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3 years ago

If f(x) = x4 − x3 + x2 and g(x) = −x2, where x ≠ 0, what is (f ⁄g)(x)?

Mathematics

1 answer:

sergey [27]3 years ago

6 0

Answer:

-x² + x -1

Step-by-step explanation:

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Nonlinear Systems of Equations

zheka24 [161]

The square root and cube root identities are proved.

According to the statement

we have to find that the use of the square root identity (x − y)2 = x2 − 2xy + y2

And use of cube root identity a3 + b3 = (a + b)(a2 − ab + b2).

So, For this purpose, we know that the

A. Let us assume the two conditions.

So,

2x + 3y = 6 -(1)

4x + 7y = 8 -(2)

Here we use elimination method

So, Multiply 4 with (1) and 2 with (2)

8x + 12y = 24

8x + 14y = 16

Now eliminate x from these equations

-2y = 8

here y is -4.

and the x become

2x + 3y = 6

2x -12 = 6

2x = 18

x = 9.

B. For the use of identity $(x- y)^{2} = x^{2} - 2xy + y^{2}$

Let us assume a number 26 and 28 then fill it in the condition then

$(28- 26)^{2} = 28^{2} - 2(28)(26) + 26^{2}$

Then

$(28- 26)^{2} = 784 - 1456 + 676$

$(28- 26)^{2} = 4$

And we have to prove the cube root identity then

The identity is

$a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})$

Then let us assume the number 8 and 9 then

$a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})$

$8^{3} + 9^{3} = (8 + 9)(8^{2} - 8*9 + 9^{2})$

$8^{3} + 9^{3} = (17)(64 - 72 + 81)$

$8^{3} + 9^{3} = (17)(73)$

$8^{3} + 9^{3} = (1241)$

Hence by this way we prove the square and cube root identities.

So, The square root and cube root identities are proved.

Learn more about square root and cube root here

brainly.com/question/661780

#SPJ1

3 0

2 years ago

I will mark brainliest!!!!

nata0808 [166]

Answer:

24 ft^2

Step-by-step explanation:

The small aquarium:

1 * 3 * 2 = 6 ft^2

The large aquarium

(1 + 1) * (3 + 2) * (2 + 1)

2 * 5 * 3 = 30 ft^2

Difference between the larger aquarium and the smaller aquarium:

30 - 6, or 24.

This means that the answer to this question is a, 24 ft^2

5 0

3 years ago