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2 years ago

find the volume of a rectangular prism if the length is 3x^2, the width is 2xand the height is x^2+3x+5

1 answer:

3 0

You are given the length of a rectangular prism of 3x^2, width of 2x and height of x^2 + 3x +5. You are required to find the volume of a rectangular prism. Using the equation V = l x w x h, we multiply the three dimensions.

V = l x w x h

V = (3x^2)(2x)( x^2 + 3x +5)

V = 2x (3x^4 + 9x^3 + 15x^2)

V = 6x^5 + 18x^4 + 30x^3

The volume of the rectangular prism is 6x^5 + 18x^4 + 30x^3.

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Will rate7 you brainliest

Vilka [71]

Answer:

$\Large \boxed{\sf \bf \ \ \dfrac{x^2-x-6}{x^2-3x+2} \ \ }$

Step-by-step explanation:

Hello, first of all, we will check if we can factorise the polynomials.

$\boxed{x^2+6x+8}\\\\\text{The sum of the zeroes is -6=(-4)+(-2) and the product 8=(-4)*(-2), so}\\\\x^2+6x+8=x^2+2x+4x+8=x(x+2)+4(x+2)=(x+2)(x+4)$

$\boxed{x^2+3x-10}\\\\\text{The sum of the zeroes is -3=(-5)+(+2) and the product -10=(-5)*(+2), so}\\\\x^2+3x-10=x^2+5x-2x-10=x(x+5)-2(x+5)=(x+5)(x-2)$

$\boxed{x^2+2x-15}\\\\\text{The sum of the zeroes is -2=(-5)+(+3) and the product -15=(-5)*(+3), so}\\\\x^2+2x-15=x^2-3x+5x-15=x(x-3)+5(x-3)=(x+5)(x-3)$

$\boxed{x^2+3x-4}\\\\\text{The sum of the zeroes is -3=(-4)+(+1) and the product -4=(-4)*(+1), so}\\\\x^2+3x-4=x^2-x+4x-4=x(x-1)+4(x-1)=(x+4)(x-1)$

Now, let's compute the product.

$\dfrac{x^2+6x+8}{x^2+3x-10}\cdot \dfrac{x^2+2x-15}{x^2+3x-4}\\\\\\=\dfrac{(x+2)(x+4)}{(x+5)(x-2)}\cdot \dfrac{(x+5)(x-3)}{(x+4)(x-1)}\\\\\\\text{We can simplify}\\\\=\dfrac{(x+2)}{(x-2)}\cdot \dfrac{(x-3)}{(x-1)}\\\\\\=\large \boxed{\dfrac{x^2-x-6}{x^2-3x+2}}$

So the correct answer is the first one.

Thank you.

7 0

3 years ago

Tiffany catches a fish that weighs 12.3 pounds. Frank catches a fish that weighs 2.5 times as much as Tiffanys fish. How many po

stiks02 [169]

You just multiply. It's 30.75 pounds

5 0

3 years ago

there are 26 members of the baseball team that also run track. there are 48 boys on the track team. how many boys run only track

vladimir2022 [97]

Answer:

Step-by-step explanation:

48 - 26 = 22

7 0

3 years ago

This right rectangular prism is filled with -foot unit cubes.

KonstantinChe [14]

Answer:

The answer would be 36.

Step-by-step explanation:

3x3x9 is 36ft.

5 0

3 years ago

Please help me please please

vladimir1956 [14]

Answer:

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Step-by-step explanation:

-5/4 as a fratcion

4 0

3 years ago