1.4 Rewriting Equations
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- Dennis McDonald
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1 Friday Homework: begin weekly review Ask your science teacher what formulas you are going to use in science this year (X- Credit) 1 st : Put your homework and Corrections in the yellow folder 2 nd : Take out planner, spiral, and math facts 3 rd : Warm up: is a brief homework quiz- Take your time, go back over your steps when you finish. 4 th : After you finish warm up do math facts and set up Cornell Notes 1.4 Rewriting Equations Essential Question: What is a key step to solving for a specific variable?
2 Dress Code Math Facts
3 Vocabulary: Literal equations: An equation that has two or more variables
4 A. Solve x + y = 15 for x. x + y = 15 y y x = y + 15 Locate x in the equation. Since y is added to x, subtract y from both sides to undo the addition.
5
6 Solve for y:
7 Solve for y: 4.2x =.007y +.49
8 Solve for y:
9 Solve for y: 2π = 5y + 4
10 Monday Homework: 1.4 textbook pg. 30 #3, 6, 9, 10, 11, 12, 14, 16, 18, and 19 1 st : Fill out planner. Take out spiral, and math facts. 2 nd : Warm Up sheet in 2 squares. Do warm up first, then make corrections to Friday s quiz on the BACK of your warm up sheet. 3 rd : After you finish warm up & quiz corrections, practice math facts. SATELLITE TV: Provider A charges $75 for installation and charges $39.95 per month for the basic package. Provider B offers free installation and charges $39.95 per month for the basic package. Your neighbor subscribes to Provider A the same month you subscribe to Provider B. After how many months is your neighbor s total cost the same as your total cost for satellite TV? 1 3 9x 6 = 3x + 2
11 2 nd, 5/6 th, 7 th hrs The Plan for this week: Monday: Finish lesson 1.4 Tuesday: Critical thinking activity Wednesday: Review for Unit 1 test Thursday: Review for Unit 1 test Friday: Unit 1 test and spin for group points
12 4 th hr The Plan for this week: Monday: Finish lesson 1.4 Tuesday: Review for Unit 1 test Wednesday: Review for Unit 1 test Thursday: Unit 1 test & critical thinking task Friday: Survivor Lipsink contest during 4 th hr & spin for group points
13 Dress Code Math Facts 3 minute timer
14 Last Week s Challenge Answer =273 Thus a=6, b=9, c=2
15 Challenges of the Week If a+1 = b+2 = c+3 = d+4 = a+b+c+d+5, then a+b+c+d =?? & Find formulas used in science and/or business. Rewrite the formulas for two different variables.
16 1.4 Rewriting Formulas Essential Question: How can you use a formula for measurement to write a formula for a different measurement? Science formulas?
17 A formula is an equation that states a rule for a relationship among quantities. In the formula d = rt, d is isolated. You can "rearrange" a formula to isolate any variable by using inverse operations. This is called solving for a variable. Solving for a Variable Step 1 Locate the variable you are asked to solve for in the equation. Step 2 Identify the operations on this variable and the order in which they are applied. Step 3 Use inverse operations to undo operations and isolate the variable.
18 Solve pq = x for q. pq = x Locate q in the equation. Since q is multiplied by p, divide both sides by p to undo the multiplication.
19 The formula for an object s final velocity is f = i gt, where i is the object s initial velocity, g is acceleration due to gravity, and t is time. Solve for i. f = i gt f = i gt + gt +gt f + gt = i Locate i in the equation. Since gt is subtracted from i, add gt to both sides to undo the subtraction.
20 What Do You Think? Solve 5 b = 2t for t. 5 b = 2t Locate t in the equation. Since t is multiplied by 2, divide both sides by 2 to undo the multiplication.
21 Your Turn: Solve the formula d = rt for t. Find the time in hours that it would take Ernst Van Dyk to travel 26.2 miles if his average speed was 18 miles per hour. d = rt Locate t in the equation. Since t is multiplied by r, divide both sides by r to undo the multiplication. Now use this formula and the information given in the problem. Van Dyk s time was about 1.46 hours.
22 The formula for the area of a triangle is A = bh, where b is the length of the base, and h is the height. Solve for h. A = bh 2A = bh Locate h in the equation. Since bh is multiplied by, divide both sides by to undo the multiplication. Since h is multiplied by b, divide both sides by b to undo the multiplication.
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24 Solve for V Locate V in the equation. VD = m Since m is divided by V, multiply both sides by V to undo the division. Since V is multiplied by D, divide both sides by D to undo the multiplication.
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26 The formula C = d gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol in your answer. Locate d in the equation. Since d is multiplied by, divide both sides by to undo the multiplication. Now use this formula and the information given in the problem. Now use this formula and the information given in the problem. The bowl's diameter is inches.
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28 Draw a horizontal line across the bottom of today s notes Summarize today s lesson. Describe how to solve for r in the equation d = rt
29 Your turn: white Boards Solve for the indicated variable for h P = R C for C C = R P 3. 2x + 7y = 14 for y 4. for m m = x(k 6 ) 5. for C C = Rt + S
30 Part 2 Euler s formula, V E + F = 2, relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron. Solve Euler s formula for F. F = 2 V + E How many faces does a polyhedron with 8 vertices and 12 edges have? 6
31
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Solve y = 0.7y 0.3
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