Mathematics

Characteristics of roots and word problem: * Solution by form root: To solve a quadratic equation by factoring, we use the ff. theorem; x=d if and only if x=±?d Ex. 1.) x²-6=0 x²=16 x=±?16 x=+/-4 The solution set is {-4, 4} 2.) x²=5 X=±?5 The solution set is {-?5, +?5 3.) (x 1)²=3 X 1 = ±?3 X = 1 ±?3 The solution set is {1 + ?3, 1 - ?3} EXERCISES: 1.X² - 81 = 0 2.3X² - 75 = 0 3. X² - 12X + 35 = 0 4. 2X² - 6X 80 = 0 5. 6X² - 15X = 9 * WORD PROBLEM: 1.) Find a twain-digit number much(prenominal) that the tens digit exceeds the units digit by 3 and the number is 4 less than the sum of the squ atomic number 18s of its digits. permit x is the units digit x + 3 the tens digit The require two digit number is 10(x + 3) + x The equation is x² + (x + 3)² - 4 = 10(x + 3) + x x² + + x² + 6x + 9 4 = 10x + 30 + x 2x² - 5x 25 = 0 (2x + 5)(x 5) = 0 2x + = 0; x 5= 0 X= -5/2 ; x= 5 we reject -5/2 and accept x = 5 X = 5(units) and (x + 3) = 8(tens) The required two-digit number is 85. 2.) Esther Grey preserve encode one knave ahead of Isabela Jean by one minute. Together they can finish 27 summons in one time of day. How long does it tax return each to finish encoding one page?

Let x be the number of transactions for Esther Grey to encode one page X = 1 be the number of minutes for Isabel Jean to encode one page. The fractional parts rick done by both to finish one page is 1/x and 1/x + 1 Since there are 27 pages to be finished in one hour or 60 minutes, then the desired equation is 1/x + 1/x + 1 = 27/60 (1/x + 1/x + 1= 9/20)(20(x)(x + 1)) 20(x + 1) + 20x = 9x(x + 1) 20x + 20 + 20x = 9x² + 9 9x² - 31x 20 = 0 (9x + 5)(x 4) = 0 9x + 5 = 0; x 4 = 0 X= -5/9; x = 4 We reject x= -5/9 and accept x = 4. 3.) By increasing the average speed of Joels railway car by 10 kilometers per hour, he would have save 36 minutes in traveling a distance of cxx kilometers. Find the average... If you want to get a full essay, establish it on our website: Orderessay

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