The document discusses transforming formulas by rearranging them to solve for different variables. It provides examples of solving formulas for length, area, perimeter, and others. It emphasizes that when transforming a formula, the same operations must be applied to both sides. The document also gives real-world examples of using transformed formulas to solve for time, temperature, and number of hits in baseball.

1. Chapter 7: Section 7: Transforming Formulas January 14 th , 2009 A Weird Concept Day

2. Warm Up: Evaluate each Formula for the values given. Distance: d = rt, r = 80 km/hr, t = 4 hr. Perimeter of a rectangle: P = 2l + 2w, l = 9m, w = 7m. D = 320 km P = 32 km

3. Compound Inequalities Compound inequalities are two inequalities joined by the word AND or the word OR . X > 4 and X ≤ 6: A solution of a compound inequality joined by AND is any number that makes both inequalities true . X ≤ -2 or X > 3: A solution of a compound inequality joined by OR is any number that makes at least one of the inequalities true .

4. Graphing Compound Inequalities X > -3 AND X ≤ 5 X > 20 OR X < 19 Hint: Graph them separately for OR compound inequalities. Hint: Figure out where X overlaps, then fill in the middle for AND compound inequalities.

5. Transforming Formulas Remember: Formulas show the relationship between two or more qualities. Qualities are variables that stand for stuff. Like, Perimeter = P and A = Area. Use (+, -, x, ÷) Properties of Equality to transform a formula to represent one quantity in terms of another. Basically, rearrange formulas so that they look different but still do the same thing .

6. Solve the Area Formula for L = Length The area formula is A = LW Or, Area = Length times Width. Solve for Length . How do we get L by itself? Division Property of Equality Divide both sides by W . Simplify. Length now equals Area divided by Width . L = A/W

7. Try These : Solve for the variable indicated in Red. P = S + C H = ( K /J) I = P RT Hint: Undo all of the quantities on the same side of the RED quantity so that all of the non-red quantities are on the opposite side from the RED quantity you’re solving for. Non-Red = RED

8. Multiple Steps Can Be Needed You may need to use more than one step of equality to solve these problems. For Example: Solve the Perimeter formula for L. (P = 2 L + 2W) P – 2W = 2 L + 2W – 2W  Sub. 2W P – 2W = 2 L  Simplify (P – 2W)/2 = 2 L /2  Divide by 2 (P – 2W)/2 = L  Simplify/Solution

9. Remember! When you are doing multiple steps, you have to apply each step to both sides COMPLETELY!

10. Try These: Solve for the Red Quantity 5 A + 7 = B P = 2L + 2 W Y = ( X /3) + 8

11. Real-World Examples You plan a 425-mile trip to Bryce Canyon National Park in Utah. You estimate you will average 500 miles/hour. To find about how long the trip will take, solve the distance formula D = RT for t. Then substitute to find the time. It will take you about 8.5 hours to complete the trip.

12. Temperature An exchange student in your class wants to know the Celsius equivalent of 77 °F. First solve the formula F = (9/5) C + 32 for C . Then substitute to find the temperature. 77 °F is 25°C.

13. Whose On First? Solve the batting average formula, A = (H/N) for H. Find the number of hits, H, a batter needs in 40 times at bat, N, to have an average of 0.275. H = AN, 11 hits.

14. Assignment #58 Page 367 : 1-15all, and Page 364 : 1-9 all (Graphing). Easy problems, lots of graphing. Remember to graph with elevated arrows and rays. 24 Problems.