Dyingontheinside
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The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. time (hours) 4, 6, 8, 10 distance (miles) 212, 318, 424, 530

Respuesta :

[tex]\bf \begin{array}{ccll} \stackrel{\stackrel{x}{hours}}{time}&\stackrel{\stackrel{y}{miles}}{distance}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 4&212\\ \boxed{6}&\boxed{318}\\ 8&424\\ \boxed{10}&\boxed{530} \end{array}\\\\ -------------------------------[/tex]

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 6}}\quad ,&{{ 318}})\quad % (c,d) &({{ 10}}\quad ,&{{ 530}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{530-318}{10-6}\implies \cfrac{212}{4} \\\\\\ \stackrel{\textit{average rate of change}}{\cfrac{53}{1}}[/tex]

recall the top is distance, and the bottom is hours, so 53 miles for every 1 hour.  So the object or vehicle is moving at 53 mph on average.

Answer:

The car travels 53 miles per hour.

Step-by-step explanation:

time (hours)           4       6      8       10

distance (miles)   212   318   424   530

The rate of change can be given as:

[tex]\frac{318-212}{6-4}[/tex] = [tex]\frac{106}{2}[/tex] = 53 mph

[tex]\frac{424-318}{8-6}[/tex] = [tex]\frac{106}{2}[/tex] = 53 mph

Hence, the rate of change is 53 mph or we can say the car travels 53 miles per hour.

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