Answer:
(1, 0.5)
Step-by-step explanation:
From the graph attached,
x-values are representing the number of games downloaded,
y - values are representing the total cost.
Unit rate means rate of 1 game downloaded.
If we represent this in terms of coordinates,
x- value (game downloaded) = 1
y - value (price of one game download) = $0.5
Therefore, point (1, 0.5) will represent the unit rate.
Option (2) on the top row will be the answer.
We will investigate how to determine Hamilton paths and circuits
Hamilton path: A path that connect each vertex/point once without repetition of a point/vertex. However, the starting and ending point/vertex can be different.
Hamilton circuit: A path that connect each vertex/point once without repetition of a point/vertex. However, the starting and ending point/vertex must be the same!
As the starting point we can choose any of the points. We will choose point ( F ) and trace a path as follows:
The above path covers all the vertices/points with the starting and ending point/vertex to be ( F ). Such a path is called a Hamilton circuit per definition.
We will choose a different point now. Lets choose ( E ) as our starting point and trace the path as follows:
The above path covers all the vertices/points with the starting and ending point/vertex are different with be ( E ) and ( C ), respectively. Such a path is called a Hamilton path per definition.
One more thing to note is that all Hamilton circuits can be converted into a Hamilton path like follows:
The above path is a hamilton path that can be formed from the Hamilton circuit example.
But its not necessary for all Hamilton paths to form a Hamilton circuit! Unfortunately, this is not the case in the network given. Every point is in a closed loop i.e there is no loose end/vertex that is not connected by any other vertex.
The value of x in the trapezoid given, to the nearest tenth, is: 10.5.
<h3>What is a Trapezoid?</h3>
A trapezoid is a quadrilateral that has two sides only that are parallel to each other.
<h3>What is the Area of a Trapezoid?</h3>
To find the area of a trapezoid, the formula used is expressed as: 1/2(a + b) × h, where:
- a and b are length of the two base sides that are parallel.
- h is the height of altitude of the trapezoid.
Given the following:
Area of trapezoid = 174 units²
AP = 6
PB = x + 3
CD = 2x + 6
AC = 10
Using the formula, we variables in the formula are:
a = AP + PB = 6 + x + 3 = x + 9
b = CD = 2x + 3
h = PC = √(AC² - AP²)
h = √(10² - 6²) = 8
Plug in the values into 1/2(a + b) × h:
174 = 1/2(x + 9 + 2x + 3) × 8
174 = 1/2(3x + 12) × 8
174 = (3x + 12) × 4
174 = 12x + 48
174 - 48 = 12x
126 = 12x
126/12 = x
10.5 = x
x = 10.5
Learn more about the trapezoid on:
brainly.com/question/1463152
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C. 2x + 4 = 2x + 6 is the correct answer. It has no solution.