Question
The perimeter of the shape below is 21x^2−5x + 4
. Find the length of the missing side.
(1 point)
Responses
4x^2+5
−14x^2+12x−8
14x^2−12x+8
4x^2−8
. Find the length of the missing side.
(1 point)
Responses
4x^2+5
−14x^2+12x−8
14x^2−12x+8
4x^2−8
Answers
Answer
left side is 2x - 3
right side is 2x - 3
bottom is 7x^2 + 3x + 2
the top is the missing side
right side is 2x - 3
bottom is 7x^2 + 3x + 2
the top is the missing side
Answered by
GPT-4o mini
To find the length of the missing side of the shape, we need to use the information provided about the perimeter.
The perimeter of a shape is the sum of the lengths of all its sides. Let's assume the shape has \( n \) sides, and we know the total perimeter is given by \( 21x^2 - 5x + 4 \).
If we know the lengths of some of the sides of the shape (let's denote them as \( S_1, S_2, ..., S_{n-1} \)) and we are trying to find the length of the missing side (let's call it \( S_n \)), we can express the perimeter as:
\[
P = S_1 + S_2 + ... + S_{n-1} + S_n
\]
To find the missing side \( S_n \), we rearrange this formula:
\[
S_n = P - (S_1 + S_2 + ... + S_{n-1})
\]
In the absence of specific values for the other sides, we can assume that the total perimeter \( P = 21x^2 - 5x + 4 \) is the given perimeter of the shape.
Given the choices for the length of the missing side, we can test each option in conjunction with the perimeter formula:
1. **Option: \( 4x^2 + 5 \)**
2. **Option: \( -14x^2 + 12x - 8 \)**
3. **Option: \( 14x^2 - 12x + 8 \)**
4. **Option: \( 4x^2 - 8 \)**
Since the other sides are not provided explicitly, we don't know the specific lengths that need to be subtracted from the perimeter. However, we can approach this through potential logical deductions or assumptions about their nature (for example, if they are all non-negative, or if some are in specific forms).
To summarize with clarity:
To find the specific missing side length quantitatively, more specific lengths of other sides are necessary. However, if given these choices, one method is to assume that the remaining sides could balance out to meet the total perimeter based on values selected.
In this context, without specific other values, the options remain presented without numeric extraction.
If you could provide additional context or other side lengths, we could calculate this with adjustment.
If you are looking for a suitable match/applicable calculation, you can perform:
Let's test each response option with the example given:
The process would involve basic combination and parameterization, subsequently isolating other non-matching terms against \( 21x^2 - 5x + 4 \).
So unless additional context on other side lengths is provided, anyone of the choices could potentially act specifically depending on provided lengths.
Do you have other sides provided? If so, please share for a concrete answer!
The perimeter of a shape is the sum of the lengths of all its sides. Let's assume the shape has \( n \) sides, and we know the total perimeter is given by \( 21x^2 - 5x + 4 \).
If we know the lengths of some of the sides of the shape (let's denote them as \( S_1, S_2, ..., S_{n-1} \)) and we are trying to find the length of the missing side (let's call it \( S_n \)), we can express the perimeter as:
\[
P = S_1 + S_2 + ... + S_{n-1} + S_n
\]
To find the missing side \( S_n \), we rearrange this formula:
\[
S_n = P - (S_1 + S_2 + ... + S_{n-1})
\]
In the absence of specific values for the other sides, we can assume that the total perimeter \( P = 21x^2 - 5x + 4 \) is the given perimeter of the shape.
Given the choices for the length of the missing side, we can test each option in conjunction with the perimeter formula:
1. **Option: \( 4x^2 + 5 \)**
2. **Option: \( -14x^2 + 12x - 8 \)**
3. **Option: \( 14x^2 - 12x + 8 \)**
4. **Option: \( 4x^2 - 8 \)**
Since the other sides are not provided explicitly, we don't know the specific lengths that need to be subtracted from the perimeter. However, we can approach this through potential logical deductions or assumptions about their nature (for example, if they are all non-negative, or if some are in specific forms).
To summarize with clarity:
To find the specific missing side length quantitatively, more specific lengths of other sides are necessary. However, if given these choices, one method is to assume that the remaining sides could balance out to meet the total perimeter based on values selected.
In this context, without specific other values, the options remain presented without numeric extraction.
If you could provide additional context or other side lengths, we could calculate this with adjustment.
If you are looking for a suitable match/applicable calculation, you can perform:
Let's test each response option with the example given:
The process would involve basic combination and parameterization, subsequently isolating other non-matching terms against \( 21x^2 - 5x + 4 \).
So unless additional context on other side lengths is provided, anyone of the choices could potentially act specifically depending on provided lengths.
Do you have other sides provided? If so, please share for a concrete answer!
Answered by
GPT-4o mini
Thank you for providing the sides of the shape. With this information, we can find the length of the missing side (the top side) knowing that the perimeter is made up of the following sides:
- Left side = \( 2x - 3 \)
- Right side = \( 2x - 3 \)
- Bottom side = \( 7x^2 + 3x + 2 \)
- Top side = \( L \) (the missing side)
The perimeter \( P \) of the shape is given as:
\[
P = \text{Left side} + \text{Right side} + \text{Bottom side} + \text{Top side}
\]
So we can write this as:
\[
P = (2x - 3) + (2x - 3) + (7x^2 + 3x + 2) + L
\]
Combining the known sides:
\[
P = (2x + 2x + 3x + 7x^2) + (-3 - 3 + 2) + L
\]
This simplifies to:
\[
P = 7x^2 + 7x - 4 + L
\]
Since we know the total perimeter is:
\[
P = 21x^2 - 5x + 4
\]
We can set these two expressions for \( P \) equal:
\[
7x^2 + 7x - 4 + L = 21x^2 - 5x + 4
\]
Now, let's isolate \( L \):
\[
L = (21x^2 - 5x + 4) - (7x^2 + 7x - 4)
\]
Now, we will simplify this further:
1. Distributing the negative sign:
\[
L = 21x^2 - 5x + 4 - 7x^2 - 7x + 4
\]
2. Combine like terms:
\[
L = (21x^2 - 7x^2) + (-5x - 7x) + (4 + 4)
\]
\[
L = 14x^2 - 12x + 8
\]
The length of the missing side (top side) is:
\[
\boxed{14x^2 - 12x + 8}
\]
This matches one of the response options you provided earlier.
- Left side = \( 2x - 3 \)
- Right side = \( 2x - 3 \)
- Bottom side = \( 7x^2 + 3x + 2 \)
- Top side = \( L \) (the missing side)
The perimeter \( P \) of the shape is given as:
\[
P = \text{Left side} + \text{Right side} + \text{Bottom side} + \text{Top side}
\]
So we can write this as:
\[
P = (2x - 3) + (2x - 3) + (7x^2 + 3x + 2) + L
\]
Combining the known sides:
\[
P = (2x + 2x + 3x + 7x^2) + (-3 - 3 + 2) + L
\]
This simplifies to:
\[
P = 7x^2 + 7x - 4 + L
\]
Since we know the total perimeter is:
\[
P = 21x^2 - 5x + 4
\]
We can set these two expressions for \( P \) equal:
\[
7x^2 + 7x - 4 + L = 21x^2 - 5x + 4
\]
Now, let's isolate \( L \):
\[
L = (21x^2 - 5x + 4) - (7x^2 + 7x - 4)
\]
Now, we will simplify this further:
1. Distributing the negative sign:
\[
L = 21x^2 - 5x + 4 - 7x^2 - 7x + 4
\]
2. Combine like terms:
\[
L = (21x^2 - 7x^2) + (-5x - 7x) + (4 + 4)
\]
\[
L = 14x^2 - 12x + 8
\]
The length of the missing side (top side) is:
\[
\boxed{14x^2 - 12x + 8}
\]
This matches one of the response options you provided earlier.
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