How many halves are in one and one-half?
2 answers:
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Using the stated transformation, the graph of g(2x) is given at the end of the answer.
<h3>Horizontal stretch and compression</h3>An horizontal stretch or an horizontal compression happens when a constant is multiplied at the domain of the function, as follows:
g(x) = f(ax).
The definition of stretch or compression depends on the value of the constant a, as follows:
- If a > 1, it is a compression by a factor of 1/a.
- If a < 1, it is a stretch by a factor of 1/a.
In this problem, the rule is:
f(x) = g(2x).
Meaning that f(x) is an horizontal compression by a factor of 1/2 of g(x), and then the vertices are given as follows:
- (0,0).
- (1,-4).
- (2,-2).
That is, in each vertex, the x-coordinate was divided by 2, and thus the graph with these vertices is given at the end of the answer.
More can be learned about transformations at brainly.com/question/28725644
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Answer:
- distance traveled: 30 m
- displacement: 21.4 m
Step-by-step explanation:
You want the distance traveled and the displacement after walking 17 m south and 13 m east.
<h3>Distance</h3>The distance traveled is the sum of the lengths of each leg of the trip:
17 m + 13 m = 30 m
You have traveled a distance of 30 m.
<h3>Displacement</h3>The displacement is the distance from your final position to your starting position. If you draw a diagram of the journey, you see the displacement is the hypotenuse of a right triangle with legs 17 m and 13 m. The Pythagorean theorem can help you find this length:
h = √(a² +b²)
h = √(17² +13²) = √(289 +169) = √458 ≈ 21.401
At the end of your walking, you are 21.4 m from where you started.
