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# Recent problems solved by 'Earlsdon'

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 Polynomials-and-rational-expressions/51648: how do you factor a problem such as: a-squared - b-squared + 6b - 9?1 solutions Answer 34451 by Earlsdon(6287)   on 2006-09-10 19:10:08 (Show Source): You can put this solution on YOUR website!Factor: Try this:
 Average/51584: my son has a problem like this to figure it out what is the missing number -1, ?, -3 1/2, ?, -6, -7 1/4, ?, ?. 1 solutions Answer 34401 by Earlsdon(6287)   on 2006-09-10 14:38:19 (Show Source): You can put this solution on YOUR website!Provide the missing numbers: -1, ?, -3 1/2, ?, -6, -7 1/4, ?, ?, First, you'll notice that the numbers are getting smaller (more negative) so it is possible that subtraction involved. You can test this on the two adjacent numbers in the set...-6, and -7 1/4 You can see that if you subtract -7 1/4 from -6 you'll get a difference of 1 1/4. So, if you subtract 1 1/4 from the first number (-1) you'll get -2 1/4 Now subtract 1 1/4 from -2 1/4 and you'll get -3 1/2...so it seem to work with a common difference of 1 1/4 The missing numbers are: -2 1/4, -4 3/4, -8 1/2, -9 3/4.
 Coordinate-system/51583: I have the following problem; Write the equation of the line which passes through the point (2,1) and is parallel to the equation y = 5/2x + 6. My answer is y= 5/2x - 1 is this correct? Please help.1 solutions Answer 34399 by Earlsdon(6287)   on 2006-09-10 14:23:54 (Show Source): You can put this solution on YOUR website!Sorry, but no cigar! You do have the first term corect ( but the y-intercept (b) is not right. Let's start with what you have done. To find the value of b, you need to substitute the x- and y-coordinates of the given point (2, 1) Simplify this. Subtract 5 from both sides of the equation. Now you can write the equation: Here are the two lines on a graph: Red line. Green line.
 Radicals/51398: This question is from textbook Amsco's Mathematics B The question requires that the problem be written in it's simplest form. I need to check if my answer is correct. 6 square root 4/31 solutions Answer 34337 by Earlsdon(6287)   on 2006-09-09 22:04:24 (Show Source): You can put this solution on YOUR website!Simplify: Rewrite this as: Now you can take the square root of 4 (that's 2) and put it outside the radical. Simplifying this, you get:
 Coordinate-system/51380: Please help me solve the following problem; Write the eqation of the line that passes through the point?(2,1) and is parallel to the line with the eqation y=5/2x + 6. I honestly do not know where to even begin on this.1 solutions Answer 34336 by Earlsdon(6287)   on 2006-09-09 22:00:16 (Show Source): You can put this solution on YOUR website!Let's write the required equation of the line in the "slope-intercept" form: Where: m is the slope of the line and b is the y-intercept of the line. Remember that parallel lines have the same slope. So, your new line is parallel the the line whose equation is: Comparing this with the slope-intercept form: you can see that the slope of this line is and, because the new line is parallel to this, it too will have a slope of . So, step 1, for the new line, you can write: Now all you need to do is to find the value of b, the y-intercept of the new line. You can do this by substituting the x- and y-coordinates of the given point (2, 1) into the equation and solve for b. Simplify this. Subtract 5 from both sides of the equation. You can write the final equation now that you have the slope and the y-intercept : ...and that's it!
 Equations/51395: how do you do this problem? 1/a + 2/b = 3/c Solve for b. I have tired my brain out trying to solve this problem!! Thanks!!1 solutions Answer 34334 by Earlsdon(6287)   on 2006-09-09 21:45:01 (Show Source): You can put this solution on YOUR website!Ok. give your brain a rest and let's see what can be done with this: Solve: for b. First, subtract from both sides. Now combine the two fractions on right side. Next, multiply both sides by ac Then multiply both sides by b Finally, divide both sides by (3a-c) So,
 Rate-of-work-word-problems/51327: This question is from textbook college algebra Please help...got stuck on this problem for long time...thank you!! "Fencing Dog Pens" Clint is constructing 2 adjacent rectangular dog pens. Each pen will be three times as it is wide, and the pens will share a common long side. If Clint has 65ft of fencing, what are the dimensions of each pen??1 solutions Answer 34274 by Earlsdon(6287)   on 2006-09-09 12:36:52 (Show Source): You can put this solution on YOUR website!I assume that you meant to write..."Each pen will be three times as long as it is wide,..." If we let the width be W, then the length of each pen will be: L = 3W. From the problem description, the two adjacent pens will have three long sides and four short sides. Each long side will be 3W in length and there are three of these, so we have 3(3W) = 9W. This is the total of the lengths. The short sides (Widths) wll each be W in length and there are four of these, so we have 4(W) = 4W This the total of the widths. Adding up all of these, we get: 9W + 4W = 13W and this is equal to the total length of the fence (perimeter) of 65 feet. 13W = 65 Divide both sides by 13. W = 5 feet. This is the length of each width, but there are four of these, so we have the total for the widths is: 4(5) = 20 feet. The length, L = 3W = 3(5) = 15 feet The three lengths is then: 3(15) = 45 feet. Each pen measures: (L X W) = 15 ft. by 5 ft. Check: Adding up the the total widths and the total lengths, we get: 20 ft + 45 ft = 65 ft.
 Linear_Equations_And_Systems_Word_Problems/51329: Michael rented a truck for one day. There was a rental fee of \$20.99, and there also was a charge of 25 cents for each mile. Michael paid \$95.74 when he returned the truck. For how many miles did he drive the truck? 1 solutions Answer 34270 by Earlsdon(6287)   on 2006-09-09 12:14:32 (Show Source): You can put this solution on YOUR website!Michael paid a total of \$95.74 when he returned the truck. So, if we first deduct (subtract) the rental fee of \$20.99 to see what he actually paid for mileage. Then we can divide the remainder by \$0.25 to see how many miles he drove. (Total cost - rental fee)/\$0.25 = number of miles driven. (\$95.74 - \$20.99}/\$0.25 = (\$74.75)/\$0.25 = 299 So Michael paid for 299 miles
 sets-and-operations/51320: Find values for m and b in the following system so that the solution to te system is ( -3, 4). 5x + 7y = b mx + y = 221 solutions Answer 34261 by Earlsdon(6287)   on 2006-09-09 10:45:05 (Show Source): You can put this solution on YOUR website!Find the values of m and b given the solution to the system is (-3, 4): 5x + 7y = b mx +y = 22 Substitute the x- and y-coordinates from the given point (-3, 4) into each equation and solve for the b and m. 5(-3) + 7(4) = b Simplify. -15 + 28 = b b = 13 mx + y = 22 m(-3) + 4 = 22 Subtract 4 from both sides of the equation. -3m = 18 Divide both sides by -3. m = -6 You can verify these solutions by substituting b = 13 and m = -6 into the appropriate equation and doing the math. Try this yourself.
 Radicals/51295: This question is from textbook I worked this out sqrt(3x+3)- 9 = 0; I came up with x=2 and checking the problem by plugging 2 in, I came up with 81 not = to 9. Can someone advise please? 1 solutions Answer 34229 by Earlsdon(6287)   on 2006-09-08 23:31:19 (Show Source): You can put this solution on YOUR website!Solve: Add 9 to both sides of the equation. Square both sides. Subtract 3 from both sides. Divide both sides by 3. Check:
 Linear-systems/51170: how does the graphfor the following equations look? y=x-1/2 and y=3x+11 solutions Answer 34202 by Earlsdon(6287)   on 2006-09-08 18:06:15 (Show Source): You can put this solution on YOUR website!Graph: The red line. The green line.
 Volume/51174: Harriet's family just purchased an above ground circular swimming pool. The diameter of the pool is 12 feet. The depth of the pool is 4 feet. How much water is needed to completely fill the pool? Use the formula V=(pie)r(squared)h. Let (pie)=3.141 solutions Answer 34201 by Earlsdon(6287)   on 2006-09-08 18:01:43 (Show Source): You can put this solution on YOUR website!The first step, of course, is to find the volume of the circular (really cylindrical) swimming pool. Where: r (radius) is 6 ft. and h (depth) is 4 ft. Making these substitutions: cubic feet. The next step is to discover how many cubic feet are occupied by 1 U.S. gallon of water. 1 U.S. gallon = 0.1336816 cubic feet. So, how many of these will fit into 452.16 cubic feet? This sounds like a division problem, so we'll divide 452.16 cubic feet by 0.0336816 cubic feet /gallon. Gallons (Aproximately)
 Triangles/51273: isbn 0618372628 Find the perimeter of a right triangle with legs that measure 5cm and 9cm.1 solutions Answer 34196 by Earlsdon(6287)   on 2006-09-08 16:46:25 (Show Source): You can put this solution on YOUR website!Since you are given the lengths of only the two legs, you need to find the length of the hypotenuse of this right triangle before you can find the perimeter. Use the Pythagorean theorem to find the length of the hypotenuse, c. Substitute a = 5 and b = 9 cm. (Approximately} The perimeter is: cm (Approximately)
 Polynomials-and-rational-expressions/51274: This question is from textbook I am drawing a blank on this; do I multiply or add the denominators? (x-1/3)*(x+1/3)1 solutions Answer 34195 by Earlsdon(6287)   on 2006-09-08 16:36:37 (Show Source): You can put this solution on YOUR website!Multiply: Use FOIL to multiply these two factors. Simplify this.
 Linear-equations/51250: Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth. I thought that the first step would be to create an equation y= 3.25x + 1800 But I need to find the slope, which requires 2 points (y2-y1 over x2-x1). I am not sure what formula I shoudl start with to arrive at the slope, as requested. 1 solutions Answer 34180 by Earlsdon(6287)   on 2006-09-08 10:47:29 (Show Source): You can put this solution on YOUR website!I know this is algebra and it seems like everything in algebra requires an equation of some sort. But sometimes, a little common sense will get the job done with a lot less confusion. Try this. The definition of slope is "rise over run". In your problem, you could say Tom "rose" (in reverse) 1800 feet while he "ran" (horizontally) 3.25 miles. So the slope here is Rise/Run = 1800 ft./3.25 miles. But you'll need to change the units so that they are the same, either all in feet or all in miles. All in feet seems to be the better approach, so how many feet are there in 3.25 miles? Well, 1 mile = 5280 ft. Multiply both sides by 3.25 3.25 mies = 3.25(5280) ft. 3.25 miles = 17160 ft. Now we can calculate the slope: But you need to round to the nearest hundreth. The slope is 0.10
 Linear-equations/51248: Please help: Determine the equation of the line that has a slope of 4 and passes through the point (2,8). Write the equation in slope intercept form1 solutions Answer 34179 by Earlsdon(6287)   on 2006-09-08 10:32:37 (Show Source): You can put this solution on YOUR website!Write the equation in slope-intercept form: You are given the slope, m = 4, so you can write: Now you need to find the value of b, the y-intercept. This is easily done because you were also given a point (2, 8) through which the line passes. So you substitute the (x, y) of the given popint (2, 8) into the equation and solve for b. Simplify. Subtract 8 from both sides of the equation. So b = 0. Now you can write the final equation of the line whose slope is 4 and which passes through the point (2, 8). Just out of curiosity, let's see what that looks like on a graph:
 Trigonometry-basics/51136: This question is from textbook Alegra 2 and Incremental Development The volume of a circular cylinder is 250pi cm cube. What is the height of the cylinder? Radius is 5 1 solutions Answer 34107 by Earlsdon(6287)   on 2006-09-07 18:28:57 (Show Source): You can put this solution on YOUR website!The volume of a right circular cylinder is given by: Let's first solve this for the height, h, by dividing both sides by . Now you can substitute , and You can cancel the and Simplify. cm.
 Trigonometry-basics/51134: ok i dont know what categorey it goes in.. but i need help on changing trinomials into binomials. I am a visual learner so please show me how to convert them. 1 solutions Answer 34106 by Earlsdon(6287)   on 2006-09-07 18:19:50 (Show Source): You can put this solution on YOUR website!It seems to me that you are into "factoring" trinomials, which is basically a process of converting trinomials into binomial factors. Of course, not all trinomials can be factored, but "factoring trinomials" constitutes an entire lesson for those that can be factored. Here's an elementary example: Factor the following expression: The factors will be two "binomials" of the following form: You'll need to find the values of a and b. These two binomial factors, when multiplied together will result in the original trinomial expression. Comparing the binomial factors with the trinomial, you can write this: so this means that: a+b = 3 and a*b = 2 What are the possibilities? a = 1 and b = 2 or a = 2 and b = 1 Let's try these in the binomial forms and see what we get. Multiply these factors using the FOIL method. Simplifying this, we get: The original trinomial! You would get exactly the same result if you used: a = 2 and b = 1
 Linear-equations/51131: Aqueducts were once used to carry water from rivers using gravity. Water flowing too quickly might damage an aqueduct, but water flowing too slowly might not keep the aquiducts clear. One of the best and most common designs for an aqueduct was to raise it 3 meters for every kilometer in length. What is the slope of an aqueduct built with this design? I need help in understanding how to find the slope from this word problem because I don't understand anything about word problems. So if you could please help me to solve this problem step by step it would be helpful. 1 solutions Answer 34101 by Earlsdon(6287)   on 2006-09-07 18:00:27 (Show Source): You can put this solution on YOUR website!Remember the basic definition of slope..."Rise over Run" In your problem, the aqueduct rises 3 meters (Rise = 3) for every kilometer (1,000 meters) in length (Run = 1,000 meters). So the slope is Rise/Run = 3/1000 = 0.003 Does this help?
 Expressions-with-variables/51130: This question is from textbook Algebra I please help me with this problem the product of \$25 and the number "M" of club memberships is greater than or equal to \$5001 solutions Answer 34099 by Earlsdon(6287)   on 2006-09-07 17:54:26 (Show Source): You can put this solution on YOUR website!Presumably you want to solve for M? Divide both sides of the inequality by 25.
 Geometry_proofs/51105: Hello! Here's my question: In triangle KLM, P is the midpoint of the line segment LM. Prove that if PL = PK = PM, angle LKM = 90 degrees. I have been struggling on this question for quite some time now. All I found out from the web is to introduce a point O so that KPO is a line segment with P at the midpoint, and then show that KLOM is a rectangle. Please Help! Thank You!1 solutions Answer 34096 by Earlsdon(6287)   on 2006-09-07 17:48:15 (Show Source): You can put this solution on YOUR website!I'm not certain that the following constitutes a "proof" in the formal sense of the word, but it certainly provides a demonstration. If you accept the principle that "An angle inscribed in a semi-circle is a right angle", then read the following: The line segment LM is the diameter of a circle. The mid-point of LM is therefore the center of this circle and PL and PM are both radii of this circle and they, of course, are equal. Point K is a point on the circumference of the circle, not coincident with either L or M. The segment PK is also a radius of the circle, so that: PL = PK = PM Segments KL and KM form the other two sides of a triangle. The angle LKM is inscribed in a semi-circle and is, therefore, a right angle. A right angle = 90 degrees.
 Expressions-with-variables/51107: a and b is unknown express x in terms of a and b. ax-5.6=bx+12.11 solutions Answer 34087 by Earlsdon(6287)   on 2006-09-07 17:14:54 (Show Source): You can put this solution on YOUR website!Express x in terms of a and b. Add 5.6 to both sides of the equation. Now subtract bx from both sides. Factor out the x. Finally, divide both sides by (a-b)
 Equations/51108: Find the two solutions to this equation. ax^2+8ax=01 solutions Answer 34085 by Earlsdon(6287)   on 2006-09-07 17:08:29 (Show Source): You can put this solution on YOUR website!Find the two solutins: First, factor out an x. Apply the zero product principle. x = 0 and/or ax+8a = 0 x = 0 is one of the two solutions. Subtract 8a from both sides. Divide both sides by a. x = -8 is the other solution.
 absolute-value/51086: This question is from textbook solve the following equations for y: 5x-y=10 x+4y=-8 0.1x+o.5y=3.5 2x=3y+9 5x-6y+12=0 x-2xy=1 I do not understand how i am suppost to solve for y? can you please explain how to solve for y in these problems?1 solutions Answer 34064 by Earlsdon(6287)   on 2006-09-07 11:36:24 (Show Source): You can put this solution on YOUR website!Solving for y simply means that you must get the y on one side of the equals sign by itself using the standard rules of algebra. 1) 5x-y = 10 Here, you would first add y to both sides of the equation. 5x = 10+y Then you subtract 10 from both sides. 5x-10 = y Many teachers like to see the dependent variable (y in this case) on the left side, so rewrite this as: y = 5x-10...and there you have it. 2) x+4y = -8 In this one, you would subtract x from both sides. 4y = -x-8 then you divide both sides by 4. y = -(1/4)x - 2 Do you see the idea here? You want to rewrite each equation so that it's in the form...y = something. Let's do one more: 0.1x + 0.5y = 3.5 Here, you need to get rid of the decimals in a way that leaves you with integral (whole number) numbers of y. You can do this by multiplying everything by 2. (2)0.1x + (2)0.5y = (2)3.5 Simplify this. 0.2x + y = 7 Now subtract 0.2x from both sides. y = -0.2x + 7 Ok now try the others on your own. If you are still having trouble with it, repost.
 Linear_Equations_And_Systems_Word_Problems/51074: This question is from textbook Applied College Algebra The height, in feet, of a rock,above the Colorado River that is thrown from the north rim of the Grand Canyon is given by Height = 5700 - 16t^2, where t is the number of seconds after the rock above the river 5 seconds after it is released.1 solutions Answer 34058 by Earlsdon(6287)   on 2006-09-07 11:02:02 (Show Source): You can put this solution on YOUR website!It seems as though you might have missed part of the problem statement. Do you have to find the height of the rock 5 seconds after it is dropped from the North Rim at a height of 5700 feet? Using the given function: Substitute t = 5 and solve for h. feet. The height of the rock would be 5300 feet five seconds after it was dropped from a height of 5700 feet.
 Radicals/51085: I have been away from school the past few days because i was sick, and i am really not understanding these questions. i am also not sure if this is the right section to be asking this question in, but nothing else seemed to fit (x^2-64)/(5x) * (10x^2)/(x+8) 1. what i thought to do is factor the denomanator so it would be (x+8)(x-8)/(5x) * (10x^2)/(x+8) then the two x + 8's cancel out....once u have the final answer as (x-8)/(5x) * (10x^2)/1---do u just multiply?? and how do u multiply??1 solutions Answer 34055 by Earlsdon(6287)   on 2006-09-07 10:50:23 (Show Source): You can put this solution on YOUR website!Well, it looks like you haven't lost your touch. Your initial step was quite correct. I am assuming that the task is to simplify the given expression. You correctly factored the numerator of the first fraction. and you also correctly cancelled the (x+8)'s At this point, you can cancel 5x's in the denominator and from the in the numerator. Finally, you can multiply these two factors.
 Expressions-with-variables/50986: I need the method for solving this more than the answer, but both would be appreciated: Mark launched a model rocket using an engine which will generate a speed of 180 feet per second. The formula h = rt - 16t squared gives the height of an object projected upward at a rate of r feet per second after t seconds. After how many seconds will Mark's rocket reach a height of 464 feet? After how many seconds will it be at that height again? Thank you.1 solutions Answer 34031 by Earlsdon(6287)   on 2006-09-06 22:08:54 (Show Source): You can put this solution on YOUR website!Step 1. Rewrite your equation in the form of a quadratic function. This is function for the height, h, of an object propelled upwards as a function of time, t. Here, r is given as 180 ft/sec. This fits the situation of Mark's rocket. You are being asked to find at what time, t, will the height, h, be 464 feet. Because your equation is quadratic, you can expect to get two solutions. Step 2. Set h(t) = 464 in the quadratic equation above and solve for t. Put this into standard form by subtracting 464 from both sides. Step 3. Solve the quadratic equation for t by the most convenient method. You can simplify this equation a bit by dividing through by -4 to get: Now you can factor this. Apply the zero product principle: and/or If then t = 4 If then or The two solution are: The height of the rocket will reach 464 feet in 4 seconds, ascending. The height of the rocket will be at 464 feet again in 7.25 seconds descending.
 Expressions-with-variables/51055: I dont understand how to solve problems such as this.... 5x-16=3x1 solutions Answer 34026 by Earlsdon(6287)   on 2006-09-06 21:33:21 (Show Source): You can put this solution on YOUR website!Solve for x: The idea is to get the x onto one side of the equals sign. Start by subtracting 3x fom both sides of the equation. Now add 16 to both sides. Finally, divide both sides by 2. Check: Set x = 8 in the original equation. Simplify. It checks!
 Expressions-with-variables/51054: two fifths the cube of a number what is the algebraic expression 1 solutions Answer 34024 by Earlsdon(6287)   on 2006-09-06 21:28:53 (Show Source): You can put this solution on YOUR website!If n is the number, it would look like:
 Rational-functions/51049: Please help me write the perimeter P of a square as a function of the area.1 solutions Answer 34022 by Earlsdon(6287)   on 2006-09-06 21:26:54 (Show Source): You can put this solution on YOUR website!Let the sides of the square = s The perimeter would be: The area of the square would be: Take the square root of both sides. Subsitute this s into the equation for the perimeter.