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2 years ago

Which expression is equivalent to x6 – 9?

Mathematics

2 answers:

Lorico [155]2 years ago

7 0

Answer:

$(x^{3})^{2} -3^{2}$

Step-by-step explanation:

we have

$x^{6}-9$

we know that

$x^{6}-9=(x^{3})^{2} -3^{2}$

Applying difference of square

$(x^{3})^{2} -3^{2}=(x^{3}+3)(x^{3}-3)$

coldgirl [10]2 years ago

4 0

If you would like to know the equal expression to the x^6 - 9, you can do this using the following steps:

x^6 - 9 = (x^3)^2 - 3^2
(x^3)^2 = x^3 * x^3 = x^6
3^2 = 3 * 3 = 9

The correct result would be (x^3)^2 - 3^2.

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Answer:

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Step-by-step explanation:6/5

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Sliva [168]

Answer:

The graph of g(x) is wider.

Step-by-step explanation:

Parent function:

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New function:

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Transformations:

For a > 0

$f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}$

$f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}$

$\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of}\:a\\ & \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a\\\end{aligned}$

$\begin{aligned} y=f(ax) \implies & f(x) \: \textsf{stretched/compressed horizontally by a factor of} \: a\\& \textsf{If }a > 1 \textsf{ it is compressed by a factor of}\: a\\ & \textsf{If }0 < a < 1 \textsf{ it is stretched by a factor of}\: a\\\end{aligned}$

If the parent function is shifted ¹/₄ unit up:

$\implies g(x)=x^2+\dfrac{1}{4}$

If the parent function is shifted ¹/₄ unit down:

$\implies g(x)=x^2-\dfrac{1}{4}$

If the parent function is compressed vertically by a factor of ¹/₄:

$\implies g(x)=\dfrac{1}{4}x^2$

If the parent function is stretched horizontally by a factor of ¹/₂:

$\implies g(x)=\left(\dfrac{1}{2}x\right)^2$

Therefore, a vertical compression and a horizontal stretch mean that the graph of g(x) is wider.

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1 year ago

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Answer:

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2 years ago

An English teacher has 6 short stories, 4 novels, and 23 poems to choose from. How many ways can he assign one of each to his cl

Karolina [17]

Answer:

552

Step-by-step explanation:

This is a problem of permutation which can be solved by rule of fundamental counting principle.

This principle states that if there "m" ways of doing one thing and "n" ways of doing other. Then no. of ways in which both the things can be done together is "m*n". This can be extended for m, n, p,r, s things and so on.

example: if there are 5 shirts and 3 trousers then number of ways in which the shirts and trousers can be worn is 5*3 = 15 ways.

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The given problem is on similar concepts.

here 6 short stories, 4 novels, and 23 poems have to be assigned to his class.

Thus it can be done in 6*4*23 = 552 ways.

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Answer:

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