Mathematics: Factories 54m3n + 81m4n2 b) 15x2y3z + 25x3y2z + 35x2y2z

Factories 54m3n + 81m4n2 b) 15x2y3z + 25x3y2z - id5438142152325323510602761, LaughterLies

Ответ:

highflylex279

17.03.2022

Mathematics

Part a)

Given the expression

$54m^3n\:+\:81m^4n^2$

Apply exponent rule: $a^{b+c}=a^ba^c$

$54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn$ ∵ m^4n^2=m^3mnn

Rewrite 81 as 3 · 27

Rewrite 54 as 2 · 27

$=2\cdot \:27m^3n+3\cdot \:27m^3mnn$

Factor out the common term: 27m³n

$=27m^3n\left(2+3mn\right)$

Therefore,

$54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn=27m^3n\left(2+3mn\right)$

Part B)

Given the expression

15x^2y^3z+25x^3y^2z+35x^2y^2z

Apply exponent rule: $a^{b+c}=a^ba^c$

15x^2y^3z+25x^3y^2z+35x^2y^2z=15x^2y^2yz+25x^2xy^2z+35x^2y^2z

Rewrite as

$=3\cdot \:5y^2x^2zy+5\cdot \:5y^2x^2zx+7\cdot \:5y^2x^2z$

Factor out common term 5y²x²z

$=5y^2x^2z\left(3y+5x+7\right)$

Therefore,

$15x^2y^3z+25x^3y^2z+35x^2y^2z=5y^2x^2z\left(3y+5x+7\right)$

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Ответ:

syrai7404

03.11.2022

Mathematics

3 units

Step-by-step explanation:

The volume of the pyramid is given by the formula ...

V = 1/3Bh

where B is the base area and h is the height.

Filling in the given numbers, we find the base area to be ...

147 = (1/3)B(9)

49 = B . . . . . . . divide by 3

The square prism with the same volume will have a height given by ...

V = Bh

147 = 49h . . . . . . . fill in the known numbers

147/49 = h = 3 . . . divide by 49

The square prism has a height of 3 units.

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Factories 54m3n + 81m4n2 b) 15x2y3z + 25x3y2z + 35x2y2z

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