Which expression is equivalent to 2.8k 8.47
0.07(4k-12) A
B 0.7(4k-12)
C 5.6k
D -5.6k
The correct answer and explanation is:
Let’s solve the expression:
2.8k+8.47−0.07(4k−12)2.8k + 8.47 – 0.07(4k – 12)
First, distribute −0.07-0.07 across the terms inside the parentheses:
0.07(4k−12)=0.07×4k−0.07×120.07(4k – 12) = 0.07 \times 4k – 0.07 \times 12
=0.28k−0.84= 0.28k – 0.84
Now, substitute this back into the original expression:
2.8k+8.47−(0.28k−0.84)2.8k + 8.47 – (0.28k – 0.84)
Next, remove the parentheses and simplify:
2.8k+8.47−0.28k+0.842.8k + 8.47 – 0.28k + 0.84
Combine like terms:
- Combine the kk-terms:
2.8k−0.28k=2.52k2.8k – 0.28k = 2.52k - Combine the constant terms:
8.47+0.84=9.318.47 + 0.84 = 9.31
So the simplified expression becomes:
2.52k+9.312.52k + 9.31
Now, let’s compare this with the provided options:
- A) 0.7(4k−12)0.7(4k – 12) simplifies to 0.7×4k−0.7×12=2.8k−8.40.7 \times 4k – 0.7 \times 12 = 2.8k – 8.4, which is not the same.
- B) 0.7(4k−12)0.7(4k – 12) also simplifies to 2.8k−8.42.8k – 8.4, which is incorrect.
- C) 5.6k5.6k is simply a linear term and doesn’t match our expression.
- D) −5.6k-5.6k is a negative linear term and doesn’t match either.
None of the answers exactly match, but it seems that the closest match or correct simplified version would be derived by adjusting or re-checking the provided options, possibly in terms of simplifications not shown here. If this is the intended final exam question, please double-check the problem details.