Asked by Scar
Determine which of the following ordered pairs is a solution to the equation 3x−8=−4y.(1 point)
Responses
(0,2)
left parenthesis 0 comma 2 right parenthesis
(0,−2)
left parenthesis 0 comma negative 2 right parenthesis
(−1,1)
left parenthesis negative 1 comma 1 right parenthesis
(1,1)
Responses
(0,2)
left parenthesis 0 comma 2 right parenthesis
(0,−2)
left parenthesis 0 comma negative 2 right parenthesis
(−1,1)
left parenthesis negative 1 comma 1 right parenthesis
(1,1)
Answers
Answered by
Scar
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.
Sam believes (−4,−7) is a solution.
Sam believes left parenthesis negative 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.
Peter believes (−4,7) is a solution.
Responses
Mary believes (4,−7) is a solution.
Mary believes left parenthesis 4 comma negative 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.
Fiona believes (4,7) is a solution.
Fiona believes left parenthesis 4 comma 7 right parenthesis is a solution.
Peter believes (−4,7) is a solution.
Answered by
Scar
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
(3,12)
left parenthesis 3 comma 12 right parenthesis
(3,7)
left parenthesis 3 comma 7 right parenthesis
(3,45)
left parenthesis 3 comma 45 right parenthesis
(3,14)
Responses
(3,12)
left parenthesis 3 comma 12 right parenthesis
(3,7)
left parenthesis 3 comma 7 right parenthesis
(3,45)
left parenthesis 3 comma 45 right parenthesis
(3,14)
Answered by
Scar
Which of the following ordered pairs is part of the solution set for the equation y=2x+5 ?
(1 point)
Responses
(7,1)
left parenthesis 7 comma 1 right parenthesis
(1,7)
left parenthesis 1 comma 7 right parenthesis
(3,−1)
left parenthesis 3 comma negative 1 right parenthesis
(1,2)
(1 point)
Responses
(7,1)
left parenthesis 7 comma 1 right parenthesis
(1,7)
left parenthesis 1 comma 7 right parenthesis
(3,−1)
left parenthesis 3 comma negative 1 right parenthesis
(1,2)
Answered by
Scar
Which of the following ordered pairs is part of the solution set for the equation y=5x2−2 ?
(1 point)
Responses
(−1,3)
left parenthesis negative 1 comma 3 right parenthesis
(1,5)
left parenthesis 1 comma 5 right parenthesis
(−1,43)
left parenthesis negative 1 comma 43 right parenthesis
(−1,5)
(1 point)
Responses
(−1,3)
left parenthesis negative 1 comma 3 right parenthesis
(1,5)
left parenthesis 1 comma 5 right parenthesis
(−1,43)
left parenthesis negative 1 comma 43 right parenthesis
(−1,5)
Answered by
GPT-4o mini
To determine which of the given ordered pairs is a solution to the equation \(3x - 8 = -4y\), we will substitute the values of \(x\) and \(y\) from each ordered pair into the equation and check if the equation holds true.
1. For \((0, 2)\):
\[
3(0) - 8 = -4(2) \\
-8 = -8 \quad \text{(True)}
\]
2. For \((0, -2)\):
\[
3(0) - 8 = -4(-2) \\
-8 = 8 \quad \text{(False)}
\]
3. For \((-1, 1)\):
\[
3(-1) - 8 = -4(1) \\
-3 - 8 = -4 \\
-11 = -4 \quad \text{(False)}
\]
4. For \((1, 1)\):
\[
3(1) - 8 = -4(1) \\
3 - 8 = -4 \\
-5 = -4 \quad \text{(False)}
\]
The only ordered pair that satisfies the equation \(3x - 8 = -4y\) is \((0, 2)\).
1. For \((0, 2)\):
\[
3(0) - 8 = -4(2) \\
-8 = -8 \quad \text{(True)}
\]
2. For \((0, -2)\):
\[
3(0) - 8 = -4(-2) \\
-8 = 8 \quad \text{(False)}
\]
3. For \((-1, 1)\):
\[
3(-1) - 8 = -4(1) \\
-3 - 8 = -4 \\
-11 = -4 \quad \text{(False)}
\]
4. For \((1, 1)\):
\[
3(1) - 8 = -4(1) \\
3 - 8 = -4 \\
-5 = -4 \quad \text{(False)}
\]
The only ordered pair that satisfies the equation \(3x - 8 = -4y\) 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 the values of \(x\) and \(y\) from each ordered pair into the equation and check if the equation holds true.
1. For \((4, -7)\):
\[
1.5(4) - 2(-7) = 8 \\
6 + 14 = 8 \\
20 \neq 8 \quad \text{(False)}
\]
2. For \((-4, -7)\):
\[
1.5(-4) - 2(-7) = 8 \\
-6 + 14 = 8 \\
8 = 8 \quad \text{(True)}
\]
3. For \((4, 7)\):
\[
1.5(4) - 2(7) = 8 \\
6 - 14 = 8 \\
-8 \neq 8 \quad \text{(False)}
\]
4. For \((-4, 7)\):
\[
1.5(-4) - 2(7) = 8 \\
-6 - 14 = 8 \\
-20 \neq 8 \quad \text{(False)}
\]
The only ordered pair that satisfies the equation \(1.5x - 2y = 8\) is \((-4, -7)\). Therefore, Sam is correct in believing that \((-4, -7)\) is a solution.
1. For \((4, -7)\):
\[
1.5(4) - 2(-7) = 8 \\
6 + 14 = 8 \\
20 \neq 8 \quad \text{(False)}
\]
2. For \((-4, -7)\):
\[
1.5(-4) - 2(-7) = 8 \\
-6 + 14 = 8 \\
8 = 8 \quad \text{(True)}
\]
3. For \((4, 7)\):
\[
1.5(4) - 2(7) = 8 \\
6 - 14 = 8 \\
-8 \neq 8 \quad \text{(False)}
\]
4. For \((-4, 7)\):
\[
1.5(-4) - 2(7) = 8 \\
-6 - 14 = 8 \\
-20 \neq 8 \quad \text{(False)}
\]
The only ordered pair that satisfies the equation \(1.5x - 2y = 8\) is \((-4, -7)\). Therefore, Sam is correct in believing that \((-4, -7)\) is a solution.
Answered by
GPT-4o mini
To determine which of the given ordered pairs is a part of the solution set for the equation \(y = 4x + 2\), we will plug in the \(x\) values from each ordered pair into the equation and check if the resulting \(y\) value matches.
1. For \((3, 12)\):
\[
y = 4(3) + 2 \\
y = 12 + 2 \\
y = 14 \quad \text{(Does not match; 12 ≠ 14)}
\]
2. For \((3, 7)\):
\[
y = 4(3) + 2 \\
y = 12 + 2 \\
y = 14 \quad \text{(Does not match; 7 ≠ 14)}
\]
3. For \((3, 45)\):
\[
y = 4(3) + 2 \\
y = 12 + 2 \\
y = 14 \quad \text{(Does not match; 45 ≠ 14)}
\]
4. For \((3, 14)\):
\[
y = 4(3) + 2 \\
y = 12 + 2 \\
y = 14 \quad \text{(Matches; 14 = 14)}
\]
The only ordered pair that satisfies the equation \(y = 4x + 2\) is \((3, 14)\).
1. For \((3, 12)\):
\[
y = 4(3) + 2 \\
y = 12 + 2 \\
y = 14 \quad \text{(Does not match; 12 ≠ 14)}
\]
2. For \((3, 7)\):
\[
y = 4(3) + 2 \\
y = 12 + 2 \\
y = 14 \quad \text{(Does not match; 7 ≠ 14)}
\]
3. For \((3, 45)\):
\[
y = 4(3) + 2 \\
y = 12 + 2 \\
y = 14 \quad \text{(Does not match; 45 ≠ 14)}
\]
4. For \((3, 14)\):
\[
y = 4(3) + 2 \\
y = 12 + 2 \\
y = 14 \quad \text{(Matches; 14 = 14)}
\]
The only ordered pair that satisfies the equation \(y = 4x + 2\) is \((3, 14)\).
Answered by
GPT-4o mini
To determine which of the given ordered pairs is part of the solution set for the equation \(y = 2x + 5\), we will substitute the values of \(x\) and \(y\) from each ordered pair into the equation and check if the equation holds true.
1. For \((7, 1)\):
\[
y = 2(7) + 5 \\
y = 14 + 5 \\
y = 19 \quad \text{(Does not match; 1 ≠ 19)}
\]
2. For \((1, 7)\):
\[
y = 2(1) + 5 \\
y = 2 + 5 \\
y = 7 \quad \text{(Matches; 7 = 7)}
\]
3. For \((3, -1)\):
\[
y = 2(3) + 5 \\
y = 6 + 5 \\
y = 11 \quad \text{(Does not match; -1 ≠ 11)}
\]
4. For \((1, 2)\):
\[
y = 2(1) + 5 \\
y = 2 + 5 \\
y = 7 \quad \text{(Does not match; 2 ≠ 7)}
\]
The only ordered pair that satisfies the equation \(y = 2x + 5\) is \((1, 7)\).
1. For \((7, 1)\):
\[
y = 2(7) + 5 \\
y = 14 + 5 \\
y = 19 \quad \text{(Does not match; 1 ≠ 19)}
\]
2. For \((1, 7)\):
\[
y = 2(1) + 5 \\
y = 2 + 5 \\
y = 7 \quad \text{(Matches; 7 = 7)}
\]
3. For \((3, -1)\):
\[
y = 2(3) + 5 \\
y = 6 + 5 \\
y = 11 \quad \text{(Does not match; -1 ≠ 11)}
\]
4. For \((1, 2)\):
\[
y = 2(1) + 5 \\
y = 2 + 5 \\
y = 7 \quad \text{(Does not match; 2 ≠ 7)}
\]
The only ordered pair that satisfies 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 ordered pair into the equation and check if the calculated \(y\) value matches the \(y\) value in the ordered pair.
1. For \((-1, 3)\):
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 = 3 \quad \text{(Matches; 3 = 3)}
\]
2. For \((1, 5)\):
\[
y = 5(1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 = 3 \quad \text{(Does not match; 5 ≠ 3)}
\]
3. For \((-1, 43)\):
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 = 3 \quad \text{(Does not match; 43 ≠ 3)}
\]
4. For \((-1, 5)\):
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 = 3 \quad \text{(Does not match; 5 ≠ 3)}
\]
The only ordered pair that satisfies the equation \(y = 5x^2 - 2\) is \((-1, 3)\).
1. For \((-1, 3)\):
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 = 3 \quad \text{(Matches; 3 = 3)}
\]
2. For \((1, 5)\):
\[
y = 5(1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 = 3 \quad \text{(Does not match; 5 ≠ 3)}
\]
3. For \((-1, 43)\):
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 = 3 \quad \text{(Does not match; 43 ≠ 3)}
\]
4. For \((-1, 5)\):
\[
y = 5(-1)^2 - 2 \\
y = 5(1) - 2 \\
y = 5 - 2 = 3 \quad \text{(Does not match; 5 ≠ 3)}
\]
The only ordered pair that satisfies the equation \(y = 5x^2 - 2\) is \((-1, 3)\).