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3 years ago

10

John has a box that is in the shape of a cube (i.

1 answer:

Artemon [7]3 years ago

5 0

A box (cube) has all equal edges or sides (s), thus the volume (v) of the cube is:
$v = {s}^{3} \\ 27 \: {in}^{3} = {s}^{3} \\ \sqrt{( {s}^{3}) } = \sqrt{( {27in}^3)} \\ s = 3 \: in$
So since each side or edge around is 3 in, then the length around the square bottom of the box = 4×3 = 12 in

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What is the product of<br> (5^-4)(5^-3)

Nataliya [291]

Answer:

option one is the correct answer

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Find the value of x and y. Triangle MNP = triangle TUS

xenn [34]

Answer:

x = 32, y = 51

Step-by-step explanation:

Since the triangles are congruent then corresponding sides and angles are congruent, that is

∠ U = ∠ N

∠ N = 180° - (142 + 24)° = 180° - 166° = 14° , then

2x - 50 = 14 ( add 50 to both sides )

2x = 64 ( divide both sides by 2 )

x = 32

and

NP = US

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2(32) - y = 13

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- y = - 51 ( multiply both sides by - 1 )

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3 years ago

Sum of positive roots of the equation (x2 - 12x + 35) (x2 + 10x + 24) = 504 is

Digiron [165]

Answer:

(3)11

Step-by-step explanation:

We are given that

$(x^2-12x+35)(x^2+10x+24)=504$

We have to find the sum of positive roots of the equation.

$x^2(x^2+10x+24)-12x(x^2+10x+24)+35(x^2+10x+24)=504$

$x^4+10x^3+24x^2-12x^3-120x^2-288x+35x^2+350x+840=504$

$x^4-2x^3-61x^2+62x+840-504=0$

$x^4-2x^3-61x^2+62x+336=0$

Factor of 336

2,3,4,6,8,7,

Let x=2

$2^4-2^4-61(2^2)+62(2)+336\neq0$

x=2 is not the root of equation

x=-2

$(-2)^4-2(-2)^3-61(-2)^2+62(-2)+336=0$

Hence x=-2 is the root of equation.

x+2 is a factor of equation.

x=3

$3^4-2(3^3)-61(3^2)+62(3)+336=0$

Therefore, x=3 is the root of equation.

$(x+2)(x-3)(x^2-x-56)=0$

$(x+2)(x-3)(x^2-8x+7x-56)=0$

$(x+2)(x-3)(x(x-8)+7(x-8))=0$

$(x+2)(x-3)(x-8)(x+7)=0$

$x-8=0\implies x=8$

$x+7=0\implies x=-7$

Positive roots are 3 and 8

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Option (3) is true.

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3 years ago

The statement ‘5 is added to 9 times a certain number n and the result is 32’ is represented by? *

salantis [7]

Answer:

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.:.n is represented by 3

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3<br> 1<br> 5<br> ×<br> 1<br> 1<br> 8<br> Give your answer as a mixed number in its simplest form.

Inga [223]

Answer:

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Step-by-step explanation:

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