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3 years ago

Using the binomial theorem, expand the expression (4 + y) to the power of 4

Mathematics

1 answer:

Flauer [41]3 years ago

8 0

Answer:

When raised to the power of 4, the binomial (4 + y) expands to:

$y^4 + 16y^3 + 96y^2 + 256y + 256$

Step-by-step explanation:

$(4 + y)^4 \\= (y^2 + 8y + 16)^2\\= y^4 + 8y^3 + 16y^2 + 8y^3 + 64y^2 + 128y + 16y^2 + 128y + 256\\= y^4 + 16y^3 + 96y^2 + 256y + 256$

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Help me for 8 and 9?????

Digiron [165]

8. In A, because those trees are in the deciduous.
9. All of these forests contains life and lot and lots of trees.

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3 0

3 years ago

associate in a department store earns a commission on each suit and each pair of shoes sold. One week, she earned $47 in commiss

Len [333]

Answer: the commission that she earns for selling each suit is $13

the commission that she earns for selling each pair of shoes is $8

Step-by-step explanation:

Let x represent the commission that she earns for selling each suit.

Let y represent the commission that she earns for selling each pair of shoes.

One week, she earned $47 in commission for selling 3 suits and a pair of shoes. It means that

3x + y = 47 - - - - - - - - - - 1

The next week, she earned $107 in commission for selling 7 suits and 2 pairs of shoes. It means that

7x + 2y = 107 - - - - -- - - - -2

Multiplying equation 1 by 2 and equation 2 by 1, it becomes

6x + 2y = 94

7x + 2y = 107

-x = -13

x = 13

Substituting x = -13 ,into equation 1, it becomes

3×13 + y = 47

39 +y = 47

y = 47 - 39 =

y = 8

7 0

4 years ago

suppose that n is a positive integer written in base 10. prove that n is divisible by 3 if and only if the sum of its decimal di

Goshia [24]

Modulo - The result of multiplying the original number by three and the result of multiplying the digits by three must be the same.

What is modulo?

In mathematics, the phrase modulo, which literally means "with respect to a modulus of," is frequently used to claim that two different mathematical objects can be regarded as comparable if their difference is explained by a third component.

Using the Fermat's little theorem:

$x^n-1 =(x-1)(x^{n-1}+x^{n-2}+....+x+1)$

when x=10. You may easily establish the identity by multiplying it term by word. All terms cancel, excluding the first and last ones. Therefore, any power of ten minus one is divisible by nine, and consequently, by three

Now consider a multi-digit natural number, 43617 for example.

$43617= 4*10^4+3*10^3+6*10^2+1*10+7$

$= 4*9999+3*999+6*99+1*9+(4+3+6+1+7)$

Other than the sum of the digits, every term on the right is divisible by 3. The result of multiplying the original number by three and the result of multiplying the digits by three must be the same.

to learn more about exponents and power visit:

brainly.com/question/19120853

#SPJ4

5 0

2 years ago

What is the sign of -4x\cdot y\cdot 0^6−4x⋅y⋅0 6 minus, 4, x, dot, y, dot, 0, start superscript, 6, end superscript when xxx and

castortr0y [4]

Answer:

non-negative

Step-by-step explanation:

Given

$-4x\cdot y\cdot 0^6$