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)

Answer 1

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 \((0, 2)\).

Answer 2

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.

Answer 3

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 \((-4, -7)\).

Answer 4

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

Answer 5

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:

\((3, 14)\).

Answer 6

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 7

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 \((1, 7)\).

Answer 8

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 9

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 \((-1, 3)\).

Answer 10

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) $

Answer 11

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.