To expand the expression \(\frac{7}{10}(5d + 6)\), you can distribute \(\frac{7}{10}\) to both terms inside the parentheses:
\[ \frac{7}{10} \cdot 5d + \frac{7}{10} \cdot 6 \]
Now, calculate each term:
- \(\frac{7}{10} \cdot 5d = \frac{35d}{10} = 3.5d\)
- \(\frac{7}{10} \cdot 6 = \frac{42}{10} = 4.2\)
Thus, the expanded form is:
\[ 3.5d + 4.2 \]
However, if we keep it as fractions, you can also write:
\[ \frac{35}{10}d + \frac{42}{10} \]
This simplifies to:
\[ \frac{35}{10}d + \frac{42}{10} \]
So, the answer to the expansion is:
\[ \frac{35}{10}d + \frac{42}{10} \]
which can also be expressed as:
\[ 35d + 42 \]
If we consider the options provided, the correct response is:
35d + 42.