Add the polynomial expressions 2r^2−3r+4 and −2r^2+3r+6 .(1 point)

To add the polynomial expressions \( 2r^2 - 3r + 4 \) and \( -2r^2 + 3r + 6 \), you combine the like terms.

Here are the steps:

1. Write the expressions together:
\[
(2r^2 - 3r + 4) + (-2r^2 + 3r + 6)
\]

2. Combine the like terms:
- For \( r^2 \) terms: \( 2r^2 + (-2r^2) = 0r^2 \) (which simplifies to \( 0 \))
- For \( r \) terms: \( -3r + 3r = 0r \) (which simplifies to \( 0 \))
- For the constant terms: \( 4 + 6 = 10 \)

3. Put it all together:
\[
0r^2 + 0r + 10 = 10
\]

So, the sum of the two polynomial expressions is \( 10 \).

Add the expressions. Expression 1: −3k+4k3−2 Expression 2: 9k2−3k3+4k−3 (2 points)

()k3+ ()k2+*)k+()

To add the polynomial expressions \( -3k + 4k^3 - 2 \) (Expression 1) and \( 9k^2 - 3k^3 + 4k - 3 \) (Expression 2), we will combine like terms.

Here are the steps:

1. Write the expressions together:
\[
(4k^3 - 3k + 4 - 2) + (-3k^3 + 9k^2 + 4k - 3)
\]

2. Combine the like terms:
- For \( k^3 \) terms: \( 4k^3 + (-3k^3) = 1k^3 \)
- For \( k^2 \) terms: There is no \( k^2 \) term in Expression 1, so we have \( 0k^2 + 9k^2 = 9k^2 \)
- For \( k \) terms: \( -3k + 4k = 1k \)
- For the constant terms: \( -2 + (-3) = -5 \)

3. Put it all together:
\[
1k^3 + 9k^2 + 1k - 5
\]

Now, filling in the blanks based on the format given:
- Coefficient for \( k^3 \): \( 1 \)
- Coefficient for \( k^2 \): \( 9 \)
- Coefficient for \( k \): \( 1 \)
- Constant term: \( -5 \)

So the result is:
\[
(1)k^3 + (9)k^2 + (1)k + (-5)
\]

Simplify (9x2−6x+2)−(x2+4x−39) .(1 point)

The difference of the polynomials is () .

To simplify the expression \( (9x^2 - 6x + 2) - (x^2 + 4x - 39) \), we will follow these steps:

1. Distribute the negative sign across the second polynomial:
\[
9x^2 - 6x + 2 - x^2 - 4x + 39
\]

2. Combine like terms:
- \( x^2 \) terms: \( 9x^2 - x^2 = 8x^2 \)
- \( x \) terms: \( -6x - 4x = -10x \)
- Constant terms: \( 2 + 39 = 41 \)

3. Putting it all together gives us:
\[
8x^2 - 10x + 41
\]

So the difference of the polynomials is:
\[
(8x^2 - 10x + 41)
\]

Thus, the answer to fill in the blank is:
\[
8x^2 - 10x + 41
\]

Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference. (2 points)

9x^2 + ()x + 13 – 2x^2 + 12x +() ()x^2 + 5x + 2

To fill in the blanks in the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference, we start with the expressions you provided:

1. **First Expression:** \( 9x^2 + bx + 13 \) (we need to find \( b \)).
2. **Second Expression:** \( - (2x^2 + 12x + c) \) (we need to find \( c \)).
3. **Resulting Difference:** \( dx^2 + 5x + 2 \) (we need to find \( d \) and confirm the coefficient for \( x \)).

### Step 1: Write the subtraction equation
\[
(9x^2 + bx + 13) - (2x^2 + 12x + c) = dx^2 + 5x + 2
\]

### Step 2: Perform the operation
First, distribute the negative sign:
\[
9x^2 + bx + 13 - 2x^2 - 12x - c = dx^2 + 5x + 2
\]

### Step 3: Combine like terms
Combine the \( x^2 \), \( x \), and constant terms on the left side:
- \( x^2 \) terms: \( 9x^2 - 2x^2 = 7x^2 \)
- \( x \) terms: \( bx - 12x \)
- Constant terms: \( 13 - c \)

The equation now looks like:
\[
(7x^2 + (b - 12)x + (13 - c)) = dx^2 + 5x + 2
\]

### Step 4: Equate coefficients
Now we can set up equations based on the coefficients:

1. For \( x^2 \): \( 7 = d \)
2. For \( x \): \( b - 12 = 5 \)
3. For the constant: \( 13 - c = 2 \)

### Step 5: Solve for \( b \) and \( c \)
- From \( b - 12 = 5 \):
\[
b = 5 + 12 = 17
\]

- From \( 13 - c = 2 \):
\[
c = 13 - 2 = 11
\]

### Step 6: Fill in the blanks
Thus, the filled polynomial equation is:
\[
9x^2 + (17)x + 13 - (2x^2 + 12x + 11) = (7)x^2 + 5x + 2
\]

Final blanks filled:
- \( () = 17 \)
- \( () = 11 \)
- \( () = 7 \)

The complete equation is:
\[
9x^2 + \mathbf{17}x + 13 - (2x^2 + 12x + \mathbf{11}) = \mathbf{7}x^2 + 5x + 2
\]

Simplify (14x2−3x+2.25)+(0.75x2+2x−14) .(1 point)

The sum of the polynomials is ().

To simplify the expression \( (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \), we'll combine the like terms.

### Step 1: Write the expression together
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]

### Step 2: Combine like terms
- **For \( x^2 \) terms:**
\[
14x^2 + 0.75x^2 = 14.75x^2
\]

- **For \( x \) terms:**
\[
-3x + 2x = -1x \quad (\text{or simply } -x)
\]

- **For the constant terms:**
\[
2.25 - 14 = -11.75
\]

### Step 3: Write the result
Combining all these, the sum is:
\[
14.75x^2 - x - 11.75
\]

Thus, the sum of the polynomials is:
\[
\boxed{14.75x^2 - x - 11.75}
\]

Wrong answer it was x^2-x+2

Apologies for the confusion. Let's carefully add the polynomial expressions again step by step to see where the mistake might have occurred.

Given:
- First polynomial: \( 14x^2 - 3x + 2.25 \)
- Second polynomial: \( 0.75x^2 + 2x - 14 \)

### Step 1: Align the expressions
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]

### Step 2: Combine like terms
- **For \( x^2 \) terms:**
\[
14x^2 + 0.75x^2 = 14.75x^2
\]

- **For \( x \) terms:**
\[
-3x + 2x = -1x \quad (\text{or simply } -x)
\]

- **For the constant terms:**
\[
2.25 - 14 = -11.75
\]

### Step 3: Combine all terms
Putting it all together, we have:
\[
14.75x^2 - x - 11.75
\]

### Check against your result
You mentioned the sum was \( x^2 - x + 2 \). Let's analyze this equation:

If we factor \( 14.75x^2 - x - 11.75 \) to see if it could simplify to something closer to your result:
- The leading coefficient is quite different, and therefore, I believe my arithmetic regarding constants and coefficients didn't lead to that result.

Let's try it another way:

1. **Convert values**:
- \( 2.25 = \frac{9}{4} \)
- \( -14 \) remains \( -14 \)

2. **Combine all together**:
Combine the equations directly using a common approach:
\[
14x^2 + 0.75x^2 = 14.75x^2 \quad \Rightarrow \quad \text{Not equal to the given } x^2
\]
These are inconsistent. It seems I may have overlooked a clarity.

### Recalculate:
Please clarify if the original terms should have been different. I will assist in ensuring the accuracy based on the original polynomials you provided. Thank you.