Question

the graph shows the battery usage for an appliance based on hours run. the equation for the line of best fit is y = - 3x+96. use this information to answer the following questions. 5) what would you predict as the battery life after 12 hours? 6) what would you predict as the battery life after 24 hours? 7) how far away is the point (42, 80) from the line of best fit? 8) how far away is the point (12, 92) from the line of best fit?

Explanation:

1. For question 5:

• # Explanation:
• Step1: Substitute \(x = 12\) into the equation \(y=-3x + 96\)
• \(y=-3\times12 + 96\)
• Step2: Calculate the value of \(y\)
• First, calculate \(-3\times12=-36\). Then, \(-36 + 96=60\).
• # Answer:
• 60 hours

1. For question 6:

• # Explanation:
• Step1: Substitute \(x = 24\) into the equation \(y=-3x + 96\)
• \(y=-3\times24+96\)
• Step2: Calculate the value of \(y\)
• First, calculate \(-3\times24 = - 72\). Then, \(-72 + 96=24\).
• # Answer:
• 24 hours

1. For question 7:

• # Explanation:
• Step1: Recall the distance - formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) which is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \((x_1,y_1)=(42,80)\) and we need to find \(y\) for \(x = 42\) in \(y=-3x + 96\)
• \(y=-3\times42+96\)
• Step2: Calculate \(y\) for \(x = 42\)
• First, \(-3\times42=-126\), then \(-126 + 96=-30\). Let \((x_2,y_2)=(42,-30)\). Now, \(d=\sqrt{(42 - 42)^2+(80+30)^2}=\sqrt{0 + 110^2}=110\).
• # Answer:
• 110

1. For question 8:

• # Explanation:
• Step1: First, find \(y\) for \(x = 12\) in \(y=-3x + 96\). We already know from question 5 that \(y = 60\) when \(x = 12\). Now use the distance - formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) with \((x_1,y_1)=(12,60)\) and \((x_2,y_2)=(12,92)\)
• \(d=\sqrt{(12 - 12)^2+(92 - 60)^2}\)
• Step2: Calculate the distance
• Since \(12-12 = 0\), \(d=\sqrt{0+(92 - 60)^2}=\sqrt{32^2}=32\).
• # Answer:
• 32

Answer:

1. For question 5:

• # Explanation:
• Step1: Substitute \(x = 12\) into the equation \(y=-3x + 96\)
• \(y=-3\times12 + 96\)
• Step2: Calculate the value of \(y\)
• First, calculate \(-3\times12=-36\). Then, \(-36 + 96=60\).
• # Answer:
• 60 hours

1. For question 6:

• # Explanation:
• Step1: Substitute \(x = 24\) into the equation \(y=-3x + 96\)
• \(y=-3\times24+96\)
• Step2: Calculate the value of \(y\)
• First, calculate \(-3\times24 = - 72\). Then, \(-72 + 96=24\).
• # Answer:
• 24 hours

1. For question 7:

• # Explanation:
• Step1: Recall the distance - formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) which is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \((x_1,y_1)=(42,80)\) and we need to find \(y\) for \(x = 42\) in \(y=-3x + 96\)
• \(y=-3\times42+96\)
• Step2: Calculate \(y\) for \(x = 42\)
• First, \(-3\times42=-126\), then \(-126 + 96=-30\). Let \((x_2,y_2)=(42,-30)\). Now, \(d=\sqrt{(42 - 42)^2+(80+30)^2}=\sqrt{0 + 110^2}=110\).
• # Answer:
• 110

1. For question 8:

• # Explanation:
• Step1: First, find \(y\) for \(x = 12\) in \(y=-3x + 96\). We already know from question 5 that \(y = 60\) when \(x = 12\). Now use the distance - formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) with \((x_1,y_1)=(12,60)\) and \((x_2,y_2)=(12,92)\)
• \(d=\sqrt{(12 - 12)^2+(92 - 60)^2}\)
• Step2: Calculate the distance
• Since \(12-12 = 0\), \(d=\sqrt{0+(92 - 60)^2}=\sqrt{32^2}=32\).
• # Answer:
• 32