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3 years ago

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

2 answers:

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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Solve: 2 + = 2. Give solutions in interval [0, 2)

Dovator [93]

$\because\cos 2x+\sin x=\sin 2x$ $\because\sin 2x=2\sin xcosx$ $\because\cos 2x=\cos ^2x-\sin ^2x$

→ Substitute cos 2x and sin 2x by their expressions

$\therefore\cos ^2x-\sin ^2+\sin x=2\sin x\cos x$

→ Subtract both sides by sin x

$\cos ^2x-\sin ^2x=2\sin xcosx-\sin x$

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

$\therefore\cos ^2x-\sin ^2x=\sin x(2\cos x-1)$

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

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1 year ago

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).

Neporo4naja [7]

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:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: 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 Vertical Shift.

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 Reflection.

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

Domain of a function 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]

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

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Natasha_Volkova [10]

Answer:

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Step-by-step explanation:

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ale4655 [162]

Step-by-step explanation:

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Alexus [3.1K]

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