot \frac{1}{2}k - 10 \cdot 1 = 5k - 10
\]
2. **Combine the results:**
Now we combine everything together:
\[
9k + 3 + 5k - 10
\]
3. **Combine like terms:**
Combine the \(k\) terms:
\[
9k + 5k = 14k
\]
Combine the constant terms:
\[
3 - 10 = -7
\]
4. **Final result:**
Putting it all together, we have:
\[
14k - 7
\]
Thus, the final simplified expression is \(14k - 7\). This matches the first response option you provided.
1. **Distribute \(9\) and \(10\):**
\[
9(k + \frac{1}{3}) = 9k + 9 \cdot \frac{1}{3} = 9k + 3
\]
\[
10(\frac{1}{2}k - 1) = 10 \cdot \frac{1}{2}k - 10 \cdot 1 = 5k - 10
\]
2. **Combine the results:**
Now we combine everything together:
\[
9k + 3 + 5k - 10
\]
3. **Combine like terms:**
Combine the \(k\) terms:
\[
9k + 5k = 14k
\]
Combine the constant terms:
\[
3 - 10 = -7
\]
4. **Final result:**
Putting it all together, we have:
\[
14k - 7
\]
Thus, the final simplified expression is \(14k - 7\). This matches the first response option you provided.
Answered by
GPT-4o mini
Let's simplify the expression \(4(g - 2) + (g + 2)\) using the properties of operations, particularly the distributive property.
1. **Distribute \(4\) in the first term:**
\[
4(g - 2) = 4g - 8
\]
2. **Write out the entire expression:**
\[
4g - 8 + (g + 2)
\]
3. **Combine like terms:**
Combine the \(g\) terms:
\[
4g + g = 5g
\]
Combine the constant terms:
\[
-8 + 2 = -6
\]
4. **Final result:**
Putting it all together, we get:
\[
5g - 6
\]
Therefore, the final simplified expression is \(5g - 6\), which corresponds to the first response option provided.
1. **Distribute \(4\) in the first term:**
\[
4(g - 2) = 4g - 8
\]
2. **Write out the entire expression:**
\[
4g - 8 + (g + 2)
\]
3. **Combine like terms:**
Combine the \(g\) terms:
\[
4g + g = 5g
\]
Combine the constant terms:
\[
-8 + 2 = -6
\]
4. **Final result:**
Putting it all together, we get:
\[
5g - 6
\]
Therefore, the final simplified expression is \(5g - 6\), which corresponds to the first response option provided.
Answered by
GPT-4o mini
Let's simplify the expression \((h + k) - (2k - h)\) using the properties of operations, particularly the distributive property and combining like terms.
1. **Rewrite the expression:**
We need to distribute the negative sign into the second term:
\[
(h + k) - (2k - h) = h + k - 2k + h
\]
2. **Combine like terms:**
Now, combine the \(h\) terms and the \(k\) terms:
\[
h + h = 2h
\]
\[
k - 2k = -k
\]
3. **Putting it all together:**
Combine the results:
\[
2h - k
\]
So, the final result of \((h + k) - (2k - h)\) is \(2h - k\).
Thus, the correct response is:
**2h − k**.
1. **Rewrite the expression:**
We need to distribute the negative sign into the second term:
\[
(h + k) - (2k - h) = h + k - 2k + h
\]
2. **Combine like terms:**
Now, combine the \(h\) terms and the \(k\) terms:
\[
h + h = 2h
\]
\[
k - 2k = -k
\]
3. **Putting it all together:**
Combine the results:
\[
2h - k
\]
So, the final result of \((h + k) - (2k - h)\) is \(2h - k\).
Thus, the correct response is:
**2h − k**.
Answered by
GPT-4o mini
Let's simplify the expression \((p - 3) - (2.4 + 2p)\) using the properties of operations.
1. **Rewrite the expression:**
Distribute the negative sign into the second term:
\[
(p - 3) - (2.4 + 2p) = p - 3 - 2.4 - 2p
\]
2. **Combine like terms:**
Now, combine the \(p\) terms and the constant terms:
- The \(p\) terms:
\[
p - 2p = -p
\]
- The constant terms:
\[
-3 - 2.4 = -5.4
\]
3. **Putting it all together:**
Combine the results:
\[
-p - 5.4
\]
So, the final result of \((p - 3) - (2.4 + 2p)\) is \(-p - 5.4\).
Thus, the correct response is:
**−p − 5.4**.
1. **Rewrite the expression:**
Distribute the negative sign into the second term:
\[
(p - 3) - (2.4 + 2p) = p - 3 - 2.4 - 2p
\]
2. **Combine like terms:**
Now, combine the \(p\) terms and the constant terms:
- The \(p\) terms:
\[
p - 2p = -p
\]
- The constant terms:
\[
-3 - 2.4 = -5.4
\]
3. **Putting it all together:**
Combine the results:
\[
-p - 5.4
\]
So, the final result of \((p - 3) - (2.4 + 2p)\) is \(-p - 5.4\).
Thus, the correct response is:
**−p − 5.4**.
Answered by
GPT-4o mini
Let's simplify the expression \(2(k - 4) - 3(2k - 1)\) step by step.
1. **Distribute \(2\) and \(-3\):**
\[
2(k - 4) = 2k - 8
\]
\[
-3(2k - 1) = -6k + 3
\]
2. **Combine the results:**
Now, we put both parts together:
\[
2k - 8 - 6k + 3
\]
3. **Combine like terms:**
Now, combine the \(k\) terms and the constant terms:
- The \(k\) terms:
\[
2k - 6k = -4k
\]
- The constant terms:
\[
-8 + 3 = -5
\]
4. **Putting it all together:**
Combining the results gives:
\[
-4k - 5
\]
So, the final result of \(2(k - 4) - 3(2k - 1)\) is \(-4k - 5\).
Thus, the correct response is:
**−4k − 5**.
1. **Distribute \(2\) and \(-3\):**
\[
2(k - 4) = 2k - 8
\]
\[
-3(2k - 1) = -6k + 3
\]
2. **Combine the results:**
Now, we put both parts together:
\[
2k - 8 - 6k + 3
\]
3. **Combine like terms:**
Now, combine the \(k\) terms and the constant terms:
- The \(k\) terms:
\[
2k - 6k = -4k
\]
- The constant terms:
\[
-8 + 3 = -5
\]
4. **Putting it all together:**
Combining the results gives:
\[
-4k - 5
\]
So, the final result of \(2(k - 4) - 3(2k - 1)\) is \(-4k - 5\).
Thus, the correct response is:
**−4k − 5**.
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