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# Recent problems solved by 'Earlsdon'

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 Miscellaneous_Word_Problems/124539: The number N, in millions, of hearing impaired individuals of age x can be approximated by: N = -0.00006x^3 + 0.006x^2 - 0.1x + 1.3 Approximate to the nearest million the number of hearing impaired individuals of ages 50 - 60. N = (squiggly lines) ___________ million individuals of age 50. N = (squiggly lines) ___________ million individuals of age 60. Please help, I submitted this yesterday and noone seemed to have answered. I tried calculating and kept coming up with 0 and that can't be the answer. Thank you!1 solutions Answer 91273 by Earlsdon(6287)   on 2008-02-03 11:42:29 (Show Source): You can put this solution on YOUR website! Substitute x = 50 round to the nearest million... Million, approximately. Substitute x = 60 Round to the nearest million... Million, approximately.
 Polynomials-and-rational-expressions/124528: Simplify by combining like terms. 1) 5 square root of 8 MINUS 2 square root of 50 PLUS square root of 18 2) 3 square root of 5 MINUS square root of 451 solutions Answer 91272 by Earlsdon(6287)   on 2008-02-03 10:23:38 (Show Source): You can put this solution on YOUR website!Simplify: 1) The technique to use here is to factor the quantity under the radical (the radicand) looking for perfect squares in the factors. When you do find a factor that is a perfect square, take its square root and move the result outside of the radical. Like this: the 4 is a perfect square and its square root is 2, so you can rewrite this as: = See the idea? Simplifying, we get: 2) Simplify: =
 Geometry_Word_Problems/124364: Area of a painting. A rectangular painting with a width of x centimeters has an area of x^2+50x square centimeters. Find a binomial that represents the length. 1 solutions Answer 91146 by Earlsdon(6287)   on 2008-02-02 10:55:46 (Show Source): You can put this solution on YOUR website!Start with the formula for the area of a rectangle: The area, A, is given as: The width is given as: Find L: Factor an x from the binomial on the left side then divide both sides by x. Divide by x. The length is represented by the binomial
 Linear_Equations_And_Systems_Word_Problems/124363: Rectangular state: One side of a rectangular stage is 2 meters longer than the other. If the diagnonal is 10 meters, then what are the lenths of the sides?1 solutions Answer 91145 by Earlsdon(6287)   on 2008-02-02 10:47:07 (Show Source): You can put this solution on YOUR website!The diagonal of the stage(10m) represents the hypotenuse of a right triangle whose legs are the width (W) and the length (L) of the rectangle. But the problem states that the length (L) is 2 meters longer than the width (W), so the length can be expressed as: L = W+2. Now we can apply the Pythagorean theorem () to solve this problem since we are dealing with a right triangle. c is the hypotenuse of the right triangle, or the diagonal of the rectangular stage which is given as 10m. a and b are the width of the stage (W) and the length of the stage (L = W+2). Make the appropriate substitutions into the Pythagorean formula to get: Substitute L = W+2 Divide through by 2 to simplify a bit. Subtract 50 from both sides. Solve this quadratic equation by factoring. Apply the zero product principle. or If then If then Discard this solution as the width, W, must be a positive value. The width is 6 meters. The length is 8 meters. Check: Substitute c = 10, a = 8, and b = 6. OK!
 Miscellaneous_Word_Problems/124225: A GROCER MIXED GRAPE JUICE AT \$2.25 PER GALLON WITH CRANBERRY JUICE AT \$1.75 PER GALLON. HOW MANY GALLONS OF EACH SHOULD BE USED TO MAKE 20 GALLONS OF CRANBERRY/GRAPE JUICE WHICH WILL COST \$2.10 PER GALLON?1 solutions Answer 91030 by Earlsdon(6287)   on 2008-02-01 11:17:20 (Show Source): You can put this solution on YOUR website!Let's start by assigning variables to the unknown quantities. Let x = the required number of gallons of grape juice at \$2.25 per gallon. Now, because we want to make a total of 20 gallons of cranberry/grape juice mix, we will need to add (20-x) gallons of cranberry juice at \$1.75 per gallon. At the end we'll have (hopefully) the required 20 gallons of cranberry/grape juice mix at \$2.10 per gallon. Now we can write the equation that will tell us how much of each we will need. x(\$2.25)+(20-x)(\$1.75) = 20(\$2.10) Simplify and solve for x. 2.25x + 35 - 1.75x = 42 Combine like-terms. 0.5x+35 = 42 Subtract 35 from both sides. 0.5x = 7 Divide both sides by 0.5 x = 14 So we'll need 14 gallons of grape juice @ \$2.25 per gallon plus (20-x) 6 gallons of cranberry juice @ \$1.75 per gallon to obtain 20 gallons of cranberry/grape juice mix @ \$2.10 per gallon.
 Linear-equations/124234: Help!!!! I am so confused with graphing..here is the question What is the equation of a line parallel to y = -x + 3 through the point (2,4) Can someone help?1 solutions Answer 91029 by Earlsdon(6287)   on 2008-02-01 10:51:39 (Show Source): You can put this solution on YOUR website!First, you want to write the new equation in the "slope-intercept" form (y = mx+b) unless instructed otherwise. Second, recall that parallel lines have identical slopes, so if you know the slope of the line whose equation is given (y = -x+3), then you autmatically know the slope of any line parallel to this. Compare the given equation which is already in the slope-intercept form with the general form: y = -x+3 y = mx+b You can see that the slope, m, of the given equation is -1. So the slope of the new equation will be -1 because the new line is parallel to the given line. Ok, now you can write the slope (m = -1) into the general equation: y = -x+b Now you need to find the value of b, the y-intercept. You do this by substituting the x and y of the above equation with the x and y values taken from the given point (2, 4) through which the new line passes. y = -x+b Substitute x = 2 and y = 4 4 = -2+b Add 2 to both sides. 6 = b This is the y-intercept of the new line so now you can write the final equation: y = -x+6 I hope this clarifies the problem for you!
 Linear-equations/124238: I am so lost when it comes to story problems..can someone help walk me through the steps so that i can become more proficient at them? Thanks... Frozen yogurt costs \$2 plus 50 cents for every topping. Express the total cost of a cup of yogurt as a function of the number of toppings chosen. So confused....1 solutions Answer 91027 by Earlsdon(6287)   on 2008-02-01 10:30:49 (Show Source): You can put this solution on YOUR website!Ok, the cost of the frozen yogurt is constant at \$2.00. The cost of the toppings varies and depends on the number of toppings you select, so let's call this variable, x, and for every topping you choose, it will cost \$0.50 So you can express the total cost (C) of a cup of frozen yogurt as the sum of the fixed cost (\$2.00) of the frozen yogurt plus the variable cost (x dollars) of the number (x) of toppings at \$0.50 each. C = \$2.00 + x(\$0.50)
 Functions/124237: This question is from textbook Precalculus Can you plese help me answer this question? Given that the volume V of a circular cylinder of fixed height is profortional to the square of its radius r, we may write this formula as a power function as follows. My answer options are: A. V=ksqrt(r) B. V=kr^2 C. V=kr d. V=k^2r Please help, I highly appreciate it. Thanks 1 solutions Answer 91026 by Earlsdon(6287)   on 2008-02-01 10:21:41 (Show Source): You can put this solution on YOUR website!The volume, V, of a right circular cylinder is proportional to the square of its radius, r, can be expressed as follows: where k is the proportionality constant.
 Trigonometry-basics/123996: Ok, so I have my Honors Algebra 2 FINAL tomorrow and there is this certain type of problem I just don't understand. No matter how many times I try these types of problems I just can't seem to get them right. Could someone maybe explain to me how to do the following type of problem? That would be a huge help. I'm hoping that maybe a second explanation other than the one from my teacher will help me finally understand. You could use this problem as an example. Directions: Solve each equation for 1 solutions Answer 90959 by Earlsdon(6287)   on 2008-01-31 18:57:23 (Show Source): You can put this solution on YOUR website!Try this: (I hope I got this right): Subtract from both sides. Now divide both sides by -6. Now you are looking for the angle theta whose cosine is or: or degrees. In radians: Radians. Check:(Degrees) Substitute Check: (Radians) Substitute
 Divisibility_and_Prime_Numbers/123940: What are the factors of 120?1 solutions Answer 90913 by Earlsdon(6287)   on 2008-01-31 11:46:59 (Show Source): You can put this solution on YOUR website!What are the factors of 120? In other words, what numbers (integers) will divide into 120 without a remainder? 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
 Rectangles/123943: The width of a rectangle is 3 meters less than the length. The perimeter is 14 meters. Find the width. 1 solutions Answer 90910 by Earlsdon(6287)   on 2008-01-31 11:37:08 (Show Source): You can put this solution on YOUR website!Start with the formula for the perimeter of a rectangle: You are given that the width (W) is 3 meters less than the length, L, so W = L-3. You are also given the perimeter, P = 14 meters. Making the appropriate substitutions into the formula, you'll get: Simplify and solve for L Combine like-terms. Add 6 to both sides. Divide both sides by 4. The length is 5 meters. meters. The width is 2 meters. Check: meters.
 Rectangles/123937: The sum of two angles in a triangle totals 62.5 degrees. What is the other angle's measure?1 solutions Answer 90907 by Earlsdon(6287)   on 2008-01-31 10:45:57 (Show Source): You can put this solution on YOUR website!You can work this out! The sum of the three angles in any triangle is 180 degrees. If you know that two of the angles add up to 62.5 degrees, then the measure of the third angle must be...? 180 degrees - 62.5 degrees =
 Equations/123676: Please help me solve this equation: Factor the trinomial s^2-15s+50 1 solutions Answer 90737 by Earlsdon(6287)   on 2008-01-30 15:01:17 (Show Source): You can put this solution on YOUR website!What equation??? What you have here is an expression, and expressions can't be "solved" but they can be simplified, or, given enough data, they can be evaluated. Factor the trinomial: The factors will look like: where: and It's not too hard to see that if and , then = and =, so, the factors of the trinomial are:
 Polynomials-and-rational-expressions/123644: Please help me solve this equation: Add (6+3x+9x2+8x3)+ (4-3x+9x2-8x3)1 solutions Answer 90700 by Earlsdon(6287)   on 2008-01-30 12:42:13 (Show Source): You can put this solution on YOUR website!First, one small correction! This is not an "equation" but an "expression" because there is no = sign. In an equation, you would have something on the left side equal to something on the right side. Ok, Add: First, group the like-term: Perform the indicated addition/subtraction: Finally...
 Expressions-with-variables/123646: Please help me solve this equation: 3(x+4)=5(x-2) x=1 solutions Answer 90695 by Earlsdon(6287)   on 2008-01-30 12:26:32 (Show Source): You can put this solution on YOUR website!Solve for x: First, apply the "distributive property" Now subtract 3x from both sides. Then add 10 to both sides. Finally, divide both sides by 2. Check: Substitute x = 11. Simplify. OK!
 Exponents-negative-and-fractional/123339: Can you please help me? I have tried working it out but it doesn't check out right. (x+7)^3/2=271 solutions Answer 90522 by Earlsdon(6287)   on 2008-01-29 10:38:59 (Show Source): You can put this solution on YOUR website!Solve for x: Raise both sides to the 2/3 power.
 Problems-with-consecutive-odd-even-integers/123186: This question is from textbook Practice Workbook Hi I need help I have no Idea how to solve these problems or what steps to take it seems easy but I dont know what Im doing please help me. An example of a queshtion is Find thee consecutive odd integers whose sum is 117. Thanks Dominik1 solutions Answer 90400 by Earlsdon(6287)   on 2008-01-28 16:29:38 (Show Source): You can put this solution on YOUR website!Let x = the first odd integer, then x+2 will be the next consecutive odd integer and x+4 will be the next consecutive odd integer after that. The sum of these is equal to 117, so you can write the equation: Combine like-terms. Subtract 6 from both sides. Finally, divide both sides by 3. This is the first odd integer. This is the next consecutive odd integer. This is the next consecutive odd integer. Check" OK!
 Length-and-distance/123094: Directions are to solve: The perimeter of a rectangle is 180 feet. the width of the rectangle is equal to one-half the length. find the length and width of the rectangle. I solved this problem and my answer was L=60, W=30. Am i correct? If not please explain and show how you got the other answer.1 solutions Answer 90377 by Earlsdon(6287)   on 2008-01-28 11:37:26 (Show Source): You can put this solution on YOUR website!Congratulations, your answer is correct. Don't forget the dimensions. W = 30 feet, L = 60 feet.
 Surface-area/123120: Area of a sail. A triangular sail has an area of x2 + 5x + 6 square meters and a height of x + 3 meters. Find the lenge of the sail's base. (Area = x2 + 5x + 6m2)1 solutions Answer 90373 by Earlsdon(6287)   on 2008-01-28 11:25:08 (Show Source): You can put this solution on YOUR website!Given the area (A) of a triangular sail: sq.m. and its height (h): m., find the length of its base (b). Start with the formula for the area of a triangle: Make the approriate substitutions from the given data of A and h: Multiply both sides by 2. Now divide both sides by (x+3). You could use synthetic division or regular long divion, but either way, you get: The length of the base is m.
 Exponential-and-logarithmic-functions/123127: If f(x)= 1/(2x) and g(x) = 3+x find (and simplify) the defining equation of the composition function f\circle g.1 solutions Answer 90370 by Earlsdon(6287)   on 2008-01-28 11:06:31 (Show Source): You can put this solution on YOUR website!Given: and , find: this can also be written: , so...
 Equations/123126: What is the formula to solve this equation: Six men can build a house in 3 days. Assuming that all the workmen work at the same rate, how many men would it take to build the house in 1 day?1 solutions Answer 90368 by Earlsdon(6287)   on 2008-01-28 10:54:04 (Show Source): You can put this solution on YOUR website!Well, I don't know about a formula, but here's one way to go about it! Find the daily rate of building by the 6 men. If it takes 6 men to build a houes in three days, then the 6 men can build 1/3 of the house in one day! So you could write: 6 men = 1/3 house/day. But you want to know how many men it would take to build the house in 1 day, so multiply both sides by 3. 3(6 men) = 3(1/3 house)/day. 18 men = 1 house/day.
 Numeric_Fractions/123116: why do u not reduce fraction 5 over 66?1 solutions Answer 90367 by Earlsdon(6287)   on 2008-01-28 10:46:48 (Show Source): You can put this solution on YOUR website!Why not reduce ? Because it can not be reduced. Why, because the numerator and the denominator have no common factor (besides 1). The factors of 5 ( a prime number) are 1 and 5. The factors of 66 ( a composite number) are 1, 2, 3, 6, 11, 22, 33, and 66 So you see, there is no common factor that can be cancelled!
 Exponential-and-logarithmic-functions/123128: The function g has defining equation g(x) = x^2-3x=2. Find (ans simplify) g(5=h). My answer: h^2-3h+12 (I don't know why this is wrong.)1 solutions Answer 90365 by Earlsdon(6287)   on 2008-01-28 10:35:31 (Show Source): You can put this solution on YOUR website!Given: Find: Substitute (5+h) for x above: Simplify. Combine like-terms.
 Linear-systems/123122: Please help? What is the property of real numbers is: 12 + 1 = 1 + 12?1 solutions Answer 90361 by Earlsdon(6287)   on 2008-01-28 10:07:16 (Show Source): You can put this solution on YOUR website!The property of real numbers demonstrated by: 12 + 1 = 1 + 12 is called "The commutative property of addition" The order in which numbers are added is not important, the result is the same.
 Quadratic_Equations/122858: This question is from textbook prentice hall algebra 2 with trigonometry Hello, I have a question relating to the application of the quadratic formula on the following problem: (d-12)=(d) - 2 The (d-12) and (d) are under a radical, but the -2 is not. I tried this a few ways, but cannot get the answer 16 from the back of the book. I really appreciate your assistance on this and thank you in advance.1 solutions Answer 90193 by Earlsdon(6287)   on 2008-01-27 14:17:27 (Show Source): You can put this solution on YOUR website!Solve for d: Square both sides. Subtract d from both sides. Subtract 4 from both sides. Divide both sides by -4 Finally, square both sides.
 Square-cubic-other-roots/122844: This question is from textbook college algebra The position of an object moving in a straight line is given by s=2tsquared - 3t, where s is in meters and t is the time in secoonds the object has been in motion. How long (to the nearest tenth) will it take the object to move 19 meters?1 solutions Answer 90174 by Earlsdon(6287)   on 2008-01-27 12:20:10 (Show Source): You can put this solution on YOUR website!The problem can be solved by letting s (the distance in meters) = 19 and solving for t (the time in seconds): Substitute s = 19: Subtract 19 from both sides. Solve this quadratic equation using the quadratic formula: and the a, b, and c, come from So here, a = 2, b = -3, and c = -19. Make the substitutions: or or Only the positive answer is meaningful here, so... It will take 3.9 seconds for the object to move 19 meters.
 Quadratic_Equations/122834: please can you show me a method of how to work out this equation x^2+9x+14=0 1 solutions Answer 90171 by Earlsdon(6287)   on 2008-01-27 11:55:53 (Show Source): You can put this solution on YOUR website!Solve for x: You can always solve a quadratic equation using the quadratic formula: and, of course, the a, b, and c come from the standard form of the equation: So, in this case, a = 1, b = 9, and c = 14 Making the appropriate substitutions into the quadratic formula, we get: or or If the given trinomial can be factored, this offers another way to solve the problem: Factor the trinomial. Apply the zero product principle. or , then... If then If then So in both cases, you get the same solutions: A third way would be to graph the equation () and identify the x-intercepts (also called "the zeros").
 Age_Word_Problems/122746: I hate these. Mr. mcgoo is 8times as old as his son, Gomer. In 3 years he will be 5 times his sones age. How old is gomer now? Thank you kind person1 solutions Answer 90103 by Earlsdon(6287)   on 2008-01-26 18:06:01 (Show Source): You can put this solution on YOUR website!Let M = McGoo's present age and G = Gomer's present age. From the problem, you can write: 1) M = 8G "McGoo is 8 times as old as his son, Gomer" 2) M+3 = 5(G+3) "In three years, he (M) will be five times his son's (G's) age" Substitute the M = 8G from equation 1) into equation 2) and solve for G. 2a) (8G)+3 = 5(G+3) Simplify. 8G+3 = 5G+15 Subtract 5G from both sides. 3G+3 = 15 Subtract 3 from both sides. 3G = 12 Finally, divide both sides by 3. G = 4 Gomer is 4 years old.
 Numbers_Word_Problems/122744: Please help me solve this equation! The sum of the squares of two consecutive even integers is 452. Find the numbers. What formula should be used to solve this? 1 solutions Answer 90100 by Earlsdon(6287)   on 2008-01-26 17:57:04 (Show Source): You can put this solution on YOUR website!Try this: Let x = the first even number, the x+2 = the next consecutive even number. From the problem description, you can write: Simplify this. Subtract 452 from both sides. Factor out a 2 to ease the calculations a bit. so that: Solve this quadratic by factoring: so then... or Now since the problem did not restrict the answers to positive integers, there are two solutions: 1) and 2) and
 Graphs/122741: Find the x - intercept y = x squared + x - 61 solutions Answer 90097 by Earlsdon(6287)   on 2008-01-26 17:44:10 (Show Source): You can put this solution on YOUR website!Find the x-intercept: The x-intercepts (there will be two of them) occur at y = 0, so... Solve by factoring: Apply the zero product principle: or so then... If then or... If then The x-intercepts are: and Check the graph: