Which expression represents the algebraic phrase "twelve times the sum of a number and seven-tenths"? $$ 12 y+\frac{7}{10} $$ $$ 12\left(y+\frac{7}{10}\right) $$ $$ \frac{7}{10} y+12 $$ $$ y\left(\frac{7}{10}+12\right) $$

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UpStudy AI · Accepted Answer

To translate the phrase "twelve times the sum of a number and seven-tenths" into an algebraic expression, we can break it down step by step:

1. **Identify the components**:
   - "a number" can be represented as $$ y $$.
   - "seven-tenths" is represented as $$ \frac{7}{10} $$.
   - "the sum of a number and seven-tenths" translates to $$ y + \frac{7}{10} $$.
   - "twelve times" indicates that we need to multiply the sum by 12.

2. **Construct the expression**:
   - The entire phrase can be expressed as $$ 12 \times (y + \frac{7}{10}) $$.

Thus, the correct expression that represents the algebraic phrase is:

$$
12\left(y+\frac{7}{10}\right)
$$

Now, let's check the provided options:

1. $$ 12 y+\frac{7}{10} $$ - This is incorrect because it does not represent the sum.
2. $$ 12\left(y+\frac{7}{10}\right) $$ - This is correct.
3. $$ \frac{7}{10} y+12 $$ - This is incorrect because it does not represent the sum correctly.
4. $$ y\left(\frac{7}{10}+12\right) $$ - This is incorrect because it does not represent the multiplication of the sum.

Therefore, the correct answer is:

$$
12\left(y+\frac{7}{10}\right)
$$
The correct expression is $$ 12\left(y+\frac{7}{10}\right) $$.

Which expression represents the algebraic phrase "twelve times the sum of a number and seven-tenths"? \( 12 y+\frac{7}{10} \) \( 12\left(y+\frac{7}{10}\right) \) \( \frac{7}{10} y+12 \) \( y\left(\frac{7}{10}+12\right) \)

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