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The volume of a rectangular prism is 2x^3 - 6x^2 + 8x , and the volume of a cube is 27x^3. What is the total volume of the prism and the cube?

Respuesta :

Space

Answer:

[tex]\displaystyle V_{P + C} = 29x^3 - 6x^2 + 8x[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle V_P = 2x^3 - 6x^2 + 8x[/tex]

[tex]\displaystyle V_C = 27x^3[/tex]

Step 2: Find Combined Volume

  1. [Set up] Add:                                                                                                     [tex]\displaystyle V_P + V_C = V_{P + C}[/tex]
  2. Substitute in variables:                                                                                    [tex]\displaystyle V_{P + C} = 27x^3 + 2x^3 - 6x^2 + 8x[/tex]
  3. Combine like terms:                                                                                        [tex]\displaystyle V_{P + C} = 29x^3 - 6x^2 + 8x[/tex]

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