Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To determine the equation that represents the relationship between the hours ([tex]$x$[/tex]) and the miles driven ([tex]$y$[/tex]), let's first observe the pattern shown in the table.
Given points:
- When [tex]$x = 3$[/tex], [tex]$y = 195$[/tex]
- When [tex]$x = 4$[/tex], [tex]$y = 260$[/tex]
- When [tex]$x = 5$[/tex], [tex]$y = 325$[/tex]
- When [tex]$x = 6$[/tex], [tex]$y = 390$[/tex]
From the question, it is stated that each [tex]$x$[/tex] value is multiplied by 65 to get each [tex]$y$[/tex] value.
Let's verify this relationship with the given points to ensure it holds true:
- For [tex]$x = 3$[/tex]: [tex]$y = 65 \times 3 = 195$[/tex]
- For [tex]$x = 4: $[/tex]y = 65 \times 4 = 260[tex]$ - For $[/tex]x = 5: [tex]$y = 65 \times 5 = 325$[/tex]
- For [tex]$x = 6: $[/tex]y = 65 \times 6 = 390[tex]$ Since the relationship holds true for all given points, the general equation representing this relationship is: \[ y = 65x \] Next, we need to determine which point could NOT be on this table. Consider the test point \((2, 100)\): Let's calculate the $[/tex]y[tex]$ value using our equation for $[/tex]x = 2[tex]$: \[ y = 65 \times 2 = 130 \] The test point \((2, 100)\) indicates that the $[/tex]y[tex]$ value should be 100. However, based on our calculated $[/tex]y[tex]$ value, for $[/tex]x = 2[tex]$, we should have $[/tex]y = 130[tex]$. Since the given $[/tex]y[tex]$ value (100) does not match the calculated $[/tex]y$ value (130), the point [tex]\((2, 100)\)[/tex] could NOT be on this table.
In conclusion:
- The equation for this situation is: [tex]\[ y = 65x \][/tex]
- The point [tex]\((2, 100)\)[/tex] could NOT be a point on this table.
Given points:
- When [tex]$x = 3$[/tex], [tex]$y = 195$[/tex]
- When [tex]$x = 4$[/tex], [tex]$y = 260$[/tex]
- When [tex]$x = 5$[/tex], [tex]$y = 325$[/tex]
- When [tex]$x = 6$[/tex], [tex]$y = 390$[/tex]
From the question, it is stated that each [tex]$x$[/tex] value is multiplied by 65 to get each [tex]$y$[/tex] value.
Let's verify this relationship with the given points to ensure it holds true:
- For [tex]$x = 3$[/tex]: [tex]$y = 65 \times 3 = 195$[/tex]
- For [tex]$x = 4: $[/tex]y = 65 \times 4 = 260[tex]$ - For $[/tex]x = 5: [tex]$y = 65 \times 5 = 325$[/tex]
- For [tex]$x = 6: $[/tex]y = 65 \times 6 = 390[tex]$ Since the relationship holds true for all given points, the general equation representing this relationship is: \[ y = 65x \] Next, we need to determine which point could NOT be on this table. Consider the test point \((2, 100)\): Let's calculate the $[/tex]y[tex]$ value using our equation for $[/tex]x = 2[tex]$: \[ y = 65 \times 2 = 130 \] The test point \((2, 100)\) indicates that the $[/tex]y[tex]$ value should be 100. However, based on our calculated $[/tex]y[tex]$ value, for $[/tex]x = 2[tex]$, we should have $[/tex]y = 130[tex]$. Since the given $[/tex]y[tex]$ value (100) does not match the calculated $[/tex]y$ value (130), the point [tex]\((2, 100)\)[/tex] could NOT be on this table.
In conclusion:
- The equation for this situation is: [tex]\[ y = 65x \][/tex]
- The point [tex]\((2, 100)\)[/tex] could NOT be a point on this table.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.