Copyright © 2013 Pearson Education, Inc. Section 2.4 Formulas

Example A residential lot is shown. Find the area of this lot. Solution The area of the rectangle: The area of the triangle: Total area = 76, ,576 = 97,836 square feet. 205 ft 372 ft 116 ft Page 125

Example A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are the pool’s dimensions.? Divide 8 Length is 3 times 40 length= 120 3w w P=2w+2l

Example In a triangle, the smaller angles are equal in measure and are one-third of the largest angle. Find the measure of each angle. Solution Let x represent the measure of each of the two smaller angles. Then the measure of the largest angle is 3x, and the sum of the measures of the three angles is given by The measure of the largest angle is 3x, thus 36 ∙ 3 = 108°. The measure of the three angles are 36°, 36°, and 108°. Page 124-5

Find the volume and the surface area of the box shown. Solution The volume of the box is V = lwh V = 12 ∙ 6 ∙ 5 V = 360 cm 3 The surface area of the box is Example 12 cm 6 cm 5 cm Page 127

Example Solve each equation for the indicated variable. a.b. Solution a. Multiply by LCD which is 5 Subtract y Page

Example Solve each equation for the indicated variable. a.b. Solution b. Subtract nm GCF is n Divide by GCF Page 129

Solving a Formula for a VariableEXAMPLE SOLUTION Solve the formula y = mx + b for m y = mx + b Think of m saying, “I really want to be alone.” y – b = mx + b – b Subtract b from both sides. y – b = mx Perform the addition. b – b = 0. Divide both sides by x to find m.

Solving a Formula for a Variable Solve for x Solve for length b

Other Formulas To calculate a student’s GPA, the number of credits earned with a grade of A, B, C, D, and F must be known. If a, b, c, d, and f represent these credit counts respectively, then Slide 10 Page 130

Example A student has earned 18 credits of A, 22 credits of B, 8 credits of C and 4 credits of D. Calculate the student’s GPA to the nearest hundredth. Solution Let a = 18, b = 22, c = 8, d = 4 and f = 0 The student’s GPA is Page 130

Example The formula is used to convert degrees Fahrenheit to degrees Celsius. Use this formula to convert 23°F to an equivalent Celsius temperature. Solution = −5°C Page 130

DONE

Objectives Formulas from Geometry Solving for a Variable Other Formulas

#20 #24 Solving a Formula for a Variable problem 20 on page 144 Solve for a Mult by 2 to remove 1/2

1 3 Solving a Formula for a Variable CP 1, 3 on pages Divide by w Solve for length l Subtract D from both sides Divide by p Solve for m

Example A tourist starts a trip with a full tank of gas and an odometer that reads 59,478 miles. At the end of the trip, it takes 8.6 gallons of gas to fill the tank, and the odometer reads 59,715 miles. Find the gas mileage for the car. Solution The distance traveled is 59,715 – 59, 478 = 237 miles and the number of gallons used is G = 8.6. Thus, Page 124

Example A cylindrical soup can has a radius of 2 ½ inches and a height of 5 5/8 inches. Find the volume of the can. Solution h r Page 128