1-1 Expressions and Formulas. Evaluate each expression if a = 2, b = 3, and c = 4.2. SOLUTION: SOLUTION: SOLUTION: SOLUTION:
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1 2. Evaluate each expression if a = 2, b = 3, and c = esolutions Manual - Powered by Cognero Page 1
2 10. VOLLEYBALL A player s attack percentage A is calculated using the formula where k represents the number of kills, e represents the number of attack errors including blocks, and t represents the total attacks attempted. Find the attack percentage given each set of values. a. b. a. Substitute k = 22, e = 11, and t = 35 in the formula. The attack percentage is about 31.4%. b. Substitute k = 33, e = 9, and t = 50 in the formula. The attack percentage is 48%. 12. Evaluate each expression if and. 14. esolutions Manual - Powered by Cognero Page 2
3 16. Substitute x = 4, y = 2.6 or, and in the expression 3y 4z + x. 18. Evaluate each expression if and. esolutions Manual - Powered by Cognero Page 3
4 20. esolutions Manual - Powered by Cognero Page 4
5 SENSE-MAKING The formula can be used to convert temperatures in degrees Fahrenheit to degrees Celsius. a. Room temperature commonly ranges from to. Determine room temperature range in degrees Celsius. b. The normal average human body temperature is. A temperature above this indicates a fever. If your temperature is, do you have a fever? Explain your reasoning. a. Substitute 64 for F in the formula. esolutions Manual - Powered by Cognero Page 5
6 Substitute 73 for F in the formula. The room temperature range is about. b. Substitute 98.6 for F in the formula. So,. Since 42 > 37, this temperature indicates a fever. 26. FINANCIAL LITERACY The profit that a business made during a year is $536,897,000. If the business divides the profit evenly for each share, estimate how much each share made if there are 10,995,000 shares. Let x be the profit made by each share. Each share made a profit of about $ esolutions Manual - Powered by Cognero Page 6
7 28. ANCIENT PYRAMID The Great Pyramid in Cairo, Egypt, is approximately meters high, and each side of its base is approximately 230 meters. a. Find the area of the base of the pyramid. Remember. b. The volume of a pyramid is, where B is the area of the base and h is the height. What is the volume of the Great Pyramid? a. Substitute in the formula. The base area of the pyramid is 52,900 m 2. b. Substitute B = 52,900 and h = in the formula. The volume of the pyramid is about 2,586,810 m Evaluate each expression if and. esolutions Manual - Powered by Cognero Page 7
8 SEARCH ENGINES Page rank is a numerical value that represents how important a page is on the Web. One formula used to calculate the page rank for a page is PR = L, where L is the page rank of the linking page divided by the number of outbound links on the page. Determine the page rank of a page in which L = 10. Substitute L = 10 in the formula PR = L. 38. FOOTBALL The following formula can be used to calculate a quarterback efficiency rating. C is the number of passes completed. A is the number of passes attempted. esolutions Manual - Powered by Cognero Page 8
9 Y is passing yardage. T is the number of touchdown passes. I is the number of interceptions. Find Peyton Manning s efficiency rating to the nearest tenth for the season statistics shown. Simplify the equation by multiplying each term by. Then find a common denominator in order to add the fractions. Substitute C = 371, A = 555, Y = 4002, T = 27, and I = 12. Peyton Manning s efficiency rating is about esolutions Manual - Powered by Cognero Page 9
10 40. GEOMETRY The area of a triangle can be found using Heron s Formula,, where a, b, and c are the lengths of the three sides of the triangle, and. Find the area of the triangle at the right. The area of the triangle is about 31.5 square inches. esolutions Manual - Powered by Cognero Page 10
11 42. MULTIPLE REPRESENTATIONS You will write expressions using the formula for the volume of a cylinder. Recall that the volume of a cylinder can be found using the formula, in which v = volume, r = radius, and h = height. a. GEOMETRIC Draw two cylinders of different sizes. b. TABULAR Use a ruler to measure the radius and height of each cylinder. Organize the measures for each cylinder into a table. Include a column in your table to calculate the volume of each cylinder. c. VERBAL Write a verbal expression for the difference in volume of the two cylinders. d. ALGEBRAIC Write and solve an algebraic expression for the difference in volume of the two cylinders. a. Sample answer: b. Sample answer: make a table to record the radius, height, and volume of each cylinder. c. Sample answer: times 2 squared times 5 minus times 4 squared times 1. d. Sample answer: 44. CHALLENGE For any three distinct numbers a, b, and c, a$b$c is defined as. Find. esolutions Manual - Powered by Cognero Page 11
12 46. CHALLENGE Let m, n, p, and q represent nonzero positive integers. Find a number in terms of m, n, p, and q that is halfway between and. Halfway between and is the average of the two: 48. WRITING IN MATH Provide an example of a formula used in everyday situations. Explain the usefulness of this formula and what happens if the formula is not used correctly. Sample answer: A formula is used to calculate the price of filling a gasoline tank in which the price = number of gallons price per gallon. If calculated incorrectly, you may underestimate or overestimate how much you will need to pay. 50. SAT/ACT If the area of a square with side x is 9, what is the area of a square of side 4x? A 36 B 144 C 212 D 324 E 1296 The area of a square of side 4x is 144 square units. The correct choice is B. esolutions Manual - Powered by Cognero Page 12
13 52. GEOMETRY In and are angle bisectors and. How many degrees are in? F 96 G 132 H 145 J 192 Let. Use the Triangle Sum Theorem for the triangle FHG. The correct choice is G. 54. The lengths of the three sides of a triangle are 10, 14, and 18 inches. Determine whether this triangle is a right triangle. Because the longest side is 18 inches, use 18 as c, the measure of the hypotenuse. Because c 2 a 2 + b 2, the triangle is not a right triangle. esolutions Manual - Powered by Cognero Page 13
14 56. MAPS On a map of the U.S., the cities Milwaukee, Wisconsin, and Charlotte, North Carolina are inches apart. The actual distance between Milwaukee and Charlotte is 670 miles. If Birmingham, Alabama and St. Petersburg Florida are 465 miles apart, how far apart are they on the map? Let x be the length of the reduced photo. The length of the reduced photo will be inches. 58. Find the product of. Use the FOIL method to find the product. 60. Evaluate each expression esolutions Manual - Powered by Cognero Page 14
15 66. esolutions Manual - Powered by Cognero Page 15
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