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2.8 Rewrite Equations and Formulas Essential Question: How do you write equations and formulas?

8 -20-14. 2.8 Rewrite Equations and Formulas Essential Question: How do you write equations and formulas?. Common Core CC.9-12.A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Warm-up :

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2.8 Rewrite Equations and Formulas Essential Question: How do you write equations and formulas?

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  1. 8-20-14 2.8 Rewrite Equations and FormulasEssential Question: How do you write equations and formulas? Common Core CC.9-12.A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations Warm-up: Define the following: Square root 8. Identity Radicand 9. ratio Perfect square 10. proportion Irrational number 11. cross products Real numbers 12. scale drawing Inverse operations 13. scale Equivalent equations 14. literal equation

  2. 2.7 Exercises 2-30 Even page 123 • 2) Measure the distance in cm, in the drawing and then substitute the value in the proportion: 4) 7 6) 6 8) 6 10) 7 12) 27 14) 26 • D 18) Distribute the 14 to both b and 2; 18b = 14b + 28, 4b = 28, b = 7 20) 2 22) 22 24) -2.5 26) 5.2 28) 7.4 30) -7.1

  3. Literal Equation • The equation ax + b = c is called a literal equation because the coefficients and constants have been replaced by letters. • When you solve a literal equation, you can use the result to solve any equation that has the same form as the literal equation.

  4. c ax + b = c – b ax = c – b x = a EXAMPLE 1 Solve a literal equation Solve ax + b =cforx. Then use the solution to solve 2x + 5 = 11. SOLUTION Solve ax + b = cfor x. STEP 1 Write original equation. Subtract bfrom each side. Assume a 0. Divide each side by a.

  5. x = = c – b 11– 5 = 3 a 2 The solution of 2x + 5 = 11 is 3. ANSWER EXAMPLE 1 Solve a literal equation Usethe solution to solve 2x + 5 = 11. STEP 2 Solution of literal equation. Substitute 2 for a, 5 for b, and 11 for c. Simplify.

  6. ; 3 ANSWER x = a – c b for Example 1 GUIDED PRACTICE Solve the literal equation for x. Then use the solution to solve the specific equation 1.a – bx =c; 12 – 5x = –3

  7. c x= ; 4 ANSWER a–b for Example 1 GUIDED PRACTICE Solve the literal equation for x. Then use the solution to solve the specific equation 2.ax = bx + c; 11x = 6x + 20

  8. Two or More Variables • An equation in two variables, such that 3x +2y = 8, or a formula in two or more variables, such as A = ½ bh, can be rewritten so that one variable is a function of the other variable(s).

  9. 3 2 3x + 2y 8 = 2y 8 – 3x = y = 4 – x EXAMPLE 2 Rewrite an equation Write 3x + 2y = 8 so that yis a function of x. Write original equation. Subtract 3xfrom each side. Divide each side by 2.

  10. The area Aof a triangle is given by the formula A = bhwhere bis the base and his the height. 1 1 2 2 a. Solve the formula for the height h. b. Use the rewritten formula to find the height of the triangle shown, which has an area of 64.4 square meters. bh a. A = bh 2A = EXAMPLE 3 Solve and use a geometric formula SOLUTION Write original formula. Multiply each side by 2.

  11. 2A 2A = h b b b. Substitute 64.4 for Aand 14 for bin the rewritten formula. h = 2(64.4) = 14 ANSWER The height of the triangle is 9.2 meters. EXAMPLE 3 Solve and use a geometric formula Divide each side by b. Write rewritten formula. Substitute 64.4 for Aand 14 for b. =9.2 Simplify.

  12. 5 4 ANSWER y = 5 – x for Examples 2 and 3 GUIDED PRACTICE 3. Write 5x + 4y = 20 so that yis a function of x.

  13. The perimeter P ofa rectangle is given by the formula P =2l +2w where l is the length and w is the width. a. Solve the formula for the width w. 4 . P P – 2l ANSWER w = orw = – l 2 2 for Examples 2 and 3 GUIDED PRACTICE

  14. ANSWER 2.4 for Examples 2 and 3 GUIDED PRACTICE b . Use the rewritten formula to find the width of the rectangle shown.

  15. 5 9 EXAMPLE 4 Solve a multi-step problem Temperature You are visiting Toronto, Canada, over the weekend. A website gives the forecast shown. Find the low temperatures for Saturday and Sunday in degrees Fahrenheit. Use the formula C = (F – 32) where Cis the temperature in degrees Celsius and Fis the temperature in degrees Fahrenheit.

  16. SOLUTION 9 5 5 9 9 5 5 9 9 5 STEP 1 Rewrite the formula. In the problem, degrees Celsius are given and degrees Fahrenheit need to be calculated. The calculations will be easier if the formula is written so that Fis a function of C. (F – 32) C = 5 9 5 9 ·(F – 32) Multiply each side by , the reciprocal of . C = 9 C F – 32 = 5 32 Add to each side. = C + 32 F EXAMPLE 4 Solve a multi-step problem Write original formula. Simplify.

  17. 9 5 The rewritten formula C + 32. = is F EXAMPLE 4 Solve a multi-step problem ANSWER

  18. 9 9 9 9 5 5 5 5 = C+ 32 F C+ 32 F = =(10)+ 32 = (14)+ 32 ANSWER ANSWER The low for Saturday is 57.2°F. The low for Sunday is 50°F. EXAMPLE 4 Solve a multi-step problem Find the low temperatures for Saturday and Sunday in degrees Fahrenheit. STEP 2 Saturday (lowof14°C) Sunday(low of10°C) =25.2 + 32 =18 + 32 = 57.2 = 50

  19. 5. Use the information in Example 4 to find the high temperatures for Saturday and Sunday in degrees Fahrenheit. ANSWER 71.6°F, 60.8°F for Example 4 GUIDED PRACTICE

  20. Classwork • 2.8 Exercises • 2-26 even • Pages 129-130

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