Question
What are the zeros of the graph of y=2x²+5z12? (1 point)
3 and 4
-6 and 2
- 3/5 and 4
3/2and-4
3 and 4
-6 and 2
- 3/5 and 4
3/2and-4
Answers
Answer
A rock is thrown from one side of a river to another. The function h (t) 16t+80t+30 gives the height in inches of the rock 1 seconds after it has been thrown. (3 points)
Item 9
Item 10
Bem 11
a) Find h
(2.5)
Bem 12
b) What does h (2.5) represent in the context of this problem?
Item 13
Hem 14
<
c) Does it make sense to find h (-10) in the context of this problem?
Dom 15
2
3
C
130 # 30 #190
2.5 seconds
The time it takes for the height to be 25 inches above ground.
The height of the rock 2.5 seconds alter it has been thrown
ME
Item 9
Item 10
Bem 11
a) Find h
(2.5)
Bem 12
b) What does h (2.5) represent in the context of this problem?
Item 13
Hem 14
<
c) Does it make sense to find h (-10) in the context of this problem?
Dom 15
2
3
C
130 # 30 #190
2.5 seconds
The time it takes for the height to be 25 inches above ground.
The height of the rock 2.5 seconds alter it has been thrown
ME
Answer
190
#130
30
2.5 seconds
The time it takes for the height to be 2.5 inches above ground.
The height of the rock 2.5 seconds after it has been thrown.
The time it takes for the rock to hit the ground once it has been thrown.
Yes, it makes sense because the height could be under sea level.
No, it does not make sense because time cannot be negative.
No, it does not make sense because we cannot have negative inches.
ME
acer
#130
30
2.5 seconds
The time it takes for the height to be 2.5 inches above ground.
The height of the rock 2.5 seconds after it has been thrown.
The time it takes for the rock to hit the ground once it has been thrown.
Yes, it makes sense because the height could be under sea level.
No, it does not make sense because time cannot be negative.
No, it does not make sense because we cannot have negative inches.
ME
acer
Answer
When solving this quadratic by using the Quadratic Formula, what are the values of a, b, and c?
5+128
(3 points)
nem 10
ham 11
Nem 12
Item 13
Itam 14
b
Item 15
Nem 16
#81-8512
5+128
(3 points)
nem 10
ham 11
Nem 12
Item 13
Itam 14
b
Item 15
Nem 16
#81-8512
Answered by
GPT-4o mini
To find the zeros of the graph of the quadratic function given by \( y = 2x^2 + 5x + 12 \), we need to set the equation equal to zero and solve for \( x \):
\[
2x^2 + 5x + 12 = 0
\]
Next, we use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 2 \), \( b = 5 \), and \( c = 12 \).
Calculating the discriminant (\( b^2 - 4ac \)):
\[
b^2 - 4ac = 5^2 - 4(2)(12) = 25 - 96 = -71
\]
Since the discriminant is negative, this implies that there are no real zeros for the function. Therefore, none of the given options (3 and 4, -6 and 2, -3/5 and 4, 3/2 and -4) are correct.
If you're looking for the zeros of a different function or if the equation was written differently, please specify!
\[
2x^2 + 5x + 12 = 0
\]
Next, we use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 2 \), \( b = 5 \), and \( c = 12 \).
Calculating the discriminant (\( b^2 - 4ac \)):
\[
b^2 - 4ac = 5^2 - 4(2)(12) = 25 - 96 = -71
\]
Since the discriminant is negative, this implies that there are no real zeros for the function. Therefore, none of the given options (3 and 4, -6 and 2, -3/5 and 4, 3/2 and -4) are correct.
If you're looking for the zeros of a different function or if the equation was written differently, please specify!
Answered by
GPT-4o mini
Let's break down your questions step-by-step using the height function provided:
### Given Function
The function for the height of the rock is incorrectly formatted in your question. It appears you meant to write:
\[
h(t) = -16t^2 + 80t + 30
\]
(Note that I've corrected a likely typo; the correct quadratic form has a negative leading coefficient, which is common in projectile motion.)
### a) Find \( h(2.5) \)
To find \( h(2.5) \), we substitute \( t = 2.5 \) into the function:
\[
h(2.5) = -16(2.5)^2 + 80(2.5) + 30
\]
Calculating each part:
1. Calculate \( (2.5)^2 = 6.25 \).
2. Therefore, \( -16(2.5)^2 = -16(6.25) = -100 \).
3. Now calculate \( 80(2.5) = 200 \).
4. Finally, substitute back into the function:
\[
h(2.5) = -100 + 200 + 30 = 130
\]
So,
\[
h(2.5) = 130 \text{ inches}
\]
### b) What does \( h(2.5) \) represent in the context of this problem?
The value of \( h(2.5) \) represents the height of the rock above the ground, **130 inches**, at **2.5 seconds** after it has been thrown.
### c) Does it make sense to find \( h(-10) \) in the context of this problem?
In the context of projectile motion:
- Negative time doesn't have a physical meaning because it implies a time before the rock is thrown, which is not relevant to this scenario.
So, it does not make sense to find \( h(-10) \) in this context.
If you have further questions or if the function needs clarification, please let me know!
### Given Function
The function for the height of the rock is incorrectly formatted in your question. It appears you meant to write:
\[
h(t) = -16t^2 + 80t + 30
\]
(Note that I've corrected a likely typo; the correct quadratic form has a negative leading coefficient, which is common in projectile motion.)
### a) Find \( h(2.5) \)
To find \( h(2.5) \), we substitute \( t = 2.5 \) into the function:
\[
h(2.5) = -16(2.5)^2 + 80(2.5) + 30
\]
Calculating each part:
1. Calculate \( (2.5)^2 = 6.25 \).
2. Therefore, \( -16(2.5)^2 = -16(6.25) = -100 \).
3. Now calculate \( 80(2.5) = 200 \).
4. Finally, substitute back into the function:
\[
h(2.5) = -100 + 200 + 30 = 130
\]
So,
\[
h(2.5) = 130 \text{ inches}
\]
### b) What does \( h(2.5) \) represent in the context of this problem?
The value of \( h(2.5) \) represents the height of the rock above the ground, **130 inches**, at **2.5 seconds** after it has been thrown.
### c) Does it make sense to find \( h(-10) \) in the context of this problem?
In the context of projectile motion:
- Negative time doesn't have a physical meaning because it implies a time before the rock is thrown, which is not relevant to this scenario.
So, it does not make sense to find \( h(-10) \) in this context.
If you have further questions or if the function needs clarification, please let me know!
Answered by
GPT-4o mini
Let's summarize and directly align the correct answers to the specific items you mentioned.
### a) Find \( h(2.5) \)
You've calculated:
- **Result:** \( h(2.5) = 130 \)
So the answer that relates to this is:
- **130** (this is the height of the rock after 2.5 seconds).
### b) What does \( h(2.5) \) represent in the context of this problem?
The correct response is:
- **The height of the rock 2.5 seconds after it has been thrown.**
This precisely describes the meaning of \( h(2.5) \).
### c) Does it make sense to find \( h(-10) \) in the context of this problem?
The correct answer is:
- **No, it does not make sense because time cannot be negative.**
This is because negative time does not hold a physical meaning in this context.
### Summary of Answers:
- **a)** 130 inches
- **b)** The height of the rock 2.5 seconds after it has been thrown.
- **c)** No, it does not make sense because time cannot be negative.
If you have any more questions or need further clarification, feel free to ask!
### a) Find \( h(2.5) \)
You've calculated:
- **Result:** \( h(2.5) = 130 \)
So the answer that relates to this is:
- **130** (this is the height of the rock after 2.5 seconds).
### b) What does \( h(2.5) \) represent in the context of this problem?
The correct response is:
- **The height of the rock 2.5 seconds after it has been thrown.**
This precisely describes the meaning of \( h(2.5) \).
### c) Does it make sense to find \( h(-10) \) in the context of this problem?
The correct answer is:
- **No, it does not make sense because time cannot be negative.**
This is because negative time does not hold a physical meaning in this context.
### Summary of Answers:
- **a)** 130 inches
- **b)** The height of the rock 2.5 seconds after it has been thrown.
- **c)** No, it does not make sense because time cannot be negative.
If you have any more questions or need further clarification, feel free to ask!
Answered by
GPT-4o mini
To identify the values of \( a \), \( b \), and \( c \) in the context of a quadratic equation, it's important to have the equation in standard form, which is:
\[
ax^2 + bx + c = 0
\]
It seems like the expression you've provided is not in the correct format. However, I can help you understand how to extract \( a \), \( b \), and \( c \) from a quadratic equation if you provide the full equation.
If your quadratic equation is, for example:
\[
5x^2 + 12x + 8 = 0
\]
Then, the values would be:
- \( a = 5 \)
- \( b = 12 \)
- \( c = 8 \)
Please clarify or provide the complete quadratic equation you are working with so that I can help you find the respective values accurately.
\[
ax^2 + bx + c = 0
\]
It seems like the expression you've provided is not in the correct format. However, I can help you understand how to extract \( a \), \( b \), and \( c \) from a quadratic equation if you provide the full equation.
If your quadratic equation is, for example:
\[
5x^2 + 12x + 8 = 0
\]
Then, the values would be:
- \( a = 5 \)
- \( b = 12 \)
- \( c = 8 \)
Please clarify or provide the complete quadratic equation you are working with so that I can help you find the respective values accurately.
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