Use the properties of operations to add 9(k+13)+10(12k−1).(1 point)Responses14k−2314 k minus Start Fraction 2 over 3 End Fraction14k−714 k minus 71912k−2319 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction14k+13
9(k+13) + 10(12k-1)
First, distribute the 9 and 10:
9k + 9(13) + 10(12k) - 10(1)
Multiply:
9k + 117 + 120k - 10
Combine like terms:
9k + 120k + 117 - 10
129k + 107
Use the properties of operations to add 9(k+1/3)+10(1/2k−1).(1 point)Responses14k−2314 k minus Start Fraction 2 over 3 End Fraction1/4k−7 1/4 k minus 7 19 1/2k−2/3 19 Start Fraction 1 over 2 End Fraction k minus Start Fraction 2 over 3 End Fraction14k+13
9(k+1/3) + 10(1/2k-1)
First, distribute the 9 and 10:
9k + 9(1/3) + 10(1/2k) - 10(1)
Multiply:
9k + 3 + 5k - 10
Combine like terms:
9k + 5k + 3 - 10
14k - 7
To add 9(k+13) + 10(12k-1), we can distribute the coefficients across the parentheses first:
= 9 * k + 9 * 13 + 10 * 12k + 10 * (-1)
Simplifying each term, we get:
= 9k + 117 + 120k - 10
Now, let's combine like terms:
= (9k + 120k) + (117 - 10)
= 129k + 107
So, 9(k+13) + 10(12k-1) simplifies to 129k + 107.
To add 9(k+13)+10(12k-1), we can use the distributive property of multiplication over addition/subtraction.
First, distribute the 9 to each term inside the parentheses:
9(k+13) = 9k + 9(13) = 9k + 117
Next, distribute the 10 to each term inside the second parentheses:
10(12k-1) = 10(12k) + 10(-1) = 120k - 10
Now, we can combine like terms by adding the similar terms together:
9k + 117 + 120k - 10
To combine similar terms, we add the coefficients of the same variables. In this case, we have two terms with k and two constant terms without any variables.
Combining the terms with the k variable:
9k + 120k = 129k
Combining the constant terms:
117 - 10 = 107
Putting it all together, the sum of 9(k+13)+10(12k-1) is:
129k + 107