Use the properties of operations to add 9(k+13)+10(12k−1).(1 point)
Responses
14k+13
14 k plus 13
14k−23
14 k minus Start Fraction 2 over 3 End Fraction
14k−7
14 k minus 7
1912k−23
19,112k - 23
To add 9(k+13) + 10(12k-1), we need to apply the distributive property and then combine like terms.
First, distribute the 9 to both terms inside the parentheses:
9(k + 13) = 9k + 9(13) = 9k + 117
Next, distribute the 10 to both terms inside the parentheses:
10(12k - 1) = 10 * 12k + 10 * (-1) = 120k - 10
Now, we have two separate expressions: 9k + 117 and 120k - 10.
To add the two expressions, we simply combine the like terms:
(9k + 117) + (120k - 10) = 9k + 120k + 117 - 10 = 129k + 107
Therefore, the answer to 9(k+13) + 10(12k-1) is 129k + 107.
Use the properties of operations to add 4(g−2)+(g+2).(1 point)
Responses
5g
5 g
5g−10
5 g minus 10
5g+10
5 g plus 10
5g−6
To add 4(g-2) + (g+2), we need to apply the distributive property and then combine like terms.
First, distribute the 4 to both terms inside the parentheses:
4(g-2) = 4g - 8
Next, distribute the 1 (which is implied) to both terms inside the parentheses:
(g+2) = g + 2
Now, we have two separate expressions: 4g - 8 and g + 2.
To add the two expressions, we simply combine the like terms:
(4g - 8) + (g + 2) = 4g + g - 8 + 2 = 5g - 6
Therefore, the answer to 4(g-2) + (g+2) is 5g - 6.
Use the properties of operations to subtract (h+k)−(2k−h).(1 point)
Responses
−k
negative k
2h−k
2 h minus k
−2h−k
negative 2 h minus k
2h+k
To subtract (h+k) - (2k-h), we need to distribute the negative sign to all terms inside the second parentheses and then combine like terms.
First, distribute the negative sign to both terms inside the second parentheses:
-(2k-h) = -2k + h
Now, we have two separate expressions: (h+k) and (-2k+h).
To subtract the two expressions, we can distribute the negative sign to the second expression and then combine like terms:
(h+k) - (2k-h) = h + k + (-2k + h) = h + k - 2k + h
Now, combine like terms:
h + k - 2k + h = 2h - k
Therefore, the answer to (h+k) - (2k-h) is 2h - k.
Use the properties of operations to subtract (p−3)−(2.4+2p).(1 point)
Responses
−p+5.4
negative p plus 5.4
p−5.4
p minus 5.4
3p−5.4
3 p minus 5.4
−p−5.4
To subtract (p - 3) - (2.4 + 2p), we need to apply the distributive property and then combine like terms.
First, distribute the negative sign to both terms inside the second parentheses:
-(2.4 + 2p) = -2.4 - 2p
Now, we have two separate expressions: (p - 3) and (-2.4 - 2p).
To subtract the two expressions, we can distribute the negative sign to the second expression and then combine like terms:
(p - 3) - (2.4 + 2p) = p - 3 - 2.4 - 2p
Now, combine like terms:
p - 3 - 2.4 - 2p = -p - 2.4 - 3 - 2p
Combine the like terms further:
-3p - 2.4 - 3 = -3p - 5.4
Therefore, the answer to (p - 3) - (2.4 + 2p) is -3p - 5.4.
Subtract: 2(k−4)−3(2k−1).(1 point)
Responses
−4k−5
negative 4 k minus 5
−4k−11
negative 4 k minus 11
−6k−18
negative 6 k minus 18
8k−11
To subtract 2(k-4) - 3(2k-1), we need to apply the distributive property and then combine like terms.
First, distribute the 2 to both terms inside the first parentheses:
2(k-4) = 2k - 2(4) = 2k - 8
Next, distribute the 3 to both terms inside the second parentheses:
3(2k-1) = 3 * 2k - 3 * 1 = 6k - 3
Now, we have two separate expressions: 2k - 8 and 6k - 3.
To subtract the two expressions, we simply combine the like terms:
(2k - 8) - (6k - 3) = 2k - 8 - 6k + 3 = -4k - 5
Therefore, the answer to 2(k-4) - 3(2k-1) is -4k - 5.