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3 years ago

Use the distributive property to write the following expression in expanded form. 5(7h + 3m)

Mathematics

1 answer:

laiz [17]3 years ago

3 0

<h3>hello!</h3>

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The distributive property states that:-

$\bigstar{\underline{\boxed{\pmb{a(b+c)=ab+ac}}}$

Simplify:-

$\bigstar{\boxed{\pmb{5(7h+3m)}}}$

$\longmapsto\sf{(5~times~7h)+)5*3m)$

$\longmapsto\sf{35h*15m}$

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Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

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Find the perimeter and area of a rectangle of cardboard measuring 15.9 cm by 11.7cm

IRISSAK [1]

The area is 186.03. lw = 15.9(11.7) = 186.03

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3 years ago

Find the total number of sides (y)

riadik2000 [5.3K]

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There are 24 sides.

Step-by-step explanation:

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3 years ago

If:

PSYCHO15rus [73]

Take some trinomial expansions to find some useful expressions and their values.

• 2nd degree expansion

$x + y + z = 7 \\\\ \implies (x+y+z)^2 = x^2+y^2+z^2+2(xy+xz+yz) = 7^2 \\\\ \implies xy+xz+yz = \dfrac{49-33}2 = 8$

• 3rd degree expansion

$x+y+z=7 \implies (x+y+z)^3 = 7^3 \\\\ \implies \\ 243 = x^3+y^3+z^3+3(x^2y+x^2z+xy^2+y^2z+xz^2+yz^2) + 6xyz \\\\ \implies \\ x^2y+x^2z+xy^2+y^2z+xz^2+yz^2 + 2xyz = \dfrac{343 - 145}3 = 66$

• 4th degree expansion

$x+y+z=7 \implies (x+y+z)^4 = 7^4 \\\\ \implies \\ 2401 = x^4+y^4+z^4+4(x^3y+x^3z+xy^3+y^3z+xz^3+yz^3) \\\\ ~~~~~~~~~~~~+ 6(x^2y^2+x^2z^2+y^2z^2) + 12(x^2yz+xy^2z+xyz^2) \\\\ \implies \\\\ x^4+y^4+z^4 = 2401 - 4(x^3y+x^3z+xy^3+y^3z+xz^3+yz^3) \\\\ ~~~~~~~~~~~~~~~~~~~~~~- 6(x^2y^2+x^2z^2+y^2z^2) - 12(x^2yz+xy^2z+xyz^2)$

Simplify:

$x^3y+x^3z+xy^3+y^3z+xz^3+yz^3 \\\\ ~~~~ = x^2 (xy+xz) + y^2 (xy+yz) + z^2 (xz + yz) \\\\ ~~~~ = x^2 (xy+xz+yz) + y^2 (xy+xz+yz) + z^2 (xy + xz + yz) - (x^2yz + xy^2z + xyz^2) \\\\ ~~~~ = (x^2+y^2+z^2) (xy+xz+yz) - xyz (x+y+z) \\\\ ~~~~ = 264 - 7xyz$

$x^2y^2+x^2z^2+y^2z^2 \\\\ ~~~~ = xy\cdot xy + xz \cdot xz + yz \cdot yz \\\\ ~~~~ = xy(xy+xz+yz) + xz(xy+xz+yz) + yz(xy+xz+yz) - 2(x^2yz+xy^2z+xyz^2) \\\\ ~~~~ = (xy+xz+yz)^2 - 2xyz(x+y+z) \\\\ ~~~~ = 64 - 14xyz$

$x^2yz+xy^2z+xyz^2 = xyz (x + y + z) = 7xyz$

Then the equation we got from the 4th degree expansion reduces to

$x^4+y^4+z^4 = 2401 - 4(264-7xyz) - 6(64-14xyz) - 12(7xyz) \\\\ ~~~~~~~~~~~~~~~~~= 961 + 28xyz$

and all we need now is the value of $xyz$ .

In the 3rd degree expansion, we have

$x^2y+x^2z+xy^2+y^2z+xz^2+yz^2 \\\\ ~~~~ = x(xy + xz) + y(xy + yz) + z(xz + yz) \\\\ ~~~~ = x(xy+xz+yz) + y(xy+xz+yz) + z(xy+xz+yz) - 3xyz \\\\ ~~~~ = (x+y+z)(xy+xz+yz) - 3xyz \\\\ ~~~~ = 56 - 3xyz \\\\ \implies (56 - 3xyz) + 2xyz = 66 \\\\ \implies xyz = -10$

So, we end up with

$x^4+y^4+z^4 = 961 - 280 = \boxed{681}$

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1 year ago

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8) = 9 cups. How to: 2*3=6. so you multiply the other side (3) by 3 so 3*3=9 cups.

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3 years ago

Solve for x for the following question

anastassius [24]

X equals 3 because i know 2 to the fifth power is 32,so 3x-4=5so 3*3=9

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3 years ago