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3 years ago

Simplify x^2+xy-yx+y^2 + y^2+yz-zy+z^2 + z^2+zx-xz+x^2

Mathematics

1 answer:

Artemon [7]3 years ago

7 0

Answer:

2x^2 + 2y^2 + 2z^2

Step-by-step explanation:

x^2+xy-yx+y^2 + y^2+yz-zy+z^2 + z^2+zx-xz+x^2

First step is to put all the same ones together

( FYI, xy and yx is the same thing, just like how

2 x 3 and 3 x 2 is the same thing) this time I'll bracket the groups to make it easier on the eyes

(x^2 +x^2) + (xy - xy) +( y^2 + y^2) + (yz - yz) +

(z^2 +z^2) + (zx - zx)

2x^2 + 2y^2 + 2z^2

All the others just cancel themselves out, for example, xy-xy

When anything minus themselves it will become 0

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Please answer both questions and show all your work. Thank you!!! :)

nignag [31]

(1) let "r" denote number of rabbits, "c" number of chickens

Set up the equations:

$r + c = 1000\\4r + 2c = 3150\\\\-2r -2c = -2000\\4r + 2c = 3150\\\\2r = 1150\implies r = 575\implies c = 425$

Answer: There are 575 rabbits and 425 chickens

(2) m - number of Mike's stamps, a - number of Andrew's stamps.

Set up equations:

$m = 4a\\m-8 = 2(a+8)\\\\4a-8=2a + 16\\2a = 24\implies a = 12\implies m = 48\\$

Answer: Mike has 48 stamps. Andrew has 12 stamps.

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3 years ago

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A textbook search committee is considering

lora16 [44]

Number of ways to select 3 books from 13 books for adoption is 286 .

Step-by-step explanation:

A Permutation is an ordered Combination. When the order does matter it is a Permutation. There are basically two types of permutation:

Repetition is Allowed: such as the lock above. It could be "333".

No Repetition: for example the first three people in a running race. You can't be first and second.

Formula is given by:

$nC_r= \frac{n!}{r! (n-r)!}$ , where n is the number of things to choose from, and we choose r of them, no repetitions, order matters. Here , n=13 , r=3.

⇒ $13C_3 = \frac{13!}{3!(13-3)!}$

⇒ $13C_3 = \frac{13!}{3!(10)!}$

⇒ $13C_3 = \frac{13(12)(11)10!}{3(2)(1)(10)!}$

⇒ $13C_3 = 13(2)(11)$

⇒ $13 C_3 = 286$

∴ Number of ways to select 3 books from 13 books for adoption is 286 .

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3 years ago

I need help with number 13 please.

Tanzania [10]

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3 years ago

When determining if you have a perfect square trinomial, what must the first and third term be?

cricket20 [7]

The expansion of a perfect square is

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In words, the square of a sum of two terms is the sum of the squares of the two terms ( $a^2$ and $b^2$ ), plus twice the product of the two terms ( $2ab$ )

So, when determining if you have a perfect square trinomial, you should have two perfect squares. Note that they don't have to be the first and third term, since you can rearrange terms as you prefer.

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3 years ago

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Gre4nikov [31]

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