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Step2247 [10]
3 years ago
11

All of the following are terminating decimals except 1/8 2/5 2/3 17/50

Mathematics
2 answers:
NNADVOKAT [17]3 years ago
4 0
First of all, what is a terminating decimal, a decimal that does keep repeating and going on forever. 1/8 = 0.125 CHECK! 2/5 = 0.4 CHECK! 2/3 = 0.666666666666666666666 BIG X! 17/50 = 0.34 CHECK! The only BIG X was 2/3 and 2/3 is our answer.

faust18 [17]3 years ago
3 0
A terminating decimal is a decimal that has numbers that DO NOT go on forever. 
To figure this out we need to divide the fractions given:

1/8=0.125

2/5=0.4

2/3=0.666666666666=> (repeating) 

17/50=0.34

As you can see the only fraction that has a repeating decimal (and is not a terminating decimal is 2/3). Therefore our answer is 2/3 

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→ Take sin x as a common factor in the right side

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From the graph, the equation has 4 solutions, the intersection points between the 2 graphs

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Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).
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The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

  1. <u>Shifting</u>: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the <em><u>y-coordinate</u></em> is<em> </em>added or subtract and the x-coordinate is unchanged, there is a <em><u>vertical</u></em> <u><em>shift</em></u>. If it is the <em><u>x-coordinate</u></em> which changes and y-coordinate is kept the same, the shift is a <em><u>horizontal</u></em> <u><em>shift</em></u>;
  2. <u>Scaling</u>: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the <em>y-coordinate</em> is multiplied or divided by a constant but x-coordinate is the same, it is a <em>vertical scaling</em>. If the <em>x-coordinate</em> is changed by a constant and y-coordinate is not, it is a <em>horizontal</em> <em>scaling</em>;
  3. <u>Reflecting</u>: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0)  (0,6)  (5,-4)  (8,0)

And the points for g(x) are:

(-5,-3)  (0,-9)   (5,1)   (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a <u>Vertical</u> <u>Shift</u>.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a <u>Reflection</u>.

<u>Range</u> <u>of</u> <u>a</u> <u>function</u> is all the values y can assume after substituting the x-values.

<u>Domain</u> <u>of</u> <u>a</u> <u>function</u> is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph            translation            domain      range

f(x)                       none                 [-5,8]          [-4,6]

g(x)                vertical shift           [-5,8]          [-9,1]

<u>In conclusion, this transformation (or translation) will affect the range of g(x)</u>

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