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1 year ago

The graph of F(x) shown below resembles the graph of G(x) = x4, but it has

Mathematics

1 answer:

DerKrebs [107]1 year ago

3 0

Using translation concepts, the equation of F(x) is:

A. $F(x) = \frac{1}{3}x^4 - 2$

<h3>What is a translation?</h3>

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The parent function is:

$G(x) = x^4$

For function F(x), we have that:

It was shifted down 2 units, hence F(x) = G(x) - 2.

It was vertically compressed by a factor of 3, hence $F(x) = \frac{1}{3}G(x) - 2$

Then the equation is:

A. $F(x) = \frac{1}{3}x^4 - 2$

More can be learned about translation concepts at brainly.com/question/28098112

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Match the expressions with their equivalent simplified expressions.

Tasya [4]

Answer:

$\sqrt[4]{\frac{16x^6y^4}{81x^2y^8}}\rightarrow\frac{2x}{3y}\\\sqrt[4]{\frac{81x^2y^{10}}{81x^6y^6}} \rightarrow\frac{3y}{2x}\\\sqrt[3]{\frac{64x^8y^7}{125x^2y^{10}}}\rightarrow\frac{4x^2}{5y}\\\sqrt[5]{\frac{243x^{17}y^{16}}{32x^7y^{21}}}\rightarrow\frac{3x^2}{2y}\\\sqrt[5]{\frac{32x^{12}y^{15}}{243x^7y^{10}}} \rightarrow\frac{2xy}{3}\\\sqrt[4]{\frac{16x^{10}y^{9}}{256x^2y^{17}}}\rightarrow\frac{x}{2y}$

Step-by-step explanation:

$\sqrt[4]{\frac{16x^6y^4}{81x^2y^8}} =\sqrt[4]{\frac{(2^4)(x^{6-2})(y^{4-8})}{(3^4)}} =\sqrt[4]{\frac{2^4x^4y^{-4}}{3^4}} =\frac{2xy^{-1}}{3}=\frac{2x}{3y}$

$\sqrt[4]{\frac{81x^2y^{10}}{81x^6y^6}} =\sqrt[4]{\frac{(3^4)(x^{2-6})(y^{10-6})}{(2^4)}} =\sqrt[4]{\frac{3^4x^{-4}y^{4}}{2^4}} =\frac{3x^{-1}y^1}{3}=\frac{3y}{2x}$

$\sqrt[3]{\frac{64x^8y^7}{125x^2y^{10}}} =\sqrt[3]{\frac{(4^3)(x^{8-2})(y^{7-10})}{(5^3)}} =\sqrt[3]{\frac{4^3x^6y^{-3}}{5^3}} =\frac{4x^2y^{-1}}{5}=\frac{4x^2}{5y}$

$\sqrt[5]{\frac{243x^{17}y^{16}}{32x^7y^{21}}} =\sqrt[5]{\frac{(3^5)(x^{17-7})(y^{16-21})}{(2^5)}} =\sqrt[5]{\frac{3^5x^{10}y^{-5}}{2^5}} =\frac{3x^2y^{-1}}{2}=\frac{3x^2}{2y}$

$\sqrt[5]{\frac{32x^{12}y^{15}}{243x^7y^{10}}} =\sqrt[5]{\frac{(2^5)(x^{12-7})(y^{15-10})}{(3^5)}} =\sqrt[5]{\frac{2^5x^{5}y^{5}}{3^5}} =\frac{2x^1y^{1}}{3}=\frac{2xy}{3}$

$\sqrt[4]{\frac{16x^{10}y^{9}}{256x^2y^{17}}} =\sqrt[4]{\frac{(2^4)(x^{10-2})(y^{9-17})}{(4^4)}} =\sqrt[4]{\frac{2^4x^{8}y^{-8}}{4^4}} =\frac{2x^{1}y^{-1}}{4}=\frac{x}{2y}$

Thus,

3 0

3 years ago

You are preparing a chemical hazard label for a new product. you know that the product is flammable. what pictogram should be on

lilavasa [31]

A graphic logo that depicts the meaning of any warning or sign through pictorial illustrations is called a pictogram. It can be used in chemicals, laboratories, geography or tourism. The label should have: Flammable and Health Hazard!

<h3>What is a pictogram?</h3>

The pictogram can be explained as: According to the above description, the label sign should have a warning sign of flammable as it can catch and cause fire, a health hazard as it can cause corrosion, carcinogenic and irritation followed by an exclamation mark.

The flammable sign depicts that the substance can cause and catch fires also it can contain pyrophoric. It is cancer-causing, respiratory irritant and toxic hence is hazardous to health.

The exclamation mark is used at the end of the sentence for showing awareness and to convey the meaning of the sign.

Therefore, Flammable and Health Hazard! the sign should be used.

To learn more about pictograms follow the link:

brainly.com/question/14266873

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5 0

2 years ago

LMNP is a rectangle. Find the value of x and the length of each diagonal LN= 4x + 13 and MP=9x - 7

Volgvan

Answer:

5/3

Step-by-step explanation:

Since the given figure is a rectangle with congruent diagonals and thus equal lengths, you can use the expressions for the diagonal lengths, set them equal, and solve the equation for x.

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2 years ago

Ted is saving for a toy. He has no money now, but

sweet-ann [11.9K]

Answer:

4D - 1

Step-by-step explanation:

So, if Ted saves $D for 4 weeks, then this amount will be equal to 4D because multiplication is simply repeated addition. We can imagine this situation as D+D+D+D, for the 4 weeks he is saving. We can simplify this to 4D in the expression.

Next, the question tells us that this will be 1 dollar more than needed. So, if we want to find the cost, we need to subtract that dollar.

Thus, the final expression is 4D - 1 because this represents 1 dollar less than the money he saves for 4 weeks.

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2 years ago

Car A travels 6 miles in 8 minutes at a constant speed. if this car continues to travel at this rate, how many minutes would it

ivanzaharov [21]

Answer:

I'm guessing 12 not sure why just guessing

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2 years ago