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 Human-and-algebraic-language/107764: A circular saw has a diameter of 18cm and 22 teeth. What is the spacing between teeth?1 solutions Answer 78526 by Nate(3500)   on 2007-11-03 10:41:54 (Show Source): You can put this solution on YOUR website!There are 22 teeth and 22 spaces between them. The Circumference - the amount of space taken by the teeth (22s where s is the amount of space taken by one tooth) is equal to the total amount of space occupied by nothing ... Divide that by the 22 spaces between the teeth and you get the individual space between two teeth. (C - 22s)/22 (18(pi) - 22s)/22 9(pi)/11 - s ... where s is in cm
 Polynomials-and-rational-expressions/107127: 1 solutions Answer 77941 by Nate(3500)   on 2007-10-30 13:56:17 (Show Source): You can put this solution on YOUR website! Doesn't work because the denominator = 0 ... no solutions
 Problems-with-consecutive-odd-even-integers/106519: find the sum of the reciprocals of two consecutive even integers if the smaller integer is x.1 solutions Answer 77537 by Nate(3500)   on 2007-10-27 10:29:52 (Show Source): You can put this solution on YOUR website!Smallest Integer = x Larger Integer = x + 2 1/x + 1/(x + 2) (x + 2)/(x(x + 2)) + x/(x(x + 2)) (2x + 2)/(x(x + 2))
 Linear-equations/106521: Given f(x)=-x^3+x^2+3x+4, find f(-1), f(0), and f(1).1 solutions Answer 77536 by Nate(3500)   on 2007-10-27 10:27:51 (Show Source): You can put this solution on YOUR website!f(x) = -x^3 + x^2 + 3x + 4 For f(0), you would set x to zero. ... Hence: f(x = 0) = f(0) f(0) = -0^3 + 0^2 + 3*0 + 4 = 4 Same with f(1) = f(x = 1) f(1) = -1^3 + 1^2 + 3*1 + 4 = -1 + 1 + 3 + 4 = 7 Now, you try f(-1).
 Linear-equations/106523: Solve the system by graphing 3x – y = 1 3x – y = 2.1 solutions Answer 77535 by Nate(3500)   on 2007-10-27 10:25:01 (Show Source): You can put this solution on YOUR website! No Solutions
 Volume/106529: if i had a dose of cough syrup to give someone and it said to give them 2.5 ml from a 1ml dropper what would that be?1 solutions Answer 77533 by Nate(3500)   on 2007-10-27 10:23:15 (Show Source): You can put this solution on YOUR website!Fill the dropper 2 and 1/2 times
 Expressions-with-variables/106530: Is the following expression true or false? Explain your answer. If r = 9 and s = -4, then r² - 2s = 73. Thank you!!1 solutions Answer 77532 by Nate(3500)   on 2007-10-27 10:22:24 (Show Source): You can put this solution on YOUR website!If r = 9 and s = -4, then r² - 2s = 73. Plug the values: r² - 2s = 73 (9)² - 2(-4) = 73 81 + 8 = 73 False
 Probability-and-statistics/106531: I have two problems if its ok: 1.) The equation 6x + 2 – 2x = 4x + 1 has no solution. Try solving this equation for x and see what happens. Explain why you cannot find a solution. 2.) An 18-foot wire is to be cut so that the longer piece is 5 times longer than the shorter piece. Find the length of each piece. Thank you!1 solutions Answer 77531 by Nate(3500)   on 2007-10-27 10:20:40 (Show Source): You can put this solution on YOUR website!1.) The equation 6x + 2 – 2x = 4x + 1 has no solution. Try solving this equation for x and see what happens. Explain why you cannot find a solution. 6x + 2 – 2x = 4x + 1 4x + 2 = 4x + 1 2 = 1 2 isn't equal to 1, so there are no values for x that will make this statement true. 2.) An 18-foot wire is to be cut so that the longer piece is 5 times longer than the shorter piece. Find the length of each piece. Shorter piece = x Longer piece = 18 - x longer piece is 5 times longer than the shorter piece 18 - x = 5(x) 18 - x = 5x 18 = 6x 3 = x Shorter piece = 3 Longer piece = 15
 logarithm/106365: log y = 1/4 log 16 + 1/3 log 64 All of the logs are a base 3 Please help I have worked every way I can and just can't seem to get the answer1 solutions Answer 77371 by Nate(3500)   on 2007-10-25 20:41:19 (Show Source): You can put this solution on YOUR website! . . . . . .
 Linear_Algebra/103895: (3x^2+4x-7)/(x-2)1 solutions Answer 75565 by Nate(3500)   on 2007-10-12 20:18:40 (Show Source): You can put this solution on YOUR website!3x^2 + 4x - 7 3x^2 + 7x - 3x - 7 (3x^2 + 7x) + (-3x - 7) x(3x + 7) - 1(3x + 7) (x - 1)(3x + 7) ... no common value ...... ......................3x + 10 + 13/(x - 2) (x - 2)....|....3x^2 + 4x - 7 ................(-).3x^2 - 6x ..................................10x - 7 .............................(-).10x - 20
 Probability-and-statistics/102763: 8 3 9 x 8 5 When a number is chosen at random from the six numbers listed above, the probability that this number will be less than 7 is 1/2. Which of the following could be the value of x? a) 6 b) 7 c) 8 d) 9 e) 101 solutions Answer 74741 by Nate(3500)   on 2007-10-07 14:15:22 (Show Source): You can put this solution on YOUR website!The probability of selecting a number less than seven is: numbers less than seven / all the possible numbers 2 / 6 is not equal to 1 / 2 Consider x as a number less than seven: 3 / 6 is equal to 1 / 2 (6)
 Geometry_Word_Problems/102765: Please help me understand this word problem. How could I solve this. Find the dimensions of a right triangle if the shortest side is 3 less than the middle one and 6 less than the hypotenuse. 1 solutions Answer 74739 by Nate(3500)   on 2007-10-07 14:12:47 (Show Source): You can put this solution on YOUR website!The middle sized side: x Smallest size: x - 3 Hypotenuse: x - 3 + 6 or x + 3 (x + 3)^2 = x^2 + (x - 3)^2 x^2 + 6x + 9 = x^2 + x^2 - 6x + 9 0 = x^2 - 12x 0 = x(x - 12) x = 0 ... not possible x = 12 ... possible Middle sized side: 12 Smallest size: 9 Hypotenuse: 15
 Expressions-with-variables/102767: I would really appericiate if you wouls help me on this problem... Two thirds of a number and three is the same as 3 multiplied by 1 less than twice the number. What is the number? Thank you very much 1 solutions Answer 74738 by Nate(3500)   on 2007-10-07 14:08:31 (Show Source): You can put this solution on YOUR website!Define the number as: x 2x/3 + 3 = 3(2x - 1) 2x/3 + 3 = 6x - 3 2x + 9 = 18x - 9 18 = 16x 9/8 = x
 Functions/102768: For f(x)=√(x-3) and g(x)=x^3 a) the domain of f b) the domain of g c) (f-g)(x) d) (fg)(x) e) the domain of (f/g)(x)1 solutions Answer 74737 by Nate(3500)   on 2007-10-07 14:05:29 (Show Source): You can put this solution on YOUR website!For f(x)=√(x-3) and g(x)=x^3 a) the domain of f The only limitation to this equation is the radical. x - 3 >= 0 x >= 3 b) the domain of g There are no limitations in the cubic equation. All Real Values c) (f-g)(x) Once again, the only limitation to this equation is tbe radical. x >= 3 d) (fg)(x) Again, only limitation is the readical. x >= 3 e) the domain of (f/g)(x) The two limitations are the radical and the denominator. x >= 3 and x can not be zero .... x >= 3
 Linear-equations/102582: Can you please help with this equation. A number is 7 less than 3 times a smaller number the difference between the number is 23.1 solutions Answer 74604 by Nate(3500)   on 2007-10-06 10:00:09 (Show Source): You can put this solution on YOUR website!smaller number = x larger number = 3x - 7 3x - 7 - x = 23 2x = 30 x = 15 numbers: 15 and 38
 Trigonometry-basics/102561: If f(x)= x(x+1) (x-4), use interval notation to give all values of x where f(x) >0.1 solutions Answer 74603 by Nate(3500)   on 2007-10-06 09:58:34 (Show Source): You can put this solution on YOUR website!f(x) = x(x + 1)(x - 4) For x = 0, x = -1, and x = 4, f(x) has the value of zero. <----------(-1)---------(0)-------------------------(4)--------> Test: f(-2) = -2(-1)(-6) = -12 f(-1/2) = (-1/2)(1/2)(-9/2) = 9/8 f(1) = (2)(-3) = -6 f(5) = 5(6)(1) = 30 <----------(-1)=========(0)-------------------------(4)========> f(x) > 0 only satisfied by f(x) > 4 and 0 > f(x) > -1 or (-1,0)U(4,+)
 Quadratic-relations-and-conic-sections/102579: solution of. x2=10y.1 solutions Answer 74601 by Nate(3500)   on 2007-10-06 09:47:40 (Show Source): You can put this solution on YOUR website!x^2/10 = y ... what solution? x - intercept or zero? (x,0) x^2/10 = 0 x^2 = 0 x = 0 (0,0)
 absolute-value/101799: This question is from textbook 1/2|d|+5>=2|d|-13 I've never seen anything like this before and it really confuses me. Please help.1 solutions Answer 74022 by Nate(3500)   on 2007-10-02 12:29:00 (Show Source): You can put this solution on YOUR website!1/2|d| + 5 >= 2|d| - 13 |d| + 10 >= 4|d| - 26 d + 10 = 4d - 26 and -d + 10 = -4d - 26 36 = 3d and 3d = -36 12 = d and d = -12 <---------[-12]-------------[12]------------> Test: d = -20 ......... 1/2(20) + 5 >= 2(20) - 13 .... 15 >= 27 d = 0 ............ 1/2|0| + 5 >= 2|0| - 13 .... 5 >= -13 d = 20 ........... 1/2(20) + 5 >= 2(20) - 13 <---------[-12]=============[12]------------> Solution: [-12,12]
 Trigonometry-basics/101198: solve each equation. assume 0<=t<=2pi and 0<=theta<=360degrees a. sin(t)=1/2 b. 2cos^2 theta - 3cos theta +1=0 c. sec theta= -5 give answer accurate to 3 decimals d. 2 cos(2t)=7cos(t) give answer accurate to 3 decimals1 solutions Answer 73692 by Nate(3500)   on 2007-09-29 19:46:29 (Show Source): You can put this solution on YOUR website!a. sin(t) = 1/2 t = pi/6 t = pi/6 and t = 5*pi/6 b. 2*cos^2(theta) - 3*cos(theta) + 1 = 0 2*cos^2(theta) - 2*cos(theta) - cos(theta) + 1 = 0 2*cos(theta)(cos(theta) - 1) - 1(cos(theta) - 1) = 0 (2*cos(theta) - 1)(cos(theta) - 1) = 0 2*cos(theta) - 1 = 0 and cos(theta) - 1 = 0 cos(theta) = 1/2 and cos(theta) = 1 theta = pi/3, 5*pi/3, 0, and 2*pi c. simple d. 2*cos(2t) = 7cos(t) 2*cos(2t) - 7*cos(t) = 0 2( cos(t + t) ) - 7*cos(t) = 0 2( cos(t)^2 - sin(t)^2 ) - 7*cos(t) = 0 2( cos(t)^2 - ( 1 - cos(t)^2 )) - 7*cos(t) = 0 2( 2*cos(t)^2 - 1) - 7*cos(t) = 0 4*cos(t)^2 - 7*cos(t) - 2 = 0 4*cos(t)^2 - 8*cos(t) + cos(t) - 2 = 0 4*cos(t)(cos(t) - 2) + 1(cos(t) - 2) = 0 (4*cos(t) + 1)(cos(t) - 2) = 0 4*cos(t) + 1 = 0 and cos(t) - 2 = 0 cos(t) = -1/4 and cos(t) = 2 ... nonexistant I do not have a calculator with the inverse process with me ...
 Numbers_Word_Problems/101218: 15 books are being bought. Some cost \$8.50 each, the remainder cost \$9.50 each. Estimate the least number of books that can be bought at \$8.50 each if the total cost must not be more than \$135.50. 1 solutions Answer 73690 by Nate(3500)   on 2007-09-29 19:10:27 (Show Source): You can put this solution on YOUR website!x = number of cheaper books y = number of more expensive books x + y = 15 or y = 15 - x 8.5x + 9.5y =< 135.5 Plug: 8.5x + 9.5(15 - x) =< 135.5 8.5x + 9.5(15 - x) =< 135.5 8.5x + 142.5 - 9.5x =< 135.5 -x =< -7 x >= 7 Atleast 7 books ... least amount being seven
 Numeric_Fractions/101223: Joan was charged \$18 interest for 1 month on a \$1200 credit card balance.What is the monthly interest rate?1 solutions Answer 73688 by Nate(3500)   on 2007-09-29 19:04:01 (Show Source): You can put this solution on YOUR website!I = PRT Interest = Principle * Rate * Time 18 = 1200 * Rate * 1 3/200 = Rate 1.5% = Rate
 Polynomials-and-rational-expressions/101222: Use synthetic Division to find the remainder in the division: x^3 - 4x^2 + 5x +3 / x+1 **The /= fraction bar not division1 solutions Answer 73687 by Nate(3500)   on 2007-09-29 19:02:03 (Show Source): You can put this solution on YOUR website!-1 .. | ...... 1 ....... -4 ....... 5 ........ 3 .................1...........-5.........10...........-7 ( x^2 - 5x + 10 - 7/(x + 1) )
 Inequalities/101206: Describe at least two real-life examples where inequalities are used either at home or on the job. Try looking in the textbook or online to see what ideas you get. Then look around you at home and at work and see what strikes you as being similar in your own life. What examples do you see? Describe at least two of them in detail.1 solutions Answer 73686 by Nate(3500)   on 2007-09-29 18:58:48 (Show Source): You can put this solution on YOUR website!I will give one example: You need atleast 140 mg of vitamin A and atleast 145 mg of vitamin B. A scoop of X food gives you 35mg of vit A and 30mg of vit B. A scoop of Y food gives you 30mg of vit A and 40mg of vit B. X food costs 8 dollars, but Y food costs 10 dollars. What is the minimum cost in order to attain all the essential vitamins. a >= 140 a = 35x + 30y 35x + 30y >= 140 and b >= 145 b = 30x + 40y 30x + 40y >= 145 and x >= 0 and y >= 0 Profit Equation: P(x,y) = 8x + 10y P(0,14/3) = 0 + 10(14/3) = 140/3 = \$46.67 P(29/6,0) = 8(29/6) + 0 = \$38.67 P(2.5,1.75) = 8(2.5) + 10(1.75) = 20 + 17.5 = \$37.5 .... Cheapest 2.5 scoops of x and 1.75 scoops of y
 Numeric_Fractions/101209: I have 41 1/2 ft. of string. I want to cut it into pieces of 3 3/4 ft of string. How many pieces did I cut. How many remain if any?1 solutions Answer 73674 by Nate(3500)   on 2007-09-29 18:28:18 (Show Source): You can put this solution on YOUR website!41.5/3.75 = 11 2/30 11 pieces and 2/30 of a 3 3/4 foot piece or 11 pieces and a 1/4 of a foot piece
 Trigonometry-basics/101199: find the exact value of each. a. cos(theta)/2 if sin(theta)=12/13 and 0 b. sin[cos^-1(0) - sin^-1(1/2)]1 solutions Answer 73661 by Nate(3500)   on 2007-09-29 16:12:00 (Show Source): You can put this solution on YOUR website!a. cos(theta)/2 if sin(theta) = 12/13 and 0 < theta < 90 degrees cos(theta)^2 = 1 - sin(theta)^2 cos(theta) = sqrt( 1 - sin(theta)^2 ) cos(theta) = sqrt( 1 - (12/13)^2 ) or cos(theta) = sqrt( 1 - 0^2 ) cos(theta) = sqrt( 25/169 ) or cos(theta) = sqrt( 1 ) cos(theta) = 5/13 or cos(theta) = 1 *cos(theta) = 1 for theta = 0 ~ Cancel cos(theta)/2 = 5/26 b. sin[cos^-1(0) - sin^-1(1/2)] sin[pi/2 - pi/6] sin[pi/3] sqrt(3)/2
 Travel_Word_Problems/101201: 2 passenger trains are traveling on the same track heading in opposite directions. the trains are currently 170 miles apart. the first train is going 9mph and the second train is going 8mph. in how many hours will these 2 trains meet and how far does each train travel?1 solutions Answer 73660 by Nate(3500)   on 2007-09-29 15:59:34 (Show Source): You can put this solution on YOUR website!First train: rate = 9 time = t distance = 9t Second train: rate = 8 time = t distance = 8t They both must travel 170 miles in order to close the distance between the two: 9t + 8t = 170 17t = 170 t = 10 hours
 Money_Word_Problems/100947: Sales--Tickets for a concert were sold to adults for \$3 and to students for \$2. If the total sold were the amount of \$ 824 and twice as many adult tickets were sold,then how many of each were sold? 1 solutions Answer 73476 by Nate(3500)   on 2007-09-27 21:26:42 (Show Source): You can put this solution on YOUR website!a = number of adult tickets s = number of student tickets a = 2s 3a + 2s = 824 Solve
 Quadratic_Equations/100951: Use the square root property to solve the following equations x^2 - 12 = 01 solutions Answer 73475 by Nate(3500)   on 2007-09-27 21:25:06 (Show Source): You can put this solution on YOUR website!x^2 - 12 = 0 x^2 = 12 x = +- sqrt(12) x = +- sqrt(4*3) x = +- 2*sqrt(3)
 Quadratic_Equations/100952: Use the square root property to solve the following equations 5x^2 - 65 = 01 solutions Answer 73474 by Nate(3500)   on 2007-09-27 21:24:16 (Show Source): You can put this solution on YOUR website!5x^2 - 65 = 0 5x^2 = 65 x^2 = 13 x = +- sqrt(13)
 Travel_Word_Problems/100961: This question is from textbook Algebra I Please help.... May rides her bike the same distance Leah walks. May rides her bike 10km/h faster than Leah walks. If it takes May 1 h and Leah 3h to travel that distance, how fast does each travel?1 solutions Answer 73473 by Nate(3500)   on 2007-09-27 21:23:35 (Show Source): You can put this solution on YOUR website!distance = rate * time Leah: rate = r time = 3 distance = 3r May: rate = r + 10 time = 1 distance = r + 10 The distances were equal: 3r = r + 10 2r = 10 r = 5