You work for a company that makes tiles for patios. A customer sent you the following picture of his patio. He said the patio is
made up of the same tiles, positioned vertically and horizontally. He says he wants to replace 3 tiles that are cracked. He didn’t tell you the dimensions of the tile itself but did tell you that the width of the patio was 8 feet. Determine the dimensions of a tile in the patio.
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The graph of a function is given. It is required to find the function that represents the graph.
Notice from the graph that the function has roots or zeros at -3,-2, and 2.
Hence, the function takes the form:
Where a is a constant to be determined.
Notice that the given graph passes through the point (0,-12).
Substitute x=0 and f(x)=-12 into the equation of the function to find a:
Hence, the function is:
Answer:
(a) The rate of change for the money earned, measured as dollars per delivery, between 0 and 2 deliveries is $2.
(b) The rate of change is the same between the two time intervals.
Step-by-step explanation:
The rate of change for a variables based on another variable is known as the slope.
The formula to compute the slope is:
(a)
Compute the rate of change for the money earned, measured as dollars per delivery, between 0 and 2 deliveries as follows:
For, <em>x</em>₁ = 0 and <em>x</em>₂ = 2 deliveries the money earned are <em>y</em>₁ = $5 and <em>y</em>₂ = $9.
The rate of change for the money earned is:
Thus, the rate of change for the money earned, measured as dollars per delivery, between 0 and 2 deliveries is $2.
(b)
Compute the rate of change for the money earned, measured as dollars per delivery, between 2 and 4 deliveries as follows:
For, <em>x</em>₁ = 2 and <em>x</em>₂ = 4 deliveries the money earned are <em>y</em>₁ = $9 and <em>y</em>₂ = $13.
The rate of change for the money earned is:
The rate of change for the money earned, measured as dollars per delivery, between 2 and 4 deliveries is $2.
Compute the rate of change for the money earned, measured as dollars per delivery, between 6 and 8 deliveries as follows:
For, <em>x</em>₁ = 6 and <em>x</em>₂ = 8 deliveries the money earned are <em>y</em>₁ = $17 and <em>y</em>₂ = $21.
The rate of change for the money earned is:
The rate of change for the money earned, measured as dollars per delivery, between 6 and 8 deliveries is $2.
Thus, the rate of change is the same between the two time intervals.