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Comprehensive Solutions for Equations and Right Triangles

Explore all solutions to equations and find exact and decimal approximations for irrational values. Calculate missing side lengths of right triangles, including decimal estimates for irrational lengths. Simplify expressions and evaluate exponential expressions without exponents.

kylee-patterson
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Comprehensive Solutions for Equations and Right Triangles

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  1. Find all solutions to each equation, find exact solutions and decimal approximations of irrational solutions 1. 2. 3. 4.

  2. 1. 2. 3. 4.

  3. 1. 2. 3. 4.

  4. 0.176(2.4) 4224 0.4224

  5. 1. 2. 3. 4.

  6. 1. 2. 3. 4.

  7. or about 3.9 64 8 15 7 49

  8. Find the exact length of the missing side of each right triangle. Also find a decimal estimate of any irrational length. 3. 2. 7 1. 8 2 3 7 8 4. 5 9

  9. Find the exact length of the missing side of each right triangle. Also find a decimal estimate of any irrational length. 3. 2. 7 1. 8 2 3 7 8 4. 5 9

  10. Pattern: Examples:

  11. Create an equivalent expression without exponents: 4. 2. 1. 3.

  12. Create two equivalent expression: Without exponents A single exponential expression Example 1:

  13. Create two equivalent expression: Without exponents A single exponential expression Example 1: Example 2:

  14. Create two equivalent expression: Evaluate Write as a single number with an exponent 1. 2. 4. 3.

  15. ? ?

  16. Evaluate: 1. 2. 3.

  17. or about 6.2 64 8 25 5 39

  18. Find the exact length of the missing side of each right triangle. Also find a decimal estimate of any irrational length. 3. 2. 8 1. 8 5 2 8 8 4. 5 10

  19. Find the exact length of the missing side of each right triangle. Also find a decimal estimate of any irrational length. 3. 2. 8 1. 8 5 2 8 8 4. 5 10

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