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Coordinate Algebra Practice EOCT Answers Unit 1 #1 A rectangle has a length of 12 m and a width of 400 cm. What is the perimeter of the rectangle? A. 824 cm B. 1600 cm C. 2000 cm D. 3200 cm Unit 1 Step 1: Change 12 meters to centimeters 12 m 1 × 100 cm 1m = 1200 cm Step 2: Find perimeter using formula P = 2L + 2W 1200 cm P = 2(1200 cm) + 2(400 cm) 400 cm P = 2400 cm + 800 cm P = 3200 cm Unit 1 #2 The tension caused by a wave moving along a string is found mv 2 using the formula T = . If m is the mass of the string in L grams, L is the length of the string in centimeters, and v is the velocity of the wave in centimeters per second, what is the unit of the tension of the string, T ? 2 m grams ( g ) 2 (cm) cm v 2 sec (sec) L (cm) 2 2 (cm) (g) 2 2 mv (sec) T (cm) L #2 2 2 Unit 1 g (cm) (cm) (g) 2 2 2 g (cm) (cm) (sec) (sec) T 2 (cm) (sec) 1 (cm) (cm) 2 1 g (cm) 1 g (cm) 1 g (cm) T 2 2 1 2 (sec) (cm) (sec) 1 (sec) 1 A. gram-centimeters per second squared B. centimeters per second squared C. grams per centimeter-second squared D. centimeters squared per second Unit 1 #3 The distance a car travels can be found using the formula d = rt, where d is the distance, r is the rate of speed, and t is time. How many miles does the car travel, if it drives at a speed of 70 miles per hour for ½ hour? A. 35 miles B. 70 miles C. 105 miles D. 140 miles d = r t 70 miles 1 2 hour d hour 1 70 miles 0.5 hour d = 35 miles hour 1 Unit 1 A certain population of bacteria has an average growth rate of 0.02 bacteria per hour. The #4 formula for the growth of the bacteria’s population is A= P (2.71828)0.02t, where P0 is the original population, and t is the time in hours. If you begin with 200 bacteria, about how many bacteria will there be after 100 hours? 0.02t A= P(2.71828) Answer A= 200(2.71828)0.02100 1478 2 A= 200(2.71828) A= 200(7.389046) = 1477.81 Unit 1 #5 The sum of the angle measures in a triangle is 180°. Two angles of a triangle measure 20° and 50°. What is the measure of the third angle? A. B. C. D. 30° 70° 110° 160° Third Angle = x x + 20° + 50° = 180° x + 70° = 180° –70° –70° x = 110° #6 A. B. C. D. Unit 1 Which equation shows P = 2l + 2w when solved for w ? 2l w P 2l P w 2 P w 2l 2 P 2l w 2 P = 2l + 2w –2l –2l P – 2l = P – 2l = 2 P – 2l = 2 2w 2w 2 w Bruce owns a business that produces widgets. He must bring in more in revenue than he pays out in costs in order to turn a profit. #7 Unit 1 It costs $10 in labor and materials to make each of his widgets. His rent each month for his factory is $4000. He sells each widget for $25. How many widgets does Bruce need to sell monthly to make a profit? A. B. C. D. 160 260 267 400 Revenue (in dollars) from selling x widgets R = 25x Cost to make x widgets C = 10x + 4000 Note: A profit occurs when enough widgets are made and sold to break even. (i.e. R = C) (Set up equation) R = C 25x = 10x + 4000 #7 Bruce owns a business that produces widgets. He must bring in more in revenue than he pays out in costs in order to turn a profit. Unit 1 It costs $10 in labor and materials to make each of his widgets. His rent each month for his factory is $4000. He sells each widget for $25. How many widgets does Bruce need to sell monthly to make a profit? A. B. C. D. 160 260 267 400 (Set up equation) Note: A minimum of 267 widgets must be sold in order to make a profit. 25x = 10x + 4000 –10x –10x 15x = 4000 15x 15 x 4000 15 267 = =