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# Recent problems solved by 'Earlsdon'

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 Trigonometry-basics/499683: need help on this problem y to the 5th power plus 7y to the 3rd power plus 12y.1 solutions Answer 337824 by Earlsdon(6287)   on 2011-09-18 12:46:46 (Show Source): You can put this solution on YOUR website!Do you want to factor this expression? First factor a y from each term. Now factor the trinomial. ...and that's the best you can do!
 Problems-with-consecutive-odd-even-integers/499658: Hi, Can you please help me solve this problem? 7/2x (seven over two X)+ 1/3(one over three)=1/x (one over x)+7/6(seven over six) I have tried solving it, but i cant even get past the first step. Thank you 1 solutions Answer 337823 by Earlsdon(6287)   on 2011-09-18 12:41:37 (Show Source): You can put this solution on YOUR website!Solve for x: Add the fractions by finding the LCDs. Simplify. Multiply both sides by . Subtact 2x from both sides. Subtract 6 from both sides. Divide both sides by 5.
 Polynomials-and-rational-expressions/499673: 12x suqared plus 82x-14=0 How do I work it out1 solutions Answer 337822 by Earlsdon(6287)   on 2011-09-18 12:25:47 (Show Source): You can put this solution on YOUR website! You can solve this by factoring. Apply the "zero product" rule. or then... so or so The roots are: and
 Evaluation_Word_Problems/499670: Hello, My problem is: Seven times what number is 1596?1 solutions Answer 337820 by Earlsdon(6287)   on 2011-09-18 12:19:30 (Show Source): You can put this solution on YOUR website!Let n = the number, so... 7n = 1596 Divide both sides by 7. n = 228 Seven times 228 is 1596.
 Volume/499666: I have a fish tank that is 80cm Wide, 50cm high and 35cm deep, how do I work out how many litres of water it holds1 solutions Answer 337819 by Earlsdon(6287)   on 2011-09-18 12:16:28 (Show Source): You can put this solution on YOUR website!First find the volume of the fish tank: W = 80cm., d = 35cm., and h = 50cm., so... cc. Now you would apply the conversion factor of: One litre = 1,000 cu.cm. Divide 140,000cc by 1,000cc/litre to find the number if litres in the fish tank. litres.
 Linear-equations/499637: if m represents the gradient of a linear graph and the equation of a linier graph is y=mx+b, what is the gradient of y=5x+2? and how do i work it out? 1 solutions Answer 337817 by Earlsdon(6287)   on 2011-09-18 12:05:03 (Show Source): You can put this solution on YOUR website!A linear equation of the form: is called the "slope-intercept" form in the U.S. The "slope", m, would be equivalent to the "gradient". Compare this with the "slope-intercept" form: and you can see that the slope (or gradient), m = 5. Does this make sense?
 Age_Word_Problems/499621: doug dave and don are counting ducks down by the pond they are havinf a contest to see who can spot the most ducks. doug counts twice as many as dave. dave counts twice as many as don. together they spotted a total of 42 ducks. how many ducks did each boy spot1 solutions Answer 337809 by Earlsdon(6287)   on 2011-09-18 11:41:17 (Show Source): You can put this solution on YOUR website!Let a = Doug's count of ducks, b = Dave's count, and c = Don's count. a = 2b "Doug counts twice as many as Dave." b = 2c "Dave counts twice as many as Don." a+b+c = 42 ""Together they spotted a total of 42 ducks." Rewrite the first equation: a = 2b Replace b = 2c to get: a = 2(2c) a = 4c Now rewrite the second equation: a+b+c = 42 Substitute a = 4c and b = 2c. 4c+2c+c = 42 Simplify. 7c = 42 Divide by 7. c = 6 and... b = 2(6) b = 12 and... a = 4c a = 4(6) a = 24. Doug spotted 24 ducks. Dave spotted 12 ducks. Don spotted 6 ducks.
 Geometry_Word_Problems/499613: A jeweler has 2 meters of gold wire. He is going to make pairs of gold earrings (each 25mm in diameter). How many pairs of earrings can he make? I wasn't very sure how to go about this, so I converted to meters to millimeters then divided by 25 and got it wrong. I would appreciate some help. -Emily 1 solutions Answer 337807 by Earlsdon(6287)   on 2011-09-18 11:28:32 (Show Source): You can put this solution on YOUR website!OK, Emily, your first step was correct and you should have got 2 meters = 2,000 mm. Now each earring requires 25mm of gold so each pair of earrings would need 50mm of gold. So you should have divided the 2,000mm of gold wire by 50 to find the number of pairs of earrings. The jeweler can make 40 pairs of earrings.
 Problems-with-consecutive-odd-even-integers/499628: How can I find 3 consecutive integers whose sum is 33? This is what I have tried. x+(x+1)+(x+2)=33 I combined the like terms next and got 3x+3=33 I then subtracted three from both sides. -3 -3 I got the answer of 3x=33 after that I divided by 3 on both sides 3x/3 33/3 I got the answer of X=11 My 3 consecutive integers are 11,12,and 13. Is my answer correct? Thank you!1 solutions Answer 337803 by Earlsdon(6287)   on 2011-09-18 11:19:48 (Show Source): You can put this solution on YOUR website!No, it isn't! When you subtracted 3 from both sides of: 3x+3 = 33 you should have got: 3x = 30 not 3x = 33, so... 3x = 30 Divide by 3 to get: x = 10 The three consecutive numbers ar: 10, 11, and 12 whose sum is 33.
 Mixture_Word_Problems/499238: i'm trying to solve this problem but i really have no idea how to do it. How many milliliters of a 6% alcohol solution must be added to 12 milliliters of a 31% alcholol solution to produce a 16% alcohol solution? 1 solutions Answer 337505 by Earlsdon(6287)   on 2011-09-17 11:48:41 (Show Source): You can put this solution on YOUR website!Let x = the required number of milliliters of 6% alcohol solution. Let's find out how much alcohol we have. The number of milliliters of alcohol in the x ml. of the 6% solution is: x(0.06) and in the 12 ml. of the 31% solution we have 12(0.31) ml. of alcohol. When added together, these are to equal (12+x)(0.16)ml. of alcohol, so we can write the equation to find x. 0.06x+0.31(12) = 0.16(12+x) Simplify and solve for x. 0.06x+3.72 = 1.92+0.16x Subtract 0.06x from both sides. 3.72 = 1.92+0.1x Subtract 1.92 from both sides. 1.8 = 0.1x Divide by 0.1 x = 18 You will need to add 18ml. of 6% alcohol solution to the 12ml. of the 31% alcohol solution to obtain (12+x = 30)ml. of 16% alcohol solution.
 test/499207: How do you work with fractional exponents such as 3 to the 1/3 power?1 solutions Answer 337470 by Earlsdon(6287)   on 2011-09-17 10:26:45 (Show Source): You can put this solution on YOUR website!With fractional exponents, such as the number in the denominator indicates the root. Example: means the cube root of 3. means the fifth root of 256 squared.
 Angles/499210: find the measure of an angle which is one fourth of its complement 1 solutions Answer 337468 by Earlsdon(6287)   on 2011-09-17 10:22:23 (Show Source): You can put this solution on YOUR website!Let A be the angle, then its complement is 90-A, so... Multiply both sides by 4. Add A to both sides. Finally, divide both sides by 5. degrees.
 Rate-of-work-word-problems/499218: With water from one hose, a swimming pool can be filled in 7 hours. A second, larger hose used alone can fill the pool in 4 hours. How long would it take to fill the pool if both hoses were used simultaneously?1 solutions Answer 337467 by Earlsdon(6287)   on 2011-09-17 10:18:08 (Show Source): You can put this solution on YOUR website! hours hours andminutes.
 Numbers_Word_Problems/499029: Five more than twice a number is 23. Find the number 1 solutions Answer 337308 by Earlsdon(6287)   on 2011-09-16 18:14:42 (Show Source): You can put this solution on YOUR website!Let n = the number, then: 2n+5 = 23 Subtract 5. 2n = 18 Divide by 2. n = 9
 Functions/498879: A box is to be removing four identical squares (with side length X) from each corner of a retangular piece of card then folding up the resulting flaps. If the piece of card is 40cm by 30cm write down a fundtion for the volume of the resulting box in terms of X. What sort of funtion is it ( quadratic, Rational, cubic or...). What is the domain of this funtion? 1 solutions Answer 337243 by Earlsdon(6287)   on 2011-09-16 13:44:05 (Show Source): You can put this solution on YOUR website!After removing the corner squares of side x, the remainder of the sides of the original rectangular cardboard will measure (40-2x) and (30-2x) and the height of the finished box will be x. The volume of this box can be expressed as: If you multiply these factors, you'll get: Clearly, this is a "cubic" function. From a practical standpoint, x cannot equal or exceed half the length of the smaller side of the original rectangle, otherwise, you could not make a box. So x can take on values:
 Travel_Word_Problems/498851: Here is the problem: If it takes you 45 minutes to clean the fish tank and it takes your sister 30 minutes. How long does it take if you work together? Is it 45X+30x=1? Help?1 solutions Answer 337242 by Earlsdon(6287)   on 2011-09-16 13:18:15 (Show Source): You can put this solution on YOUR website!Er...not quite! Try: Simplify and solve for x. Multiply both sides by 90. Divide both sides by 5. minutes.
 Quadratic_Equations/498856: I do not understand how to solve this problem. It says solve and check the following equation. 3+(√3a+3)=9 thank you1 solutions Answer 337241 by Earlsdon(6287)   on 2011-09-16 13:12:04 (Show Source): You can put this solution on YOUR website!Presumably you are required to solve for the variable a. Simplify. Subtract 6 from both sides. Divide both sides by Rationalise the denominator. Simplify. Cancel the 3's.
 Human-and-algebraic-language/498898: Okay, the gist of the math problem is.. A farmer wants to mix a bag containing 50% corn and another bag containing 90% corn to get a 30 lbs bag containing 80% corn. What I have so far for the equation is.. 0.50x + 0.90x = ??? I don't know how to 'plug-in' the other 0.80 and the weight of the bag. I hope this makes sense!! Thank you!!1 solutions Answer 337235 by Earlsdon(6287)   on 2011-09-16 12:58:47 (Show Source): You can put this solution on YOUR website!Try this! Let x = the number of pounds of the 50% corn. Then the number of pounds of the 90% corn required to make 30 pounds of 80% corn will be (30-x) and, when added together (x+(30-x) = 30) you will get 30 pounds of corn. So we can write an equation to solve for x: 0.5x+0.9(30-x) = 0.8(30) Simplify and solve for x. 0.5x+27-0.9x = 24 -0.4x+27 = 24 -0.4x = -3 x = 7.5 The farmer will need to mix 7.5 pounds of the 50% corn with (30-7.5 = 22.5)pounds of the 90% corn to obtain 30 pounds of 80% corn.
 Numeric_Fractions/498901: finding the least common multiple of 120 and 135 1 solutions Answer 337234 by Earlsdon(6287)   on 2011-09-16 12:45:50 (Show Source): You can put this solution on YOUR website!Find the LCM of 120 and 135. First, find the prime factors of each of the two numbers using exponents for repeated factors: 120: 2*2*2*3*3*3*5 = 135: 3*3*3*5 = Now, from the two lists of prime factors, take the product of the highest power of each factor. The LCD of 120 and 135 is 1080.
 Finance/498680: x^6 - 511x^3-512 = 0 find all real solutions of the equation. hi, im having trouble factoring this out..getting confused with the exponents. thank you for your time!1 solutions Answer 337125 by Earlsdon(6287)   on 2011-09-15 23:12:35 (Show Source): You can put this solution on YOUR website! Treat this as a quadratic equation in thus: Now factor this. Apply the "zero product" rule: or Now since the original equation is a 6th order equation, we can expect 6 roots. Here's how we get them: This is the sum of cubes which can be factored thus: so... Apply the "zero product" rule: so Apply the quadratic formula to get: and For the other three roots, we have: This is the difference of cubes which factors as: Apply the "zero product" rule: so Apply the quadratic formula to get: and
 Expressions-with-variables/498681: please help me solve: n+1/n+2=n-3/n+1 I do not know where to start. Thank you. 1 solutions Answer 337116 by Earlsdon(6287)   on 2011-09-15 22:16:39 (Show Source): You can put this solution on YOUR website!Solve for n: Cross-multiply: Perform the indicated multiplication. Subtract from both sides. Add n to both sides. Subtract 1 from both sides. Finally, divide both sides by 3.
 Volume/498658: FIND THE PERIMETER AND AREA OF A RIGHT TRIANGLE IF ONE LEG MEASURES 9MI AND THE OTHER LEG MEASURES 40MI. PLEASE EXPLAIN HOW TO SOLVE1 solutions Answer 337114 by Earlsdon(6287)   on 2011-09-15 22:08:35 (Show Source): You can put this solution on YOUR website!You can find the area of any triangle by: Where b = the length of the base and h = the height of the triangle. It doesn't matter which leg you call the base, so we'll say and , so... square miles. To find the perimeter, you'll need to know the length of the hypotenuse of the right triangle. Use the Pythagorean theorem: where: , , and is the length of the hypotenuse. Evaluate. Take the square root of both sides. So the length of the hypotenuse = 41 miles. Now you can add the three sides to get the perimeter P. =miles.
 Mixture_Word_Problems/498653: how do i setup an equation for the following problem i am very confused: HOW MANY POUNDS OF NUTS WORTH \$4.20 PER POUND MUST BE MIXED WITH 12 POUNDS OF NUTS WORTH \$3 PER POUND TO PRODUCE A MIXTURE THAT CAN BE SOLD FOR \$3.90 PER POUND1 solutions Answer 337108 by Earlsdon(6287)   on 2011-09-15 21:54:51 (Show Source): You can put this solution on YOUR website!Try this! Let x = the required number pounds of the nuts worth \$4.20 per pound. We can express the cost of these x pounds of nuts as: \$4.20(x). Now we want to add this to 12 pounds of nuts worth \$3.00 per pound the cost of which can be expressed as: \$3.00(12). Now if we add these together, we get: \$4.20(x)+\$3.00(12) and this sum is to equal (12+x) pounds of nut mixture to cost \$3.90 per pound. Now we can write the equation to solve for x. 4.20(x)+3.00(12) = (12+x)(3.90) Simplify. 4.2x+36 = 46.8+3.9x Subtract 3.9x from both sides. 0.3x+36 = 46.8 Now subtract 36 from both sides. 0.3x = 10.8 Finally, divide both sides by 0.3 x = 36 You will need to mix 36 pounds of nuts worth \$4.20 per pound with 12 pounds of nuts worth \$3.00 per pound to obtain 48 (12 + 36) pounds of nuts worth \$3.90 per pound.
 Sequences-and-series/498654: What is this 1/2n means one blank of a number? 1 solutions Answer 337103 by Earlsdon(6287)   on 2011-09-15 21:36:35 (Show Source): You can put this solution on YOUR website!If n is the number, then means one half of the number.
 Pythagorean-theorem/498590: Hi, trying to help my son grd 8 solve a question the hypotenuse of a right triangle is square root of 18....what are the lenghts of the legs of the triangle ?? that is all the info we are given.1 solutions Answer 337102 by Earlsdon(6287)   on 2011-09-15 21:34:49 (Show Source): You can put this solution on YOUR website!You must have been given more information about the right triangle. Look! In this case, so . Now we have: This equation has an infinite number of solutions unless you place some restrictions on a and b. Let's assume the the numbers a and b must be integers (not an unreasonable assumption), then a and b can only take on the values of and , so you'd get: or This implies that the triangle is an isosceles right triangle. No other integers for a and b would work.
 Rectangles/498614: How many times the sides of a square would increase if the area was increased by nine times?1 solutions Answer 337098 by Earlsdon(6287)   on 2011-09-15 21:08:31 (Show Source): You can put this solution on YOUR website!Let the length of the side of the square be s. The area of the square is given by: Increase the area by 9 means: and we'll show the increase in the length of the side by: , so... but so we substitute... Simplify and solve for s. Divide both sides by Take the square root. So the sides of the square (s) would increase by 3 times.