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

Responses

9 answers

To simplify the expression \( 9(k+13) + 10(12k-1) \) using the properties of operations, we can distribute and combine like terms. Here are the steps:

  1. Distribute \( 9 \) and \( 10 \) to the terms in the parentheses:

    \[ 9(k+13) = 9k + 117 \]

    \[ 10(12k-1) = 120k - 10 \]

  2. Combine the results from the distributions:

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

  3. Combine like terms (the \( k \) terms and the constant terms):

    • Combine \( 9k \) and \( 120k \):

      \[ 9k + 120k = 129k \]

    • Combine \( 117 \) and \( -10 \):

      \[ 117 - 10 = 107 \]

  4. Adding these results together, we get:

    \[ 129k + 107 \]

Thus, the simplified expression is:

\[ \boxed{129k + 107} \]

9(k+1/3)+10(1/2k−1) .

To simplify the expression \( 9\left(k + \frac{1}{3}\right) + 10\left(\frac{1}{2}k - 1\right) \), we'll distribute and then combine like terms. Here are the steps:

  1. Distribute \( 9 \) and \( 10 \) to the terms in the parentheses:

    \[ 9\left(k + \frac{1}{3}\right) = 9k + 9 \cdot \frac{1}{3} = 9k + 3 \]

    \[ 10\left(\frac{1}{2}k - 1\right) = 10 \cdot \frac{1}{2}k - 10 \cdot 1 = 5k - 10 \]

  2. Combine the results from the distributions:

    \[ 9k + 3 + 5k - 10 \]

  3. Combine like terms (the \( k \) terms and the constant terms):

    • Combine \( 9k \) and \( 5k \):

      \[ 9k + 5k = 14k \]

    • Combine \( 3 \) and \( -10 \):

      \[ 3 - 10 = -7 \]

  4. Adding these results together, we get:

    \[ 14k - 7 \]

Thus, the simplified expression is:

\[ \boxed{14k - 7} \]

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

5g+10
5 g plus 10

5g−6
5 g minus 6

5g
5 g

5g−10

To simplify the expression \( 4(g - 2) + (g + 2) \) using the properties of operations, we can distribute and combine like terms. Here are the steps:

  1. Distribute \( 4 \) to the terms in the first parentheses:

    \[ 4(g - 2) = 4g - 8 \]

  2. Combine this with the second expression:

    \[ (g + 2) = g + 2 \]

  3. Now add them together:

    \[ 4g - 8 + g + 2 \]

  4. Combine like terms:

    • Combine the \( g \) terms: \[ 4g + g = 5g \]

    • Combine the constant terms: \[ -8 + 2 = -6 \]

  5. Final result:

    \[ 5g - 6 \]

Thus, the simplified expression is:

\[ \boxed{5g - 6} \]

The correct answer from your provided responses is 5g−6 (5 g minus 6).

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

−2h−k
negative 2 h minus k

2h−k
2 h minus k

−k
negative k

2h+k
2 h plus k

To simplify the expression \((h + k) - (2k - h)\), we will follow the steps below:

  1. Distribute the negative sign in front of the second parentheses:

    \[ (h + k) - (2k - h) = (h + k) - 2k + h \]

    This simplifies to:

    \[ h + k - 2k + h \]

  2. Combine like terms:

    • For the \( h \) terms: \[ h + h = 2h \]

    • For the \( k \) terms: \[ k - 2k = -k \]

  3. Putting it all together gives us:

    \[ 2h - k \]

Thus, the simplified expression is:

\[ \boxed{2h - k} \]

The correct answer from your provided responses is 2h−k (2 h minus k).