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

Question

Responses

14k−7

14k+13

19 1/2k−2/3

14k−2/3

Answer 1

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.

Answer 2

sorry i meant "
Use the properties of operations to add 9(k+1/.3)+10(1/2k−1).

Answer 3

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.

Answer 4

Use the properties of operations to add 4(g−2)+(g+2).(1 point)
Responses

5g−6

5g+10

5g−10

5g

Answer 5

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.

Answer 6

Use the properties of operations to subtract (h+k)−(2k−h).(1 point)
Responses

−k

2h−k

−2h−k

2h+k

Answer 7

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.

Answer 8

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

Answer 9

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.

Answer 10

Subtract: 2(k−4)−3(2k−1).(1 point)
Responses

8k−11

−6k−18

−4k−11

−4k−5

Answer 11

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.