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Equations in Two Variables Quick Check 1 of 51 of 5 Items Question Determine which of the following ordered pairs is a solution...Question
Equations in Two Variables Quick Check 1 of 51 of 5 Items Question Determine which of the following ordered pairs is a solution to the equation 3x−8=−4y.(1 point) Responses (−1,1) left parenthesis negative 1 comma 1 right parenthesis (0,2) left parenthesis 0 comma 2 right parenthesis (0,−2) left parenthesis 0 comma negative 2 right parenthesis (1,1)
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Answer
The math teacher asked his students to determine a solution for 1.5x−2y=8 . Which solution below is the correct one?(1 point) Responses Mary believes (4,−7) is a solution. Mary believes left parenthesis 4 comma negative 7 right parenthesis is a solution. Fiona believes (4,7) is a solution. Fiona believes left parenthesis 4 comma 7 right parenthesis is a solution. Sam believes (−4,−7) is a solution. Sam believes left parenthesis negative 4 comma negative 7 right parenthesis is a solution. Peter believes (−4,7) is a solution.
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Select the option below that correctly shows which of the following ordered pairs is part of the solution set for the equation y=4x+2 .(1 point) Responses (3,7) left parenthesis 3 comma 7 right parenthesis (3,12) left parenthesis 3 comma 12 right parenthesis (3,14) left parenthesis 3 comma 14 right parenthesis (3,45) left parenthesis 3 comma 45 right parenthesis
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Which of the following ordered pairs is part of the solution set for the equation y=2x+5 ? (1 point) Responses (3,−1) left parenthesis 3 comma negative 1 right parenthesis (7,1) left parenthesis 7 comma 1 right parenthesis (1,2) left parenthesis 1 comma 2 right parenthesis (1,7) left parenthesis 1 comma 7 right parenthesis Skip to navigation
Answer
Which of the following ordered pairs is part of the solution set for the equation y=5x2−2 ? (1 point) Responses (−1,5) left parenthesis negative 1 comma 5 right parenthesis (−1,3) left parenthesis negative 1 comma 3 right parenthesis (−1,43) left parenthesis negative 1 comma 43 right parenthesis (1,5)
Answer
A local arcade charges $15.00 for unlimited play time for the first hour, then $5.00 per additional hour. On a piece of paper, write an equation that represents the cost to play, C , based on the number of hours played, h. Then use the equation to calculate how much it would cost to play for three hours. Enter your answer for C , including cents.(1 point) $
Answered by
GPT-4o mini
To determine which of the ordered pairs is a solution to the equation \(3x - 8 = -4y\), we will substitute each pair into the equation and see if it holds true.
1. **For the first pair \((-1, 1)\)**:
\[
3(-1) - 8 = -4(1) \\
-3 - 8 = -4 \\
-11 \neq -4 \quad \text{(not a solution)}
\]
2. **For the second pair \((0, 2)\)**:
\[
3(0) - 8 = -4(2) \\
0 - 8 = -8 \\
-8 = -8 \quad \text{(is a solution)}
\]
3. **For the third pair \((0, -2)\)**:
\[
3(0) - 8 = -4(-2) \\
0 - 8 = 8 \\
-8 \neq 8 \quad \text{(not a solution)}
\]
4. **For the fourth pair \((1, 1)\)**:
\[
3(1) - 8 = -4(1) \\
3 - 8 = -4 \\
-5 \neq -4 \quad \text{(not a solution)}
\]
So, the only solution from the provided ordered pairs is \((0, 2)\).
1. **For the first pair \((-1, 1)\)**:
\[
3(-1) - 8 = -4(1) \\
-3 - 8 = -4 \\
-11 \neq -4 \quad \text{(not a solution)}
\]
2. **For the second pair \((0, 2)\)**:
\[
3(0) - 8 = -4(2) \\
0 - 8 = -8 \\
-8 = -8 \quad \text{(is a solution)}
\]
3. **For the third pair \((0, -2)\)**:
\[
3(0) - 8 = -4(-2) \\
0 - 8 = 8 \\
-8 \neq 8 \quad \text{(not a solution)}
\]
4. **For the fourth pair \((1, 1)\)**:
\[
3(1) - 8 = -4(1) \\
3 - 8 = -4 \\
-5 \neq -4 \quad \text{(not a solution)}
\]
So, the only solution from the provided ordered pairs is \((0, 2)\).
Answered by
GPT-4o mini
To determine which of the given ordered pairs is a solution to the equation \(1.5x - 2y = 8\), we will substitute each pair into the equation and see if it holds true.
**1. For Mary’s pair \((4, -7)\)**:
\[
1.5(4) - 2(-7) = 8 \\
6 + 14 = 8 \\
20 \neq 8 \quad \text{(not a solution)}
\]
**2. For Fiona’s pair \((4, 7)\)**:
\[
1.5(4) - 2(7) = 8 \\
6 - 14 = 8 \\
-8 \neq 8 \quad \text{(not a solution)}
\]
**3. For Sam’s pair \((-4, -7)\)**:
\[
1.5(-4) - 2(-7) = 8 \\
-6 + 14 = 8 \\
8 = 8 \quad \text{(is a solution)}
\]
**4. For Peter’s pair \((-4, 7)\)**:
\[
1.5(-4) - 2(7) = 8 \\
-6 - 14 = 8 \\
-20 \neq 8 \quad \text{(not a solution)}
\]
The correct solution is Sam’s pair \((-4, -7)\).
**1. For Mary’s pair \((4, -7)\)**:
\[
1.5(4) - 2(-7) = 8 \\
6 + 14 = 8 \\
20 \neq 8 \quad \text{(not a solution)}
\]
**2. For Fiona’s pair \((4, 7)\)**:
\[
1.5(4) - 2(7) = 8 \\
6 - 14 = 8 \\
-8 \neq 8 \quad \text{(not a solution)}
\]
**3. For Sam’s pair \((-4, -7)\)**:
\[
1.5(-4) - 2(-7) = 8 \\
-6 + 14 = 8 \\
8 = 8 \quad \text{(is a solution)}
\]
**4. For Peter’s pair \((-4, 7)\)**:
\[
1.5(-4) - 2(7) = 8 \\
-6 - 14 = 8 \\
-20 \neq 8 \quad \text{(not a solution)}
\]
The correct solution is Sam’s pair \((-4, -7)\).
Answered by
GPT-4o mini
To determine which of the ordered pairs is part of the solution set for the equation \(y = 4x + 2\), we will substitute \(x = 3\) into the equation and calculate the corresponding \(y\) value. We then check which ordered pair matches that value.
1. **Substituting \(x = 3\)**:
\[
y = 4(3) + 2 \\
y = 12 + 2 \\
y = 14
\]
From our calculations, when \(x = 3\), \(y\) equals 14. Therefore, the ordered pair that corresponds to this value is \((3, 14)\).
Among the options given, the correct one is:
\((3, 14)\).
1. **Substituting \(x = 3\)**:
\[
y = 4(3) + 2 \\
y = 12 + 2 \\
y = 14
\]
From our calculations, when \(x = 3\), \(y\) equals 14. Therefore, the ordered pair that corresponds to this value is \((3, 14)\).
Among the options given, the correct one is:
\((3, 14)\).
Answered by
GPT-4o mini
To find which of the ordered pairs is part of the solution set for the equation \(y = 2x + 5\), we will substitute the \(x\) value from each pair into the equation and see if we get the corresponding \(y\) value.
1. **For the pair \((3, -1)\)**:
\[
y = 2(3) + 5 \\
y = 6 + 5 \\
y = 11 \quad \text{(not a match)}
\]
2. **For the pair \((7, 1)\)**:
\[
y = 2(7) + 5 \\
y = 14 + 5 \\
y = 19 \quad \text{(not a match)}
\]
3. **For the pair \((1, 2)\)**:
\[
y = 2(1) + 5 \\
y = 2 + 5 \\
y = 7 \quad \text{(not a match)}
\]
4. **For the pair \((1, 7)\)**:
\[
y = 2(1) + 5 \\
y = 2 + 5 \\
y = 7 \quad \text{(this is a match)}
\]
The pair that is part of the solution set for the equation \(y = 2x + 5\) is \((1, 7)\).
1. **For the pair \((3, -1)\)**:
\[
y = 2(3) + 5 \\
y = 6 + 5 \\
y = 11 \quad \text{(not a match)}
\]
2. **For the pair \((7, 1)\)**:
\[
y = 2(7) + 5 \\
y = 14 + 5 \\
y = 19 \quad \text{(not a match)}
\]
3. **For the pair \((1, 2)\)**:
\[
y = 2(1) + 5 \\
y = 2 + 5 \\
y = 7 \quad \text{(not a match)}
\]
4. **For the pair \((1, 7)\)**:
\[
y = 2(1) + 5 \\
y = 2 + 5 \\
y = 7 \quad \text{(this is a match)}
\]
The pair that is part of the solution set for the equation \(y = 2x + 5\) is \((1, 7)\).
Answered by
GPT-4o mini
To determine which of the given ordered pairs is part of the solution set for the equation \(y = 5x^2 - 2\), we will substitute the \(x\) values from each pair into the equation and check if the resulting \(y\) value matches the second value of the pair.
1. **For the pair \((-1, 5)\)**:
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 \\
y = 3 \quad \text{(not a match, expected 5)}
\]
2. **For the pair \((-1, 3)\)**:
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 \\
y = 3 \quad \text{(this is a match)}
\]
3. **For the pair \((-1, 43)\)**:
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 \\
y = 3 \quad \text{(not a match, expected 43)}
\]
4. **For the pair \((1, 5)\)**:
\[
y = 5(1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 \\
y = 3 \quad \text{(not a match, expected 5)}
\]
The ordered pair that is part of the solution set for the equation \(y = 5x^2 - 2\) is \((-1, 3)\).
1. **For the pair \((-1, 5)\)**:
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 \\
y = 3 \quad \text{(not a match, expected 5)}
\]
2. **For the pair \((-1, 3)\)**:
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 \\
y = 3 \quad \text{(this is a match)}
\]
3. **For the pair \((-1, 43)\)**:
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 \\
y = 3 \quad \text{(not a match, expected 43)}
\]
4. **For the pair \((1, 5)\)**:
\[
y = 5(1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 \\
y = 3 \quad \text{(not a match, expected 5)}
\]
The ordered pair that is part of the solution set for the equation \(y = 5x^2 - 2\) is \((-1, 3)\).
Answered by
GPT-4o mini
To represent the cost to play, \(C\), based on the number of hours played, \(h\), we can write the following piecewise equation:
\[
C =
\begin{cases}
15 & \text{if } 0 < h \leq 1 \\
15 + 5(h - 1) & \text{if } h > 1
\end{cases}
\]
This means:
- If you play for up to 1 hour, the cost is $15.
- If you play for more than 1 hour, the cost is the initial $15 plus $5 for each additional hour beyond the first.
Now let's calculate the cost to play for **three hours**:
Since \(h = 3\) (which is more than 1 hour), we use the second part of the equation:
\[
C = 15 + 5(h - 1)
\]
Substituting \(h = 3\):
\[
C = 15 + 5(3 - 1) \\
C = 15 + 5(2) \\
C = 15 + 10 \\
C = 25
\]
Therefore, the cost to play for three hours is **$25.00**.
\[
C =
\begin{cases}
15 & \text{if } 0 < h \leq 1 \\
15 + 5(h - 1) & \text{if } h > 1
\end{cases}
\]
This means:
- If you play for up to 1 hour, the cost is $15.
- If you play for more than 1 hour, the cost is the initial $15 plus $5 for each additional hour beyond the first.
Now let's calculate the cost to play for **three hours**:
Since \(h = 3\) (which is more than 1 hour), we use the second part of the equation:
\[
C = 15 + 5(h - 1)
\]
Substituting \(h = 3\):
\[
C = 15 + 5(3 - 1) \\
C = 15 + 5(2) \\
C = 15 + 10 \\
C = 25
\]
Therefore, the cost to play for three hours is **$25.00**.
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