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

Question

Responses

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

14k−7
14 k minus 7

14k+13
14 k plus 13

19 1/2k−2/3

Answer 1

To simplify the expression \(9\left(k + \frac{1}{3}\right) + 10\left(\frac{1}{2}k - 1\right)\), we can use the distributive property to expand both terms.

1. Expand the first term: \[ 9\left(k + \frac{1}{3}\right) = 9k + 9\left(\frac{1}{3}\right) = 9k + 3 \]

2. Expand the second term: \[ 10\left(\frac{1}{2}k - 1\right) = 10 \cdot \frac{1}{2}k - 10 \cdot 1 = 5k - 10 \]

3. Now, combine the results: \[ 9k + 3 + 5k - 10 \]

4. Combine like terms: \[ (9k + 5k) + (3 - 10) = 14k - 7 \]

So, the final result is: \[ \boxed{14k - 7} \]

Answer 2

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

5g+10
5 g plus 10

5g
5 g

5g−10
5 g minus 10

5g−6

Answer 3

To simplify the expression \(4(g - 2) + (g + 2)\), we will use the distributive property and combine like terms.

1. Expand \(4(g - 2)\): \[ 4(g - 2) = 4g - 8 \]

2. The second term is already expanded: \[ g + 2 \]

3. Combine the two results: \[ (4g - 8) + (g + 2) \]

4. Combine like terms: \[ (4g + g) + (-8 + 2) = 5g - 6 \]

So, the final result is: \[ \boxed{5g - 6} \]

Answer 4

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

2h+k
2 h plus k

−k
negative k

2h−k
2 h minus k

−2h−k

Answer 5

To simplify the expression \((h + k) - (2k - h)\), we will distribute the negative sign and then combine like terms.

1. Rewrite the expression: \[ (h + k) - (2k - h) = (h + k) - 2k + h \]

2. Now, combine the terms: \[ h + h + k - 2k = 2h + k - 2k \]

3. Combine like terms: \[ 2h + (k - 2k) = 2h - k \]

So the final result is: \[ \boxed{2h - k} \]

Answer 6

Use the properties of operations to subtract (p−3)−(2.4+2p).(1 point)
Responses

p−5.4
p minus 5.4

−p+5.4
negative p plus 5.4

3p−5.4
3 p minus 5.4

−p−5.4

Answer 7

To simplify the expression \((p - 3) - (2.4 + 2p)\), we will distribute the negative sign and then combine like terms.

1. Rewrite the expression: \[ (p - 3) - (2.4 + 2p) = (p - 3) - 2.4 - 2p \]

2. Now, combine the terms: \[ p - 2p - 3 - 2.4 \]

3. Combine the like terms:

   • For the \(p\) terms: \(p - 2p = -p\)
   • For the constant terms: \(-3 - 2.4 = -5.4\)

Putting it all together: \[ -p - 5.4 \]

So the final result is: \[ \boxed{-p - 5.4} \]

Answer 8

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

−4k−5
negative 4 k minus 5

8k−11
8 k minus 11

−6k−18
negative 6 k minus 18

−4k−11
negative 4 k minus 11

Answer 9

To simplify the expression \(2(k - 4) - 3(2k - 1)\), we will first distribute the constants and then combine like terms.

1. Distribute \(2\) in the first term: \[ 2(k - 4) = 2k - 8 \]

2. Distribute \(-3\) in the second term: \[ -3(2k - 1) = -6k + 3 \]

3. Now, combine the two results: \[ (2k - 8) + (-6k + 3) \]

4. Combine like terms:

   • For the \(k\) terms: \(2k - 6k = -4k\)
   • For the constant terms: \(-8 + 3 = -5\)

So we have: \[ -4k - 5 \]

Thus, the final result is: \[ \boxed{-4k - 5} \]

Answer 10

are sure all of the answers above are correct

Answer 11

Let's carefully review the previous calculations together to ensure they are accurate. I'll go through each of the expressions again, step by step.

1. Expression: \(4(g−2)+(g+2)\)

Simplification:

1. Expand \(4(g - 2)\): \[ 4g - 8 \]

2. Add the second term: \[ 4g - 8 + g + 2 \]

3. Combine like terms: \[ (4g + g) + (-8 + 2) = 5g - 6 \]

Final Result: \(5g - 6\) (Correct)

2. Expression: \((h+k)−(2k−h)\)

Simplification:

1. Rewrite as: \[ h + k - (2k - h) = h + k - 2k + h \]

2. Combine like terms: \[ (h + h) + (k - 2k) = 2h - k \]

Final Result: \(2h - k\) (Correct)

3. Expression: \((p−3)−(2.4+2p)\)

Simplification:

1. Rewrite the expression: \[ p - 3 - (2.4 + 2p) = p - 3 - 2.4 - 2p \]

2. Combine like terms: \[ (p - 2p) + (-3 - 2.4) = -p - 5.4 \]

Final Result: \(-p - 5.4\) (Correct)

4. Expression: \(2(k−4)−3(2k−1)\)

Simplification:

1. Expand \(2(k - 4)\): \[ 2k - 8 \]

2. Expand \(-3(2k - 1)\): \[ -6k + 3 \]

3. Combine the results: \[ (2k - 8) + (-6k + 3) = 2k - 6k - 8 + 3 \] \[ -4k - 5 \]

Final Result: \(-4k - 5\) (Correct)

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Conclusion: All the answers I provided in previous responses are indeed correct:

1. \(5g - 6\)
2. \(2h - k\)
3. \(-p - 5.4\)
4. \(-4k - 5\)

If you have any specific doubts or additional questions, feel free to ask!