Texas Tech University

Section 1-4: Rewriting Equations and Formulas (pages 27-34)


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Section 1-4: Rewriting Equations and Formulas (pages 27-34)

Understanding Mathematical Terms

Refer to the English-Spanish Glossary, which starts on textbook page A39, if you need help with a definition or finding a textbook page with an example for a vocabulary word.

Explorations

Read and work through Explorations 1 and 2, and Communicate Your Answer on page 27. Then check your answers below.

Answers to Explorations and Communicate Your Answer

Exploration 1 (page 27)

  1. A = bh
  2. 30 equals b times 5; Write the equation.
    6 = b; Divide each side by 5.
  3. A = bh; Write the formula.
    begin fraction A over h end fraction equals b; Divide each side by h.
  4. applied the same steps to solve; used variables instead of constants

Exploration 2 (page 27)

  1. cap A equals one half h open parentheses b sub one plus b sub two closed parentheses ; h equals begin fraction two cap A over b sub one plus b sub two end fraction ; h = 7 cm
  2. C = 2 pi r; r equals begin fraction cap C over two pi end fraction; r = 12 ft
  3. V = Bh; h equals begin fraction cap V over cap B end fraction; h = 5 yd
  4. cap V equals one third cap B h; h equals begin fraction three cap V over cap B end fraction; h = 6m

Communicate Your Answer (page 27)

  1. Solve the formula for a different variable; Sample answer: (volume of a cylinder) cap V equals pi r squared h; h equals begin fraction cap V over pi r squared end fraction

Section 1-4 Lesson (page 28)

Be sure to write down the core vocabulary and core concepts for this lesson. This lesson will need to be studied carefully. Keep in mind the idea is to use what you know about symbolically manipulating the equation to isolate the variable you need to solve for. Study Examples 1-8 carefully. Work through each one of them on your own to see if you get what is in the book.

Remember also, if you get stuck, you can go to Big Ideas Math (see "Textbooks and Materials" in the Course Introduction). You will have access to the odd-numbered problems and an on-line tutor.

Practice with the Monitoring Progress problems as you go, and then check your answers below.

Answers to Monitoring Progress (pages 28-31)
  1. y = 3 + one third x
  2. y = xbegin fraction five over two end fraction
  3. y = 5 – 2x
  4. x = y
  5. x = begin fraction m over two plus k end fraction
  6. x = begin fraction y minus three over five minus k end fraction
  7. h = begin fraction two cap A over b end fraction
  8. l equals begin fraction cap S minus pi r squared over pi r end fraction
  9. no
  10. $2500
  11. delivery: 3h, return: 4h