Question
A recipe requires 3 cups of flour for every 2 cups of sugar. How many cups of flour are needed for 8 cups of sugar?(1 point)
Responses
9
9
10
10
12
12
16
16
Question 2
In a proportional relationship, if ( y = 5 ) when ( x = 2 ), what is the value of ( y ) when ( x = 6 )?
(1 point)
Responses
10
10
12.5
12.5
15
15
20
20
Question 3
If ( y ) is directly proportional to ( x ) and ( y = 12 ) when ( x = 4 ), what is the constant of proportionality?(1 point)
Responses
1
1
2
2
3
3
4
4
Question 4
What is the solution to the equation 3𝑥−4=11?(1 point)
Responses
6
6
5
5
3
3
2
2
Question 5
What is the value of 𝑥 in the equation 3𝑥+9=0?(1 point)
Responses
-1
-1
-2
-2
-3
-3
-4
-4
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Responses
9
9
10
10
12
12
16
16
Question 2
In a proportional relationship, if ( y = 5 ) when ( x = 2 ), what is the value of ( y ) when ( x = 6 )?
(1 point)
Responses
10
10
12.5
12.5
15
15
20
20
Question 3
If ( y ) is directly proportional to ( x ) and ( y = 12 ) when ( x = 4 ), what is the constant of proportionality?(1 point)
Responses
1
1
2
2
3
3
4
4
Question 4
What is the solution to the equation 3𝑥−4=11?(1 point)
Responses
6
6
5
5
3
3
2
2
Question 5
What is the value of 𝑥 in the equation 3𝑥+9=0?(1 point)
Responses
-1
-1
-2
-2
-3
-3
-4
-4
Skip to navigation
Answers
GPT-4o mini
Here are the answers to each question:
**Question 1:**
A recipe requires 3 cups of flour for every 2 cups of sugar. To find out how many cups of flour are needed for 8 cups of sugar, you can set up the proportion:
\[\frac{3 \text{ cups of flour}}{2 \text{ cups of sugar}} = \frac{x \text{ cups of flour}}{8 \text{ cups of sugar}}\]
Cross-multiply and solve for \(x\):
\[3 \cdot 8 = 2 \cdot x\]
\[24 = 2x\]
\[x = 12\]
**Answer:** 12
---
**Question 2:**
We have the proportional relationship where \(y = 5\) when \(x = 2\). We can find the constant of proportionality \(k\):
\[k = \frac{y}{x} = \frac{5}{2}\]
Now, we want to find \(y\) when \(x = 6\):
\[y = k \cdot x = \frac{5}{2} \cdot 6 = 15\]
**Answer:** 15
---
**Question 3:**
We know that \(y\) is directly proportional to \(x\) with \(y = 12\) when \(x = 4\). Find the constant of proportionality \(k\):
\[k = \frac{y}{x} = \frac{12}{4} = 3\]
**Answer:** 3
---
**Question 4:**
To solve the equation \(3x - 4 = 11\), we can add 4 to both sides:
\[3x = 15\]
Then, divide by 3:
\[x = 5\]
**Answer:** 5
---
**Question 5:**
To find \(x\) in the equation \(3x + 9 = 0\), we can subtract 9 from both sides:
\[3x = -9\]
Then, divide by 3:
\[x = -3\]
**Answer:** -3
---
In summary, the answers to your questions are:
1. 12
2. 15
3. 3
4. 5
5. -3
**Question 1:**
A recipe requires 3 cups of flour for every 2 cups of sugar. To find out how many cups of flour are needed for 8 cups of sugar, you can set up the proportion:
\[\frac{3 \text{ cups of flour}}{2 \text{ cups of sugar}} = \frac{x \text{ cups of flour}}{8 \text{ cups of sugar}}\]
Cross-multiply and solve for \(x\):
\[3 \cdot 8 = 2 \cdot x\]
\[24 = 2x\]
\[x = 12\]
**Answer:** 12
---
**Question 2:**
We have the proportional relationship where \(y = 5\) when \(x = 2\). We can find the constant of proportionality \(k\):
\[k = \frac{y}{x} = \frac{5}{2}\]
Now, we want to find \(y\) when \(x = 6\):
\[y = k \cdot x = \frac{5}{2} \cdot 6 = 15\]
**Answer:** 15
---
**Question 3:**
We know that \(y\) is directly proportional to \(x\) with \(y = 12\) when \(x = 4\). Find the constant of proportionality \(k\):
\[k = \frac{y}{x} = \frac{12}{4} = 3\]
**Answer:** 3
---
**Question 4:**
To solve the equation \(3x - 4 = 11\), we can add 4 to both sides:
\[3x = 15\]
Then, divide by 3:
\[x = 5\]
**Answer:** 5
---
**Question 5:**
To find \(x\) in the equation \(3x + 9 = 0\), we can subtract 9 from both sides:
\[3x = -9\]
Then, divide by 3:
\[x = -3\]
**Answer:** -3
---
In summary, the answers to your questions are:
1. 12
2. 15
3. 3
4. 5
5. -3