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KATRIN_1 [288]
3 years ago
13

A pyramid has a rectangular base of length (3x + 1)cm and width xcm.

Mathematics
1 answer:
sergey [27]3 years ago
7 0

Answer:

The dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3

Step-by-step explanation:

Given

Rectangle Pyramid

Base Length = 3x + 1

Base Width = x

Height = 12

Volume = 96

Required

Dimension of the base of the pyramid

Given that the volume of the pyramid is ⅓ of the base area * the height.

This is represented mathematical as

Volume = ⅓ * base area * height.

Where

Base area = width * length

Base area = (3x + 1) * x

Base area = 3x² + x.

So,

Volume becomes

Volume = ⅓ * (3x² + x) * 12.

Volume = (3x² + x) * 4

Substitute 96 for volume

96 = (3x² + x) * 4

Divide both sides by 4

96/4 = (3x² + x) * 4/4

24 = 3x² + x

Subtract 24 fr both sides

24 - 24 = 3x² + x - 24

0 = 3x² + x - 24

3x² + x - 24 = 0

Expand

3x² + 9x - 8x - 24 = 0

Factorize

3x(x + 3) - 8(x + 3) = 0

(3x - 8)(x + 3) = 0

3x - 8 = 0 or x + 3 = 0

3x = 8 or x = -3

x = 8/3 or x = -3

Recall that

Length = 3x + 1

Width = x

For any of the above expression, x can't be less than 0; so, x = -3 can't be considered.

Substitute x = 8/3

Length = 3x + 1

Length = 3(8/3) + 1

Length = 8 + 1

Length = 9

Width = x

Width = 8/3

Hence, the dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3

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A triangle has side lengths of (7x-4)(7x−4) centimeters, (x+3)(x+3) centimeters, and (3y+2)(3y+2) centimeters. Which expression
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Answer:

<u>This assumes that the question was meant to read:</u>

"A triangle has side lengths of (7x−4) centimeters, (x+3) centimeters, and (<u>3x+2</u>) centimeters."  <u>And not </u>"A triangle has side lengths of (7x-4)(7x−4) centimeters, (x+3)(x+3) centimeters, and (3y+2)(3y+2) centimeters."

If the revision is correct, the perimeter is 11x + 1 cm

=============================================

<u>If the question was correctly written, then answer is:</u>

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===============

Step-by-step explanation:

  (7x-4) cm

+ (x+3)  cm

<u>+ (3x+2) cm</u>

11x + 1 cm

If the question was correctly written as is, then:

(7x-4)(7x−4) = 49x^2 - 56x + 16

+(x+3)(x+3)    =     + x^2   + 6x   + 9

+(3y+2)(3y+2) = <u> +9y^2  + 12 y  + 4</u>

                         50x^2 - 50x + 9y^2  + 12 y  + 29 cm

                       

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The answer is D because microcosm is a community displaying characteristics of something larger.
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