Question
Question 1
A)
Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans plants 29 daisies, how many snapdragons will he plant?
Number of
Snapdragons, x
Number of
Daisies, y
11 34
12 33
13 32
14 31
(2 points)
The equation that models the scenario is
.
Hans will plant
Snapdragons.
Question 2
A)What is the value of x in the equation 3x−4y=65
when y=4
?(1 point)
Responses
x=21.67
x is equal to 21 point 6 7
x=27
x is equal to 27
x=13.25
x is equal to 13 point 2 5
x=23
x is equal to 23
Question 3
A)Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2l+2w=62
to find the width of the run. Which statements are true of the solution? Select the three that apply.(3 points)
Responses
The value of w cannot be a negative number.
The value of w cannot be a negative number.
The value of w can be 0.
The value of w can be 0.
The value of w is 10 feet.
The value of w is 10 feet.
Substitution is used to replace the variable l with a value of 20.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w.
The subtraction property of equality is used to isolate the term with the variable w.
Question 4
A)
Jillian's school is selling tickets for a play. The ticket cost is $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50a+3.75b=2071.50
, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how many adult tickets were sold?
NOTE: Type the correct numerical value into the blank to receive credit for this question.
(1 point)
$$ adult tickets
Question 5
A)Fiona bought some socks that cost $4.95 for each pair and some belts that cost $6.55 each. Fiona spent $27.95 in all. Let a represent the number of pairs of socks purchased and b represent the number of belts purchased. Which equation models the situation?(1 point)
Responses
4.95a+6.55b=27.95
4 point 9 5 A plus 6 point 5 5 b is equal to 27 point 9 5
a+b=27.95
A plus b is equal to 27 point 9 5
6.55a+4.95b=27.95
6 point 5 5 A plus 4 point 9 5 b is equal to 27 point 9 5
a+b=11.50
A plus b is equal to 11 point 5 0
A)
Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans plants 29 daisies, how many snapdragons will he plant?
Number of
Snapdragons, x
Number of
Daisies, y
11 34
12 33
13 32
14 31
(2 points)
The equation that models the scenario is
.
Hans will plant
Snapdragons.
Question 2
A)What is the value of x in the equation 3x−4y=65
when y=4
?(1 point)
Responses
x=21.67
x is equal to 21 point 6 7
x=27
x is equal to 27
x=13.25
x is equal to 13 point 2 5
x=23
x is equal to 23
Question 3
A)Shana wants to use all 62 feet of the fencing she has to make a rectangular run for her dog. She decides to make the length of the run 20 feet. She writes and solves the equation 2l+2w=62
to find the width of the run. Which statements are true of the solution? Select the three that apply.(3 points)
Responses
The value of w cannot be a negative number.
The value of w cannot be a negative number.
The value of w can be 0.
The value of w can be 0.
The value of w is 10 feet.
The value of w is 10 feet.
Substitution is used to replace the variable l with a value of 20.
Substitution is used to replace the variable l with a value of 20.
The subtraction property of equality is used to isolate the term with the variable w.
The subtraction property of equality is used to isolate the term with the variable w.
Question 4
A)
Jillian's school is selling tickets for a play. The ticket cost is $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50a+3.75b=2071.50
, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how many adult tickets were sold?
NOTE: Type the correct numerical value into the blank to receive credit for this question.
(1 point)
$$ adult tickets
Question 5
A)Fiona bought some socks that cost $4.95 for each pair and some belts that cost $6.55 each. Fiona spent $27.95 in all. Let a represent the number of pairs of socks purchased and b represent the number of belts purchased. Which equation models the situation?(1 point)
Responses
4.95a+6.55b=27.95
4 point 9 5 A plus 6 point 5 5 b is equal to 27 point 9 5
a+b=27.95
A plus b is equal to 27 point 9 5
6.55a+4.95b=27.95
6 point 5 5 A plus 4 point 9 5 b is equal to 27 point 9 5
a+b=11.50
A plus b is equal to 11 point 5 0
Answers
GPT-4o mini
Let's address each question one by one:
**Question 1**
Based on the data provided, the number of snapdragons decreases as the number of daisies increases. You can recognize this as a linear relationship. The equation may take the form:
\[ y = -x + k \]
Where \( k \) can be deduced from the table. Let's examine the relationship with an example pair:
- When \( x = 11 \), \( y = 34 \)
- When \( x = 12 \), \( y = 33 \)
From the pattern, we can see that each time \( x \) increases by 1, \( y \) decreases by 1. Thus it follows that:
When \( y = 29 \):
\[ x + 29 = 45 \implies x = 45 - 29 = 16.\]
Thus, Hans will plant **16 snapdragons**.
---
**Question 2**
To find \( x \) in the equation \( 3x−4y=65 \) when \( y=4\), substitute \( y \) into the equation:
\[ 3x - 4(4) = 65 \]
\[ 3x - 16 = 65 \]
\[ 3x = 81 \]
\[ x = 27. \]
So the correct response is **x=27**.
---
**Question 3**
For the equation \( 2l + 2w = 62 \) with \( l = 20 \):
Substituting \( l \):
\[ 2(20) + 2w = 62 \]
\[ 40 + 2w = 62 \]
\[ 2w = 22 \]
\[ w = 11. \]
The correct statements are:
1. **The value of w cannot be a negative number.**
2. **Substitution is used to replace the variable l with a value of 20.**
3. **The subtraction property of equality is used to isolate the term with the variable w.**
(Note that the third statement about the value of \( w \) being 10 feet is false; it is actually 11 feet.)
---
**Question 4**
Using the equation \( 10.50a + 3.75b = 2071.50 \) with \( b = 82 \):
Substitution gives:
\[ 10.50a + 3.75(82) = 2071.50 \]
\[ 10.50a + 307.50 = 2071.50 \]
\[ 10.50a = 1764 \]
\[ a = \frac{1764}{10.50} = 168 \].
Thus, **168 adult tickets** were sold.
---
**Question 5**
To model Fiona’s spending on socks and belts, the correct equation is:
\[ 4.95a + 6.55b = 27.95. \]
Thus, the response is **4.95a + 6.55b = 27.95**.
---
If you need additional explanations or assistance with further questions, feel free to ask!
**Question 1**
Based on the data provided, the number of snapdragons decreases as the number of daisies increases. You can recognize this as a linear relationship. The equation may take the form:
\[ y = -x + k \]
Where \( k \) can be deduced from the table. Let's examine the relationship with an example pair:
- When \( x = 11 \), \( y = 34 \)
- When \( x = 12 \), \( y = 33 \)
From the pattern, we can see that each time \( x \) increases by 1, \( y \) decreases by 1. Thus it follows that:
When \( y = 29 \):
\[ x + 29 = 45 \implies x = 45 - 29 = 16.\]
Thus, Hans will plant **16 snapdragons**.
---
**Question 2**
To find \( x \) in the equation \( 3x−4y=65 \) when \( y=4\), substitute \( y \) into the equation:
\[ 3x - 4(4) = 65 \]
\[ 3x - 16 = 65 \]
\[ 3x = 81 \]
\[ x = 27. \]
So the correct response is **x=27**.
---
**Question 3**
For the equation \( 2l + 2w = 62 \) with \( l = 20 \):
Substituting \( l \):
\[ 2(20) + 2w = 62 \]
\[ 40 + 2w = 62 \]
\[ 2w = 22 \]
\[ w = 11. \]
The correct statements are:
1. **The value of w cannot be a negative number.**
2. **Substitution is used to replace the variable l with a value of 20.**
3. **The subtraction property of equality is used to isolate the term with the variable w.**
(Note that the third statement about the value of \( w \) being 10 feet is false; it is actually 11 feet.)
---
**Question 4**
Using the equation \( 10.50a + 3.75b = 2071.50 \) with \( b = 82 \):
Substitution gives:
\[ 10.50a + 3.75(82) = 2071.50 \]
\[ 10.50a + 307.50 = 2071.50 \]
\[ 10.50a = 1764 \]
\[ a = \frac{1764}{10.50} = 168 \].
Thus, **168 adult tickets** were sold.
---
**Question 5**
To model Fiona’s spending on socks and belts, the correct equation is:
\[ 4.95a + 6.55b = 27.95. \]
Thus, the response is **4.95a + 6.55b = 27.95**.
---
If you need additional explanations or assistance with further questions, feel free to ask!