Felix101
contestada

PLEASE HELP!!!!!


1) The table below represents the displacement of a turtle from its nest as a function of time:

Time(hours)x: 0, 1, 2, 3, 4
Displacement from best(miles)y:
5, 27, 49, 71, 93

PART A) What is the y-intercept of the function, and what does this tell you about the turtle?

PART B) Calculate the average rate of change of the function represented by the table between x=1 to x=4 hours, and tell what the average rate represents.

PART C) What would be the domain of the function if the turtle continued to walk at this rate until it traveled 225 miles from the nest?



2) PART A) Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480.

Write an equation in the standard form to represent the total rent (y) that Sam has to pay for renting the boat for x days.

PART B) Write the equation obtained by PART A using function notation.

PART C) Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

Respuesta :

TSO
Question #1

Part A:
The y-intercept can be found when x = 0. If you look at your table, when x = 0, y = 5. So the y-intercept is 5.

Part B:
[tex]\sf Slope = \frac{27-5}{1-0} = \frac{22}{1} = \boxed{22}[/tex]
The slope is 22.

Part C:
y = mx + b
y = 22x + 5

We are given 225 as the range, or in place of y.
225 = 22x + 5
220 = 22x
x = 10

The domain is 10.



Question #2

Part A:

(2,255)
(5,480)

Standard form is Ax + By = C

[tex]\sf Slope = \frac{y_2-y_1}{x_2-x_1} = \frac{480-225}{5-2} = \frac{255}{3} = \boxed{85}[/tex]

Let's plug this into this form first:
[tex]y - y_1 = m(x-x_1)\\\\y -225 = 85(x-2)\\\\y - 225 = 85x - 170\\\\y = 85x + 55[/tex]

Now, let's make it into Standard Form.
[tex]y = 85x + 55\\\\y - 85x + 55\\\\ -85x + y = 55\\\\ -1(-85x +y) = -1(55)\\\\\boxed{85x - y = -55}[/tex]
What, which is in the box, is your final answer. :)

Part B:
Function notation simply means replacing y with f(x).
We had y = 85x + 55
So your answer is:
[tex]\boxed{f(x) = 85x + 55}[/tex]

Part C:
Using the final answer which we got in Part A, we would know that the y-intercept is (0,55) and the x-intercept is (-55/85, 0). We would plot these 2 points, and then draw a line between them. :)

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