To determine which expression is equivalent to \(1,000 + 196\), we will first simplify \(1,000 + 196\):
\[ 1,000 + 196 = 1,196 \]
Now let's evaluate each of the given expressions step-by-step:
Expression A:
\(10 + 10 + 7 \cdot 28\)
Calculating \(7 \cdot 28\):
\[
7 \cdot 28 = 196
\]
So,
\[
10 + 10 + 196 = 20 + 196 = 216
\]
Thus, \(A = 216\).
Expression B:
\(10 + 10 + 10 + 14 + 14\)
Calculating:
\[
10 + 10 + 10 + 14 + 14 = 30 + 28 = 58
\]
Thus, \(B = 58\).
Expression C:
\(100 + 100 + 100 + 7 \cdot 28\)
Calculating \(7 \cdot 28\) is again \(196\):
\[
100 + 100 + 100 + 196 = 300 + 196 = 496
\]
Thus, \(C = 496\).
Expression D:
\(100 + 100 + 14 + 14\)
Calculating:
\[
100 + 100 + 14 + 14 = 200 + 28 = 228
\]
Thus, \(D = 228\).
Now, comparing the results:
- \(A = 216\)
- \(B = 58\)
- \(C = 496\)
- \(D = 228\)
None of the expressions A, B, C, or D equal \(1,196\).
Hence, none of the provided expressions is equivalent to \(1,000 + 196\).