Question

Exercise 3.1.1 1 What positive number, when subtracted from its own square gives an answer of 56? 2 Eight times the sum of a number and its reciprocal results in 34. Find this number. 3 The square of the difference between a number and 12 is twice the number. Find it. 4 The product of two numbers is 88. What are the numbers if one number is 3 more than the other? 5 The sum of four times a number and its square is 60. What is the number? 6 Twice the square of Graham's height is 6 metres more than his height. How tall is he? 7 Rachelle has taken (4x-6) hours to travel 102 km at a speed of 25x+1) kmh. How fast was she travelling? 8 The product of two consecutive odd numbers is 143. If x is the smaller of the two numbers, show that x2 + 2x - 143. Find the numbers. 9 It will take an apprentice 15 days longer than a qualified painter to complete a job. However, if three apprentices and two qualified painters work together the job can be completed in 3 days. How long would it take one apprentice to do the job? 10 At a local screening of a movie, 450 people are seated in rows such that every row contains an equal number of people. However, if there were three more people in each row the number of rows needed would be reduced by 5. How many rows are there?

1, 2 & 3 please step by step .

Answer 1

solution let the number =0 85 = x- os es-re-p> e-as- "6+28 -xx se 3 x64-8) +212-8) 20 • (-8) (x+2) to x = -2,8 8 x= since a u positive => yaw 2 Let the number ax 34 Thom, Thin , 2+ 8( 2+ + 2) = 34 ** a as 4x?+4 = 122 4x²-12x+420 4?-16x = x+4-0 4x(x-4)-1(x-4) 20 (-4) (48-1) =0 x=t," 3 thu - the number is 1 x= 4

3 Let the number = x 1. Then (x-12)² = 2x as xe²+ 144-240=2re a x²-268 +144=0 x?-187-8 x +144 20 2(x+18) -862-18) =0 as (x-18) (2-8) to 1 x=18,8 Thune Toses 8,18

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