Practice for Written Assignment 2

Transcription

1 Practice for Written Assignment 2 Solve the equation. 1) 8(k + 4) - (7k + 1) = 9 1) 2) -2x - 7-6(x + 1) = -(3x - 2) 2) 3) x = x ) 4) 5(y - 2) 3 = 2y - 2 4) 5) 1 8 (x + 16) - 1 (x - 9) = x + 2 5) 9 Solve the formula for the indicated variable. 6) A = bh, for h 6) 7) V = 1 Bh, for B 7) 3 Solve the problem. 8) Levi borrowed $7777 at 5% simple interest for 3 months. How much will the interest amount to? What is the total amount that Levi will have to pay back at the end of 3 months? Round answers to the nearest cent if necessary. 8) Use these equations to convert between the two systems. C = 5 9 (F - 32) F = 9 5 C + 32 Round answer to the nearest tenth of a degree if necessary. 9) F = 259 9) 10) C = 30 10) Solve the problem. 11) How many liters of a 30% alcohol solution must be mixed with 20 liters of a 80% solution to get a 50% solution? 11) 1

2 12) In a chemistry class, 3 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? 13) A rectangular Persian carpet has a perimeter of 232 inches. The length of the carpet is 26 in. more than the width. What are the dimensions of the carpet? 14) Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 336 miles in the same time that Dana travels 312 miles. If Chuckʹs rate of travel is 4 mph more than Danaʹs, and they travel the same length of time, at what speed does Chuck travel? 15) From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 14 miles per hour. In how many hours will they be 69 miles apart? 16) Mardi received an inheritance of $60,000. She invested part at 1.25% and deposited the remainder in tax-free bonds at 2%. Her total annual income from the investments was $900. Find the amount invested at 1.25%. 12) 13) 14) 15) 16) Indicate whether the statement is true always, sometimes, or never. 17) A real number is a complex number. 17) 18) A complex number is an imaginary number. 18) Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. 19) 8-7i 19) 20) 7 20) 21) π 21) 22) 1 22) 23) -9 23) Write the number as the product of a real number and i. 24) ) 2

3 25) ) Find the sum or difference. Write the answer in standard form. 26) (-8-2i) - (-5 + 8i) - (-9 + 4i) 26) 27) (1 + 9i) - (4 + 2i) + (8 + 2i) 27) Find the product. Write the answer in standard form. 28) (5-4i)(9 + 8i) 28) 29) i(6-9i)(5-4i) 29) 30) 7i(8-7i) 2 30) Divide. 31) 7 + 5i 7-9i 31) 32) 1 + i -1 - i 32) Solve the equation by the zero-factor property. 33) x 2 + 6x - 27 = 0 33) Solve the equation by the square root property. 34) (x - 12) 2 = 81 34) Solve the equation by completing the square. 35) x2 + 6x - 27 = 0 35) Solve the equation using the quadratic formula. 36) 7x2 + 12x + 1 = 0 36) 37) 2x2 = -12x ) Solve the equation for the indicated variable. Assume no denominator is 0. 38) A = 3πa2, for a 38) 3

4 Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. 39) s2 + 5s + 4 = 0 39) 40) t2 + 10t + 25 = 0 40) 41) v2-7v - 1 = 0 41) 42) w2-2w + 7 = 0 42) Solve the problem. 43) The outside of a picture frame has a length which is 5 cm more than width. The area enclosed by the outside of the picture frame is 104 square cm. Find the width of the outside of the picture frame. 44) A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be? 45) A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall. 46) A boat is 64 feet from the base of cliff. If the distance from the top of the cliff to the boat is 16 less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest tenth of a foot if necessary. 47) A ball is dropped from a cliff that is 432 feet high. The distance S (in feet) that it falls in t seconds is given by the formula S = 16t2. How many seconds (to tenths) will it take for the ball to hit the ground? 48) A coin is tossed upward from a balcony 166 ft high with an initial velocity of 16 ft/sec. During what interval of time will the coin be at a height of at least 70 ft? (h = -16t2 + v0t + h0.) 43) 44) 45) 46) 47) 48) Solve the equation. 49) x + 3 = x ) 50) 3x + 1 = 3 + x ) 4

5 51) (4x - 6) 2-6(4x - 6) - 7 = 0 51) 52) x 2/3 = -5x 1/3 52) Write the inequality in interval notation. 53) 53) Solve and graph the inequality. Give answer in interval notation. 54) -6(3x + 6) < -24x ) 55) x x ) Solve the problem. 56) The profit made when t units are sold, t > 0, is given by P = t2-32t Determine the number of units to be sold in order for P = 0 (the breakeven point). 56) 57) The cost of producing t units is C = 2t2 + 5t, and the revenue generated from sales is R = 3t2 + t. Determine the number of units to be sold in order to generate a profit. 57) Solve the equation. 58) 7x + 2 = 7 58) 59) 8x + 2 = -6 59) 60) 5x = 5 60) Solve the inequality. Write the solution set in interval notation. 61) x + 5 < 2 61) Write the statement as an absolute value inequality. 62) x is within 5 units of 7 62) 5

6 63) z is no less than 5 units from 8 63) 64) m is no more than 7 units from 18 64) 65) p is 5 units from 8 65) 6

7 Answer Key Testname: PRACTICE FOR WRITTEN ASSIGNMENT 2 1) ) - 3 3) 24 4) -4 5) ) h = A b 7) B = 3V h 8) $97.21; $ ) C = ) F = 86 11) 30 L 12) 1.5 L 13) Width: 45 in.; length: 71 in. 14) 56 mph 15) 3 hr 16) $40,000 17) Always 18) Sometimes 19) Nonreal complex 20) Real, complex 21) Real, complex 22) Real, complex 23) Complex, pure imaginary, nonreal complex 24) 5i 25) -6i 26) 6-14i 27) 5 + 9i 28) i 29) 69-6i 30) i 2 31) i 32) -1 33) {-9, 3} 34) {3, 21} 35) {3, -9} 7

8 Answer Key Testname: PRACTICE FOR WRITTEN ASSIGNMENT 2 36) 37) -6 ± ± ) a = ± 3πA 3π 39) Two distinct rational solutions 40) One rational solution (a double solution) 41) Two distinct irrational solutions 42) Two distinct nonreal complex solutions 43) 8 cm 44) 1.5 ft 45) 10 ft 46) 48 ft 47) 5.2 sec 48) 0 t 3 49) {6} 50) {5, 8} 13 51) 4, ) {0, -125} 53) (-2, 7] 54) (-, 9) ) [-7, ) ) t = 18 or t = 14 57) t > ) 7, ) 60) 11 5, ) (-7, -3) 62) x ) z ) m

9 Answer Key Testname: PRACTICE FOR WRITTEN ASSIGNMENT 2 65) p - 8 = 5 9