To expand the expression \( \frac{7}{10}(5d + 6) \), you distribute \( \frac{7}{10} \) to both terms inside the parentheses:
\[ \frac{7}{10} \times 5d + \frac{7}{10} \times 6 \]
Calculating each term:
- \( \frac{7}{10} \times 5d = \frac{35}{10}d = 3.5d \) or \( \frac{35}{10}d \)
- \( \frac{7}{10} \times 6 = \frac{42}{10} = 4.2 \) or \( \frac{21}{5} \)
Putting it together, we get:
\[ \frac{35}{10}d + \frac{42}{10} = 3.5d + 4.2 \] or \[ \frac{35}{10}d + \frac{21}{5} \]
From the options provided, the correct expansion of \( \frac{7}{10}(5d + 6) \) can be expressed as:
\( 35d + 42 \) or \( 5d + 21/5 \) (this is equivalent to \( 21/5 = 4.2 \))
However, considering standard formats and common expressions, let's verify the final results.
The best option from the list that aligns with the steps we took and results we calculated is:
\(35d + 42\)
Make sure to check the options to clarify, as the best representation is \( \frac{35}{10}d + \frac{21}{5} \).
Thus, Answer: 35d + 42.