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kaheart [24]
3 years ago
8

Analyze the diagram below and complete the instructions that follow.

Mathematics
1 answer:
valentinak56 [21]3 years ago
4 0

Answer:

x = 6

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtract Property of Equality

<u>Algebra I</u>

  • Terms/Coefficients/Degrees
  • Expand by FOIL (First Outside Inside Last)
  • Factoring
  • Multiple Roots

<u>Trigonometry</u>

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

  • a is a leg
  • b is another leg
  • c is the hypotenuse

Step-by-step explanation:

<u>Step 1: Identify</u>

<em>a</em> = x + 3

<em>b</em> = x

<em>c</em> = √117

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Substitute [PT]:                                                                                                (x + 3)² + x² = (√117)²
  2. Expand [FOIL]:                                                                                                 x² + 6x + 9 + x² = (√117)²
  3. Combine like terms:                                                                                       2x² + 6x + 9 = (√117)²
  4. Exponents:                                                                                                      2x² + 6x + 9 = 117
  5. [SPE] Subtract 117 on both sides:                                                                    2x² + 6x - 108 = 0
  6. Factor out GCF:                                                                                               2(x² + 3x - 54) = 0
  7. [DPE] Divide 2 on both sides:                                                                         x² + 3x - 54 = 0
  8. Factor Quadratic:                                                                                            (x - 6)(x + 9) = 0
  9. Solve roots/solve <em>x</em>:                                                                                         x = -9, 6

Since we are dealing with positive values, we can disregard the negative root.

∴ x = 6

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