Question If $$ C=y+5 $$ and $$ D=y^{2}-y-9 $$, find an expression that equals $$ 2 C-D $$ in standard fo Answer Attempt 1 out of 2

Question

UpStudy AI · Accepted Answer

To find the expression that equals $$ 2C - D $$, we will follow these steps:

1. Substitute the expressions for $$ C $$ and $$ D $$ into the equation.
2. Simplify the resulting expression.

Given:
- $$ C = y + 5 $$
- $$ D = y^2 - y - 9 $$

Now, let's calculate $$ 2C - D $$:

$$
2C = 2(y + 5) = 2y + 10
$$

Next, we substitute $$ D $$:

$$
D = y^2 - y - 9
$$

Now, we can find $$ 2C - D $$:

$$
2C - D = (2y + 10) - (y^2 - y - 9)
$$

Now, let's simplify this expression step by step:

1. Distribute the negative sign across $$ D $$:
   $$
   2C - D = 2y + 10 - y^2 + y + 9
   $$

2. Combine like terms:
   - Combine $$ 2y $$ and $$ y $$:
   $$
   2y + y = 3y
   $$
   - Combine $$ 10 $$ and $$ 9 $$:
   $$
   10 + 9 = 19
   $$

Putting it all together, we have:

$$
2C - D = -y^2 + 3y + 19
$$

Now, let's express this in standard form, which is typically written with the highest degree term first:

$$
2C - D = -y^2 + 3y + 19
$$

Thus, the final expression that equals $$ 2C - D $$ in standard form is:

$$
-y^2 + 3y + 19
$$
The expression $$ 2C - D $$ simplifies to $$ -y^2 + 3y + 19 $$.

Question If \( C=y+5 \) and \( D=y^{2}-y-9 \), find an expression that equals \( 2 C-D \) in standard fo Answer Attempt 1 out of 2