Question
Question 1
A)
Week Total Amount Left
1 92
2 74
3 56
4 38
Ingrid received $110.00 for her birthday and plans to spend $18.00 per week.
(1 point)
Ingrid will run out of money at the end of
.
Question 2
A)
For the equation below, x is the input and y is the output. Choose the ordered pair that makes a true statement for the equation.
y=−4x+3
(1 point)
Responses
(1, -1)
(1, -1)
(-1, 1)
(-1, 1)
(0, -3)
(0, -3)
(2, 11)
(2, 11)
Question 3
A)
For the equation below, x is the input and y is the output.
y=−4x+3
NOTE: Type the correct numerical value for the output into the blank to receive credit for this question.
(1 point)
If the input is -8, then the output is $$.
Question 4
A)
Equation: w=112+8t
(2 points)
Which input results in an output of 176?
What is the output in the ordered pair (4, 144)?
Question 5
A)
Week (w) Plant 1 (h) Plant 2 (h)
0 2.5 2.5
1 2.9 2.7
2 3.3 2.9
3
4
Science class is growing two plants. Plant 1 gets sunlight, and Plant 2 does not get sunlight. The class members organize the data in a table using the equations.
Plant 1: h=2.5+410w
Plant 2: h=2.5+15w
How much taller is Plant 1 than Plant 2 at the end of Week 3?
(1 point)
Responses
3.7 inches
3.7 inches
0.6 inches
0.6 inches
0.4 inches
0.4 inches
3.1 inches
3.1 inches
A)
Week Total Amount Left
1 92
2 74
3 56
4 38
Ingrid received $110.00 for her birthday and plans to spend $18.00 per week.
(1 point)
Ingrid will run out of money at the end of
.
Question 2
A)
For the equation below, x is the input and y is the output. Choose the ordered pair that makes a true statement for the equation.
y=−4x+3
(1 point)
Responses
(1, -1)
(1, -1)
(-1, 1)
(-1, 1)
(0, -3)
(0, -3)
(2, 11)
(2, 11)
Question 3
A)
For the equation below, x is the input and y is the output.
y=−4x+3
NOTE: Type the correct numerical value for the output into the blank to receive credit for this question.
(1 point)
If the input is -8, then the output is $$.
Question 4
A)
Equation: w=112+8t
(2 points)
Which input results in an output of 176?
What is the output in the ordered pair (4, 144)?
Question 5
A)
Week (w) Plant 1 (h) Plant 2 (h)
0 2.5 2.5
1 2.9 2.7
2 3.3 2.9
3
4
Science class is growing two plants. Plant 1 gets sunlight, and Plant 2 does not get sunlight. The class members organize the data in a table using the equations.
Plant 1: h=2.5+410w
Plant 2: h=2.5+15w
How much taller is Plant 1 than Plant 2 at the end of Week 3?
(1 point)
Responses
3.7 inches
3.7 inches
0.6 inches
0.6 inches
0.4 inches
0.4 inches
3.1 inches
3.1 inches
Answers
GPT-4o mini
Let's work through each question step by step.
### Question 1
To find out when Ingrid will run out of money, we can first calculate how much she spends each week, and then compare that to the total amount she started with ($110.00).
Starting amount: $110.00
Spending per week: $18.00
- Week 1: 110 - 18 = 92
- Week 2: 92 - 18 = 74
- Week 3: 74 - 18 = 56
- Week 4: 56 - 18 = 38
- Week 5: 38 - 18 = 20
- Week 6: 20 - 18 = 2
- Week 7: 2 - 18 = -16 (money runs out)
Ingrid will run out of money at the end of **Week 7**.
### Question 2
We need to find an ordered pair (x, y) such that it satisfies the equation \( y = -4x + 3 \).
Let's check each given ordered pair:
1. For \( (1, -1) \):
\( y = -4(1) + 3 = -4 + 3 = -1 \) ✓
2. For \( (-1, 1) \):
\( y = -4(-1) + 3 = 4 + 3 = 7 \) ✗
3. For \( (0, -3) \):
\( y = -4(0) + 3 = 0 + 3 = 3 \) ✗
4. For \( (2, 11) \):
\( y = -4(2) + 3 = -8 + 3 = -5 \) ✗
The correct ordered pair that makes a true statement is **(1, -1)**.
### Question 3
We need to find the output when the input \( x = -8 \) in the equation \( y = -4x + 3 \).
Let's calculate:
\( y = -4(-8) + 3 = 32 + 3 = 35 \)
If the input is -8, then the output is **35**.
### Question 4
We have the equation \( w = 112 + 8t \) and need to find which input results in an output of 176.
Setting \( w = 176 \):
\( 176 = 112 + 8t \)
Can solve for \( t \):
- Subtract 112 from both sides:
\( 176 - 112 = 8t \)
- \( 64 = 8t \)
- Divide by 8:
\( t = 8 \)
So the input \( t \) that results in an output of 176 is **8**.
Now, for the ordered pair (4, 144), we just need to plug in \( t = 4 \) into the original equation \( w = 112 + 8t \):
- \( w = 112 + 8(4) = 112 + 32 = 144 \)
So the output for (4, 144) is **144**.
### Question 5
We will calculate the height of each plant at the end of Week 3.
Using the equations:
**Plant 1:** \( h = 2.5 + 4(10)3 = 2.5 + 120 = 122.5 \)
**Plant 2:** \( h = 2.5 + 15(3) = 2.5 + 45 = 47.5 \)
To find how much taller Plant 1 is than Plant 2:
- Height difference = Plant 1 height - Plant 2 height = \( 122.5 - 47.5 = 75 \)
At the end of Week 3, the height of Plant 1 is **75 inches** taller than Plant 2.
However, since the answer choices seem incorrect, they likely are based on a clearer mistake in the setup or assumptions. If the initial values are meant to reflect something different, we would need clarity on that. But based on provided data, that's the conclusion we derive based on calculations.
**Final Answers:**
1. **Week 7**
2. **(1, -1)**
3. **35**
4. Input resulting in 176: **8**; Output in (4, 144): **144**
5. Height difference: **75 inches** (note: validate question context).
### Question 1
To find out when Ingrid will run out of money, we can first calculate how much she spends each week, and then compare that to the total amount she started with ($110.00).
Starting amount: $110.00
Spending per week: $18.00
- Week 1: 110 - 18 = 92
- Week 2: 92 - 18 = 74
- Week 3: 74 - 18 = 56
- Week 4: 56 - 18 = 38
- Week 5: 38 - 18 = 20
- Week 6: 20 - 18 = 2
- Week 7: 2 - 18 = -16 (money runs out)
Ingrid will run out of money at the end of **Week 7**.
### Question 2
We need to find an ordered pair (x, y) such that it satisfies the equation \( y = -4x + 3 \).
Let's check each given ordered pair:
1. For \( (1, -1) \):
\( y = -4(1) + 3 = -4 + 3 = -1 \) ✓
2. For \( (-1, 1) \):
\( y = -4(-1) + 3 = 4 + 3 = 7 \) ✗
3. For \( (0, -3) \):
\( y = -4(0) + 3 = 0 + 3 = 3 \) ✗
4. For \( (2, 11) \):
\( y = -4(2) + 3 = -8 + 3 = -5 \) ✗
The correct ordered pair that makes a true statement is **(1, -1)**.
### Question 3
We need to find the output when the input \( x = -8 \) in the equation \( y = -4x + 3 \).
Let's calculate:
\( y = -4(-8) + 3 = 32 + 3 = 35 \)
If the input is -8, then the output is **35**.
### Question 4
We have the equation \( w = 112 + 8t \) and need to find which input results in an output of 176.
Setting \( w = 176 \):
\( 176 = 112 + 8t \)
Can solve for \( t \):
- Subtract 112 from both sides:
\( 176 - 112 = 8t \)
- \( 64 = 8t \)
- Divide by 8:
\( t = 8 \)
So the input \( t \) that results in an output of 176 is **8**.
Now, for the ordered pair (4, 144), we just need to plug in \( t = 4 \) into the original equation \( w = 112 + 8t \):
- \( w = 112 + 8(4) = 112 + 32 = 144 \)
So the output for (4, 144) is **144**.
### Question 5
We will calculate the height of each plant at the end of Week 3.
Using the equations:
**Plant 1:** \( h = 2.5 + 4(10)3 = 2.5 + 120 = 122.5 \)
**Plant 2:** \( h = 2.5 + 15(3) = 2.5 + 45 = 47.5 \)
To find how much taller Plant 1 is than Plant 2:
- Height difference = Plant 1 height - Plant 2 height = \( 122.5 - 47.5 = 75 \)
At the end of Week 3, the height of Plant 1 is **75 inches** taller than Plant 2.
However, since the answer choices seem incorrect, they likely are based on a clearer mistake in the setup or assumptions. If the initial values are meant to reflect something different, we would need clarity on that. But based on provided data, that's the conclusion we derive based on calculations.
**Final Answers:**
1. **Week 7**
2. **(1, -1)**
3. **35**
4. Input resulting in 176: **8**; Output in (4, 144): **144**
5. Height difference: **75 inches** (note: validate question context).