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3.6 Using Formulas and Literal Equations

3.6 Using Formulas and Literal Equations. NCSCOS. 1.02 – Use formulas and algebra expressions, including iterative and recursive forms, to model and solve problems 4.01 – Use linear functions or inequalities to model and solve problems. Objective.

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3.6 Using Formulas and Literal Equations

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  1. 3.6 Using Formulas and Literal Equations NCSCOS • 1.02 – Use formulas and algebra expressions, including iterative and recursive forms, to model and solve problems • 4.01 – Use linear functions or inequalities to model and solve problems Objective • Solve literal equations for a specific variable. • Use formulas to solve problems.

  2. 3.6 Using Formulas and Literal Equations Remember, a formula shows a relationship between two or more quantities. y = mx + b Slope Intercept: Area: A = lw Ax + By = C Standard Form: d = rt Distance: m v Density: D = Circumference of a Circle: C = 2r Perimeter: P = 2l + 2w 1 2 Area of Triangle: A = bh Direct Variation: y = kx Area of Trapezoid: 1 2 Indirect Variation: k x A = h(b1 + b2) y =

  3. 3.6 Using Formulas and Literal Equations Solve for variable indicated: Solve for l Solve for t A = lw d = rt w w A d r = t = l w Solve for r Solve for r C = 2r d = rt 22 d t C = r = r 2

  4. 3.6 Using Formulas and Literal Equations Solve for the variable: k x y = solve for k y = kx solve for k x x xy = k y = k x k x y = solve for x y = kx solvefor x k y x = k k y = x k

  5. 3.6 Using Formulas and Literal Equations Solve for l P = 2l + 2w – 2w = – 2w P – 2w = 2l 2 2 P – 2w = l 2 or 1 2 P P – w = l - w = l 2

  6. 3.6 Using Formulas and Literal Equations Solve for y Solve for x x 3 -4x + 2y = 6 y = + 8 4x = + 4x – 8 = – 8 2y = 4x + 6 x 3 y – 8 = 3 3 2 2 y = 2x + 3 3y – 24 = x

  7. 3.6 Using Formulas and Literal Equations Solve for y Solve for x 23 2x + 3y = 15 y = x + 2 –2x = –2x –2 = –2 3y = –2x + 15 32 23 32 y –2 = x 3 3 3 2 3 32 y = – x + 5 y –3 = x

  8. 3.6 Using Formulas and Literal Equations Solve for y Solve for y 6x – 2y = 14 4x – 5y = 2 –6x = –6x –4x = –4x –2y = –6x + 14 –5y = –4x + 2 –2–2–2 –5–5–5 4 5 2 5 y = 3x – 7 y = x –

  9. 3.6 Using Formulas and Literal Equations Solve for y Solve for y 3x + 4y = 12 3x – 2y = 16 –3x = –3x –3x = –3x 4y = –3x + 12 –2y = –3x + 16 4 4 4 –2–2–2 3 4 3 2 y = –x + 3 y = x–8

  10. 3.6 Using Formulas and Literal Equations Solve for y Solve for y 7x + 2y = –14 2x – 3y = 10 –7x = –7x –2x = –2x 2y = –7x – 14 –3y = –2x + 10 222 –3–3–3 2 3 10 3 7 2 y = x – y = –x – 7

  11. 3.6 Using Formulas and Literal Equations Solve for b1 Solve for h 2 2 1 2 A = bh 2 2 2A = h(b1 + b2) h h 2A = bh b = b1 + b2 b 2A h 2A = h – b2–b2 b 2A – b2= b1 h

  12. 3.6 Using Formulas and Literal Equations Solve for h Solve for h 2 2 2A = h(b1 + b2) (b1 + b2) (b1 + b2) 2A = h (b1 + b2)

  13. 3.6 Using Formulas and Literal Equations Solve for V2 Solve for T2

  14. 3.6 Using Formulas and Literal Equations Solve for F Solve for y Ax + By = C -Ax = - Ax By = -Ax + C B B + 32 + 32 C B A B y = – x +

  15. 3.6 Using Formulas and Literal Equations Convert each temperature from degrees Fahrenheit to degrees Celsius: 68°F 20°C 40°C 104°F 0°C 32°F 26.6°C 80°F -5°C 23°F -23.3°C -10°F 10°C 50°F 98.6°F 37°C 100°C 212°F

  16. 3.6 Using Formulas and Literal Equations Use the formula C = 2r to find the radius, r, for each circumference problem. Use  from the calculator and round to the hundredth. C = 30 inches C = 11 inches 4.77 in 1.75 in 15.92 m C = 15 meters C = 100 meters 2.39 m 0.48 ft 8.28 ft C = 3 feet C = 52 feet 3.18 cm 0.80 cm C = 5 centimeters C = 20 centimeters 11.30 in 3.98 in C = 71 inches C = 25 inches

  17. 3.6 Using Formulas and Literal Equations You plan a 425-mi trip to Bryce Canyon National Park. You estimate you will average 50 mi/h. To find about how long the trip will take, use the distance formula: d = rt and solve for t. d = rt r = 50 mi/h d = 425-mi 425 = 50t t = d t = 425 50 50 r 50 t = 8.5 hrs t = 8.5 hrs The trip will take about 8.5 hours

  18. 3.6 Using Formulas and Literal Equations You plan a 600-mi trip to New York City. You estimate your trip will take about 10 hours. To estimate your avg. speed, use the distance formula: d = rt and solve for r. t = 10 h d = 600-mi d = rt 600 = 10r r = d r = 600 10 10 t 10 r = 60 mi/h r = 60 mi/h The avg speed is about 60mi/h

  19. 3.6 Using Formulas and Literal Equations You plan a 1426-mi trip to the Grand Canyon. You estimate you will average 62 mi/h. Find about how many hours the trip will take, if you only plan to drive 8 hours/day, then find how many days it will take. days= 23 h d = 1426 mi r = 62 mi/h 1426 = 62t 8 h/day 1426 = t 62 days= 2.875 The trip will take about 3 days. The trip will take about 23 hours. t = 23

  20. 3.6 Using Formulas and Literal Equations Bob built a wall design in the shape of a trapezoid. The area of the design is 18 sq. ft. The longer base is 7 ft. and the height of the trapezoid is 3.5 ft. Find the length of the shorter base; use the following formula: @ 3.29 ft

  21. 3.6 Using Formulas and Literal Equations The area of a trapezoid is 90 sq inches. The height of the trapezoid is 12 inches and the longer base is 9 inches. Find the length of the shorter base; use the following formula: @ 6 inches

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