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2 years ago

For the function f(x)=(x+6)^3, rind f^-1(x)

Mathematics

1 answer:

qaws [65]2 years ago

5 0

Answer:

$f^{-1}(x)=\sqrt[3]{x}-6$

Step-by-step explanation:

$f(x)=(x+6)^3$

$y=(x+6)^3$

$x=(y+6)^3$

$\sqrt[3]{x}=y+6$

$\sqrt[3]{x}-6=y$

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The diameter of a round dinner plate is 10 inches. What's the area of the plate?

Anni [7]

Lets say pi is 3.14
The area of a circle is: pi*radius squared
The radius is half the diameter so it is 5 inches.
3.14*5 squared 2
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78.5inches squared

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3 years ago

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What is the sum of the arithmetic series

docker41 [41]

Answer:

$S_ {12} = 192$

Step-by-step explanation:

The nth term of the given arithmetic sequence is

$U_n = 3 + 2n$

The first term of this series is:

$U_1 = 3 + 2(1) = 5$

The last term of this series is when

$n = 12$

$U_ {12}= 3 + 2(12)$

$U_ {12}= 3 + 24 = 27$

The sum of the first n terms of an arithmetic series when the first an last term is known is given by:

$S_n = \frac{n}{2}(a + l)$

Where a=5 is the first term and l=27 is the last term.

$S_ {12} = \frac{12}{2}(5 + 27)$

$S_ {12} =6(32) =19 2$

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3 years ago

What set of transformations could be applied to rectangle ABCD to create A″B″C″D″? 'Rectangle formed by ordered pairs A at negat

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Answer:

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2 years ago

Solve the system of equations using the linear combination method {5p-3q=-39 -2p-3q=3

VikaD [51]

Answer:

p=-6

q=3

Step-by-step explanation:

5p-3q=-39

-2p-3q=3

Multiply the second equation by -1

2p +3q = -3

Add the first equation and the modified second equation

5p-3q=-39

2p +3q = -3

---------------------

7p = -42

Divide by 7

7p/7 = -42/7

p = -6

Now we can find q

2p +3q = -3

2(-6) +3q = -3

-12 +3q = -3

Add 12 to each side

-12+12 +3q = -3+12

3q = 9

Divide by 3

3q/3 = 9/3

q=3

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2 years ago

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Nicholas has a collection of books. He has 115 fantasy and science fiction books. These books are 46% of his collection. How man

Anit [1.1K]

Given that Nicholas has a 115 fantasy and science fiction books which is 46% of his collection.

Now we have to find what is total number of books in his collection.

Let number of books in Nicholas collection = x

then number of fantasy and science fiction books = 46% of x = 0.46x

We already know that he has 115 fantasy and science fiction books, so both values will be equal and give equation:

0.46x=115

now we can solve this equation to find the answer.

$x=\frac{115}{0.46}$

x= 250

Hence final answer is:

Nicholas has 250 books in his collection.

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3 years ago

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