Use the properties of operations to add 9(k+13)+10(12k−1).
a. 14k - 2/3
b. 14k + 13
c. 14k - 7
d. 19 1/2k - 2/3
To add \(9(k+13)+10(12k−1)\), we should distribute the multiplication across addition to simplify the expression.
\(9(k+13) = 9k + 117\) (Distribute the 9)
\(10(12k−1) = 120k - 10\) (Distribute the 10)
Now, add the distributed terms together:
\(9k + 117 + 120k - 10\)
Combine like terms (the terms with \(k\) and the constant terms separately):
\(9k + 120k = 129k\)
\(117 - 10 = 107\)
The simplified form:
\(129k + 107\)
None of the options (a, b, c, d) match the correctly simplified expression \(129k + 107\), so there might be a typo in the options provided. Please verify the options and the expression to determine the correct answer.
Can you please pick one of the choices
As per the earlier calculation, the correct simplified form of the expression \(9(k+13)+10(12k−1)\) is \(129k + 107\). Since none of the available choices accurately reflect this answer, I must select the option that is closest to the correct answer.
The available options are:
a. 14k - 2/3
b. 14k + 13
c. 14k - 7
d. 19 1/2k - 2/3
The correct choice among the given options should have a coefficient of \(k\) closest to 129 and a constant term closest to 107. None of the options have these exact values, but to choose the closest one:
The option with the correct structure of a coefficient for \(k\) and a constant term is:
b. 14k + 13
While 14k is not close to 129k, it is the only option with a structure similar to what we obtained (a coefficient of \(k\) and a constant). None of the coefficients in the options are remotely close to 129, but the constant term 13 is the only positive constant as in the correct answer.
If this is an exercise and choices are fixed, there may have been an error in the transcription of the problem or the options. However, if we must select one of the given options under the assumption that there has been some error, option b. 14k + 13 would be the most structurally similar to the correct simplified expression \(129k + 107\).
To add 9(k+13)+10(12k−1), you can simplify each term inside the parentheses first and then combine like terms.
Starting with the first term, distribute the 9 across the terms inside the parentheses:
9(k+13) = 9k + 9(13) = 9k + 117
Moving on to the second term, distribute the 10 across the terms inside the parentheses:
10(12k−1) = 10(12k) - 10(1) = 120k - 10
Now, we can combine the two simplified terms:
9k + 117 + 120k - 10
Combining like terms (the terms with the same variable):
9k + 120k + 117 - 10
Combine the constant terms:
9k + 120k + 107
Now, we can combine the like terms with 'k':
(9 + 120)k + 107
Simplify further:
129k + 107
Therefore, the answer is 129k + 107.
None of the answer choices provided match the simplified expression, so none of the given options are correct.