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# Recent problems solved by 'Earlsdon'

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 Functions/178280: This question is from textbook college algebras Thank you in advance for your help. I do not understand what I need to do to find f^-1 and verify that (f o f^-1)(x)=x and (f^-1 o f )(x)=x the equation is f(x)=x/x+1 for x>-11 solutions Answer 133241 by Earlsdon(6287)   on 2009-01-24 15:58:15 (Show Source): You can put this solution on YOUR website!Verify that and for: for First, you'll need to find Start with the given function: Substitute for Now exchange x and y. Next, solve this for y. Multiply both sides by Expand the left side. Subtract xy from both sides. Factor the y from the right side. Divide both sides by Now replace the with Now you are in a position to find: Substitute recalling that Notice that where there is an x on the left side, it's replaced with on the right side. Now we'll simplify the right side. Invert and multiply. Do you think you can manage to show that ?
 Quadratic_Equations/177383: Please help. If the sides of a square are lengthened by 8cm, the area becomes 169cm^2. Find the length of the original square. Thank you.1 solutions Answer 132426 by Earlsdon(6287)   on 2009-01-19 12:02:48 (Show Source): You can put this solution on YOUR website!Let s = the length of the side of the original square. If you increase this by 8 cm (s+8) and square it ((s+8)*(s+8)) you get 169 sq.cm. So you can write: Square the left side. Subtract 169 from both sides. Factor this quadratic equation. Apply the zero product rule: or which means that... or Discard the negative solution as the length of the sides can only be positive. cm This is the length of the side of the original square. Check: OK!
 Quadratic_Equations/177348: Could someone please help me answer this question? If you are looking at a graph of a quadratic equation, how do you determine where the solutions are?1 solutions Answer 132412 by Earlsdon(6287)   on 2009-01-19 11:07:27 (Show Source): You can put this solution on YOUR website!The "solutions" or "roots" to a quadratic equation are the points on the graph of the equation where the graph (a parabola) intersects the x-axis. Of course, some parabolas will intersect the x-axis in two places (1st. graph) in which case the equation is said to have two real roots. Some parabolas will have their vertex just touching the x-axis (2nd graph). Such an equation is said to have double root or two identical roots. Other parabolas will not intersect the x-axis at all (3rd graph), in which case, the equation is said to have no real roots.
 Trigonometry-basics/177268: This question is from textbook The highest advertising sign in the world is a large letter I situated at the top of the 73-story First Interstate World Center building in Los Angeles. At a distance of 200 feet from a point directly below the sign, the angle between the ground and the top of the sign is 77.87°. To the nearest tenth, approximate the height of the top of the sign.1 solutions Answer 132348 by Earlsdon(6287)   on 2009-01-18 18:11:44 (Show Source): You can put this solution on YOUR website!Using right triangle math, in which the height (h) is the unknown and the base is 200 feet, use the tangent function (opposite over adjacent) to find h. Multiply both sides by 200. feet.
 Trigonometry-basics/177267: This question is from textbook Stonehenge in Salisbury Plains, England, was constructed using solid stone blocks weighing over 96000 pounds each. Lifting a single stone required 550 people, who pulled the stone up a ramp inclined at an angle of 9°. To the nearest tenth, approximate the distance that a stone was moved along the ramp in order to raise it to a height of 31 feet.1 solutions Answer 132342 by Earlsdon(6287)   on 2009-01-18 17:44:48 (Show Source): You can put this solution on YOUR website!Think of the ramp as a right triangle in which the hypotenuse is the ramp's slope up which the 96000-lb block of stone is to be hauled. The height (h) of this triangle is the height to which the block is to be raised. The height is opposite to the angle of 9 degrees, so you can use the sine function to solve this problem and you are trying to find the length of the hypotenuse (c). Substitute h = 31 ft. Multiply both sides by c. The sine 0f 9 degrees is 0.156, so... Divide both sides by 0.156 Round to nearest tenth. feet.
 Exponential-and-logarithmic-functions/177270: 6*(7*10^8)1 solutions Answer 132340 by Earlsdon(6287)   on 2009-01-18 17:26:22 (Show Source): You can put this solution on YOUR website!Evaluate: Multiply the 6 times 7 = 42 Expand the Final answer: or 4,200,000,000
 Money_Word_Problems/177228: This question is from textbook college algebras thank you in advance for help with this problem. I am not getting it right but would like to know where I am going wrong. Thanks \$600 for 10 years at 8.5% compounded annually. I set it up like this A=600(1+.085)^10 and I end up wiht 656 I know the answer is 1356\$ annually. Thank for showing me where I am going wrong.1 solutions Answer 132308 by Earlsdon(6287)   on 2009-01-18 11:36:26 (Show Source): You can put this solution on YOUR website!Well, I see nothing wrong with your set up. and p = 600, i = 0.085, and n = 10 years. So I would double check your order of operations.
 Polynomials-and-rational-expressions/177049: Verify algebraically, that (Fof^-1)(x)=x for f(x)=1/(2x+4)1 solutions Answer 132304 by Earlsdon(6287)   on 2009-01-18 11:07:44 (Show Source): You can put this solution on YOUR website!Your problem statement is a little unclear! Did you mean to write: Verify algebraically that for I'll assume that you did and we'll proceed. First, we find Start with the given function, but replace the with : Now exchange the x and the y. Next, solve this for y. Multiply both sides by (2y+4) Divide both sides by x. Subtract 4 from both sides. Simplify the right side. Now divide both sides by 2. Finally, replace the with Now you can find but , so... Simplifying this... so... and so for
 Linear-systems/177176: Al will rent a car for the weekend. He can choose one of two payment plans. The first plan costs \$51.98 for two days plus 15 cents per mile. The second plan costs \$39.98 for two days plus 20 cents per mile. How many miles does Al need to drive for the two plans to cost the same? 1 solutions Answer 132244 by Earlsdon(6287)   on 2009-01-17 19:09:57 (Show Source): You can put this solution on YOUR website!Let's write the cost equations (C) for both car rentals: where m = number of miles driven. Since you need to know when the costs will be equal, set these two equations equal to each other. Now you can solve for m, the number of miles. Subtract 0.15m from both sides. Now subtract 39.98 from both sides. Finally, divide both sides by 0.05 So, Al must drive 240 miles for the costs of both plan to be the same.
 Linear-equations/177173: A study showed that, your maximum ideal waist size is directly proportional to your hip size.For a woman with 40-inch hips, the maximum ideal waist size is 32 inches. What is the maximum ideal waist size for a woman with 35-inch hips?1 solutions Answer 132243 by Earlsdon(6287)   on 2009-01-17 18:59:12 (Show Source): You can put this solution on YOUR website!First, you will need to write the equation of proportion. Let W = waist size and H = hip size. where k is the constant of proportionality. You need to find the value of k, so subtitute W = 32 and H = 40. Divide both sides by 40. Now the equation of proportionality is: To find the ideal maximum waist size (W) for a woman with 35-inch hips, substitute H = 35. inches.
 Linear-systems/177175: Lena purchased a prepaid phone card for \$30. Long distance calls cost 17 cents a minute using this card. Lena used her card only once to make a long distance call. If the remaining credit on her card is \$24.05, how many minutes did her call last? 1 solutions Answer 132241 by Earlsdon(6287)   on 2009-01-17 18:50:29 (Show Source): You can put this solution on YOUR website!Lena has used \$30-\$24.05 = \$5.95 of the total value of the card. The question is...how many minutes of long-distance call can she get from \$5.95 at \$0.17 per minute. To find out, you will need to divide \$5.95 by \$0.17, so... Lena's long-distance call lasted 35 minutes.
 expressions/177171: i am trying to solve this problem..... (3x) to the -1/3 power using log table???1 solutions Answer 132239 by Earlsdon(6287)   on 2009-01-17 18:44:38 (Show Source): You can put this solution on YOUR website!It appears as though you have omitted part of the problem statement. You really need an equation to solve for x...
 Problems-with-consecutive-odd-even-integers/177196: find three consecutive integers such that the product of the two smaller inters is 2 more than ten times the largest integers.1 solutions Answer 132238 by Earlsdon(6287)   on 2009-01-17 18:33:30 (Show Source): You can put this solution on YOUR website!Let the three consecutive integers be: x, (x+1) and (x+2) "The product of the two smaller integers (x and (x+1)) is 2 more than 10 times the larger integer (x+3). Subtract 10x from both sides. Subtract 32 from both sides. Factor this quadratic equation. Apply the zero product rule. or so... or Solutions: 11, 12, and 13 -2, -1, and 0 As you can see, there are two solutions, so let;'s check them both! x = 11 OK! x = -2 OK!
 Linear-systems/177177: A total of 285 tickets were sold for the school play. The number of student tickets sold was two times the number of adult tickets sold . How many adult tickets were sold? 1 solutions Answer 132234 by Earlsdon(6287)   on 2009-01-17 18:14:44 (Show Source): You can put this solution on YOUR website!Let S = the number of student tickets sold and A = the number of adult tickets sold. From the problem, you can write: 1) S+A = 285 "A total of 285 (student plus adult) tickets were sold..." 2) S = 2A "The number of student tickets (S) sold was two times the number of adult tickets (A) sold." Substitute equation 2) (S = 2A) for S in equation 1). (2A+A) = 285 Simplify. 3A = 285 Divide both sides by 3. A = 95 This is the number of adult tickets sold. From equation 2)... S = 2A S = 2(95) S = 190 This is the number of student tickets sold.
 Linear-equations/177189: I need help with this equation and a explanantion Please. Determine the slope ans y-intercept of the line x+2y=3. Thank you.1 solutions Answer 132231 by Earlsdon(6287)   on 2009-01-17 18:05:34 (Show Source): You can put this solution on YOUR website!First, rewrite the equation in the "slope-intercept" form: y = mx+b: Subtract x from both sides of the equation. Now divide both sides by 2 to get the y by itself. Compare this with the general form of the slope-intercept: and you can see that the slope, and the y-intercept,
 Linear-systems/177163: Give an ordered pair (x,y) of numbers that satisfy the equation 4x+y=31 solutions Answer 132230 by Earlsdon(6287)   on 2009-01-17 17:59:11 (Show Source): You can put this solution on YOUR website!Rewrite the equation in the slope-intercept form: y = mx+b y = -4x+3 Now substitute any value you like for x and you will get the corresponding value of y. Let x = 5 y = -4(5)+3 y = -20+3 y = -17 So one ordered pair would be (5, -17) As you can see, there are an infinite ordered pairs that would satisfy this equation, you choose the x-value and there will be a corresponding y-value..
 Quadratic_Equations/177181: the problem I have is f(t)=2t^2-4t-1 and it asks tosolve the problem if f(2). Can some one show me how this works1 solutions Answer 132222 by Earlsdon(6287)   on 2009-01-17 17:19:28 (Show Source): You can put this solution on YOUR website!If: find f(2): You simply substitute 2 for every t in the equation and evaluate.
 Linear-systems/176907: This question is from textbook Algebra 1 The farest I have got to this question is 2a= 8 / a+b=2 a=4 on the first linear equations but I don't know where to go from here.1 solutions Answer 132218 by Earlsdon(6287)   on 2009-01-17 16:10:41 (Show Source): You can put this solution on YOUR website! Solve: and Divide both sides by 2. Substitute Subtract 4 from both sides.