The perimeter of the shape below is 21x^2−5x + 4

Question

. Find the length of the missing side.

(1 point)
Responses

4x^2−8
4 x squared minus 8

4x^2+5
4 x squared plus 5

−14x^2+12x−8
negative 14 x squared plus 12 x minus 8

14x^2−12x+8

Answer 1

To find the length of the missing side, we need to know the perimeter of the shape, which is given as \(21x^2 - 5x + 4\).

Let's assume that the shape has four sides, and we have three of them with their lengths represented as \(a\), \(b\), and \(c\). The missing side we'll call \(d\). The formula for the perimeter is:

\[ P = a + b + c + d \]

In this case, we have:

\[ 21x^2 - 5x + 4 = a + b + c + d \]

To find \(d\), we would need the total lengths of \(a\), \(b\), and \(c\). Since we don't have those values, we generally take \(a + b + c\) to be some expression that we will represent as \(S\):

\[ d = (21x^2 - 5x + 4) - S \]

However, without further information about \(a\), \(b\), and \(c\), we cannot determine \(d\) exactly.

Please provide the values of the other three sides, or at least their algebraic expressions so we can proceed to calculate the missing side.

Answer 2

bot the sides of the shape is 2x-3 and 7x^2+3x+2

Answer 3

Given that the perimeter of the shape is: \[ P = 21x^2 - 5x + 4 \] and three sides of the shape are:

• Side 1: \( 2x - 3 \)
• Side 2: \( 7x^2 + 3x + 2 \)
• Side 3: \( d \) (the missing side)

We can set up the equation for the perimeter:

\[ P = (2x - 3) + (7x^2 + 3x + 2) + d \]

Now, let's simplify the expression for the three known sides:

\[ (2x - 3) + (7x^2 + 3x + 2) = 7x^2 + 5x - 1 \]

Thus, we can write the equation for the perimeter as:

\[ 21x^2 - 5x + 4 = (7x^2 + 5x - 1) + d \]

Now, we can rearrange this to solve for \(d\):

\[ d = (21x^2 - 5x + 4) - (7x^2 + 5x - 1) \]

Now, simplifying the right side:

Step 1: Distribute the negative sign:

\[ d = 21x^2 - 5x + 4 - 7x^2 - 5x + 1 \]

Step 2: Combine like terms:

\[ d = (21x^2 - 7x^2) + (-5x - 5x) + (4 + 1) \] \[ d = 14x^2 - 10x + 5 \]

Now we have the length of the missing side, which is:

\[ d = 14x^2 - 10x + 5 \]

None of the answer choices you provided match this result. Please double-check your task or the provided options. If you are looking for a specific option for the missing side, it might be related to simplifying or re-expressing the sides. Based on our calculation, \(d = 14x^2 - 10x + 5\).

Answer 4

my bad bot there is two of the same equation. so the sides are 2x-3 2x-3 and 7x^2+3x+2

Answer 5

No problem! Now that we have the sides of the shape clarified, let's summarize the sides:

1. Side 1: \(2x - 3\)
2. Side 2: \(2x - 3\)
3. Side 3: \(7x^2 + 3x + 2\)
4. Side 4: \(d\) (the missing side)

The perimeter of the shape is given as:

\[ P = 21x^2 - 5x + 4. \]

Now, we can write the equation for the perimeter as follows:

\[ P = (2x - 3) + (2x - 3) + (7x^2 + 3x + 2) + d. \]

Combining the terms of the first three sides:

\[ (2x - 3) + (2x - 3) + (7x^2 + 3x + 2) = (2x + 2x + 3x) + (-3 - 3 + 2) + 7x^2. \]

Now simplifying this:

\[ = 7x^2 + 7x - 4. \]

Now we set this equal to the overall perimeter:

\[ 21x^2 - 5x + 4 = (7x^2 + 7x - 4) + d. \]

To find \(d\):

\[ d = (21x^2 - 5x + 4) - (7x^2 + 7x - 4). \]

Now simplifying the right side:

Step 1: Distribute the negative:

\[ d = 21x^2 - 5x + 4 - 7x^2 - 7x + 4. \]

Step 2: Combine like terms:

\[ = (21x^2 - 7x^2) + (-5x - 7x) + (4 + 4) \] \[ = 14x^2 - 12x + 8. \]

Therefore, the length of the missing side \(d\) is:

\[ d = 14x^2 - 12x + 8. \]

This matches one of the options you provided. So the answer is:

14x² − 12x + 8.