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Mice21 [21]
3 years ago
5

Use the diagram below to find x and each missing angle.

Mathematics
1 answer:
aleksandr82 [10.1K]3 years ago
8 0
Angle 1 clearly equals 37°. X=5
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The triangles are similar by the AA Similarity Postulate. Find the value of x.
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Solve the inequality for x<br> 3^(6x+18)&lt;27^(3x)
Lera25 [3.4K]

Answer:

\displaystyle 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
  • Subtraction Property of Equality

<u>Algebra I</u>

  • Terms/Coefficients
  • Factoring

<u>Algebra II</u>

  • Exponential Rule [Powering]: \displaystyle (b^m)^n = b^{m \cdot n}
  • Solving exponential equations

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

<em />\displaystyle 3^{6x + 18} < 27^{3x}<em />

<em />

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

  1. Rewrite:                                                                                                             \displaystyle 3^{6x + 18} < 3^{3(3x)}
  2. Set:                                                                                                                     \displaystyle 6x + 18 < 3(3x)
  3. Factor:                                                                                                               \displaystyle 3(2x + 6) < 3(3x)
  4. [Division Property of Equality] Divide 3 on both sides:                                  \displaystyle 2x + 6 < 3x
  5. [Subtraction Property of Equality] Subtract 3x on both sides:                       \displaystyle -x + 6 < 0
  6. [Subtraction Property of Equality] Subtract 6 on both sides:                        \displaystyle -x < -6
  7. [Division Property of Equality] Divide -1 on both sides:                                 \displaystyle x > 6
8 0
3 years ago
Read 2 more answers
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