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# Recent problems solved by 'texttutoring'

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 Numbers_Word_Problems/503230: Five times the sum of a number and two is forty. Find the number? 1 solutions Answer 339143 by texttutoring(324)   on 2011-09-23 18:06:45 (Show Source): You can put this solution on YOUR website!5(x+2)=40 x+2=40/5 x+2=8 x=8-2 x=6 The number is 6.
 Numbers_Word_Problems/503228: five times a certain number is the same as the number decreased by 52. find the number. 1 solutions Answer 339142 by texttutoring(324)   on 2011-09-23 18:05:54 (Show Source): You can put this solution on YOUR website!Let the number be x. 5x=x-52 4x = -52 x = -52/4 x = -13 Check: 5(-13)=-65 and -13 -52 = -65 So yes, both sides match. x=-13
 Numbers_Word_Problems/501633: 1.ONE NUMBER IS 19 LESS THAN THE OTHER AND THEIR SUM IS 65. 2.FIND TWO NUMBERS WHOSE SUM IS 39 AND DIFFERENCE IS 7. 3.IF TWICE NUMBER IS INCREASED BY IN THE RESULT IS 35. 1 solutions Answer 338582 by texttutoring(324)   on 2011-09-21 01:35:15 (Show Source): You can put this solution on YOUR website!1. Let x = the number, the other number would be x-19 x + x-19 = 65 2x-19=65 2x=84 x=84/2 x=42 The other number is 42-19=23. So the two numbers are 42 and 23. 2. Similar to the last one... x+x-7 = 39 2x-7=39 2x=46 x=46/2 x=23 The other number is 16. I don't understand the 3rd question, sorry. Hope that helps for the first two!
 test/498891: the measure of one side of this square is 4cm. the perimeter is?1 solutions Answer 337230 by texttutoring(324)   on 2011-09-16 11:37:45 (Show Source): You can put this solution on YOUR website!A square has 4 equal sides, so the perimter is: P = 4+4+4+4 P = 16 cm
 Travel_Word_Problems/498894: What distance can you travel if you walk 5 miles per hour for 3 hours? 1 solutions Answer 337229 by texttutoring(324)   on 2011-09-16 11:37:06 (Show Source): You can put this solution on YOUR website!There is a very convenient formula for solving these types of problems. It is D=ST, where D=distance, S=Speed, and T=Time. You are given that S= 5 mph and T = 3 hours. D=ST D=5*3 D=15 You can travel 15 miles.
 Travel_Word_Problems/498893: In still water, a boat averages 15 miles per hour. It takes the same amount of time to travel 8 miles downstream, with the current, as 4 miles upstream, against the current. What is the rate of the water's current? 1 solutions Answer 337228 by texttutoring(324)   on 2011-09-16 11:35:16 (Show Source): You can put this solution on YOUR website!You will need to use the equation D=vt for this question, where D=distance, v=velocity (or speed) and t=time. Let's isolate for time: t = D/v and list everything we know (where b stands for boat, w stands for water, d stands for downstream and u stands for upstream): Vb= 15 mph Dd = 8 miles Du = 4 miles Vd = 15+Vw Vu = 15-Vw Note that when you're travelling downstream with the current, you add the boat and water speed together. When you're travelling upstream against the current, you subtract. We know that t=D/v, and we know that tu = td, so: Dd/Vd = Du/Vu 8/(15+Vw) = 4/(15-Vw) Cross-multiply to solve for Vw: 8(15-Vw) = 4(15+Vw) 120-8Vw = 60+4Vw 60 = 12Vw Vw = 60/12 Vw = 5 The speed of the water is 5 mph. Hope that helps!
 Equations/498892: what does a = in this 2a+5=a+91 solutions Answer 337227 by texttutoring(324)   on 2011-09-16 11:27:35 (Show Source): You can put this solution on YOUR website!2a+5=a+9 Think of an algebraic equation like a balance or a teeter totter. Any operation you do to one side, you must do to the other side. Let's try to get a on the left side, and all the numbers on the right side: 2a+5=a+9 2a-a+5 = a - a + 9 a+5 = 0+9 a+5 = 9 a = 9 - 5 a = 4 Let's check it to see if it's right: 2a+5=a+9 2(4) + 5 = 4 + 9 8+5 = 4+ 9 13 = 13 Yes, it's correct. a=4 Hope that helps!
 Points-lines-and-rays/498170: A rectangular porch has a perimeter of 49 ft and a width of 6.5 ft. what is the length of the porch in feet.1 solutions Answer 336926 by texttutoring(324)   on 2011-09-15 02:16:10 (Show Source): You can put this solution on YOUR website!We know that the formula for the perimeter of a rectangle is: P = 2L + 2W In this question, we are given the values for perimeter, P, and the width, W. We can substitute these values into the equation and solve for L: P = 2L + 2W 49 = 2L + 2(6.5) 49 = 2L + 13 49 - 13 = 2L 36 = 2L 36/2 = L L = 18 The length of the porch is 18 feet. Hope this helps!
 logarithm/404442: Bill places \$10,000 in an investment account earning an annual rate of 5.1% compounded monthly. Using the formula V=P(1+r/n)^nt, where v is the value of the account in t years, P is the principal initially invested, n is the number of compounds per year, and r is the rate of interest, determine the amount of money, to the nearest cent, that Bill will have after 10 years.1 solutions Answer 285797 by texttutoring(324)   on 2011-02-04 19:07:43 (Show Source): You can put this solution on YOUR website!V=P(1+r/n)^nt Let's write down what we are given: P = 10000 r = 0.051 t = 10 years n = 12 (because it is compounded monthly, or 12 times per year) V=P(1+r/n)^nt V = 10000(1+0.051/12)^(12*10) V = 16634.93 So he will have \$16,634.93 after ten years.
 Numbers_Word_Problems/403936: The difference between 2 numbers is 16. Five times the smaller is the same as 8 less than twice the larger. Find thenumbers.1 solutions Answer 285541 by texttutoring(324)   on 2011-02-03 17:08:04 (Show Source): You can put this solution on YOUR website!Let x = the larger number Let y = the smaller number You have two variables, so you need two equations: Equation 1: x-y=16 Equation 2: 5y=2x-8 You can now use elimination or substitution to solve. I will use substitution: x-y=16 x=16+y Substitute this into the second equation: 5y=2x-8 5y=2(16+y)-8 5y=32+2y-8 5y=24+2y 3y=24 y=8 Now find x: x=16+y x=16+8 x=24 So the two numbers are 8 and 24.
 Rectangles/403881: The area of a rectangle is 35. If the length is 2 more than the width, find the dimensions of the rectangle.1 solutions Answer 285506 by texttutoring(324)   on 2011-02-03 15:32:43 (Show Source): You can put this solution on YOUR website!L=w+2 Area = Lw 35 = (w+2)w 35 = w^2 +2w 0 = w^2 + 2w -35 Factor (or use the quadratic formula): 0=(w+7)(w-5) w=-7, w=5 The width can't be a negative number, so we can't choose w=-7. The width must be 5. We know that the length is 2 more than the width, so the length must be 7. Dimensions: L=7 w=5 Area = 7x5=35
 Quadratic_Equations/403877: I am not good in math at all! I want to know how would i solve 6(p square-1)=5p1 solutions Answer 285505 by texttutoring(324)   on 2011-02-03 15:27:35 (Show Source): You can put this solution on YOUR website!Just to clarify, is this your question? If so, here's how you do it: First, get rid of the brackets by distributing the 6: Next, subtract 5p from both sides, so that the right side is zero: Rearrange so that it is in standard form: To solve this, you can either factor it (which is a pain!) or use the Quadratic Formula. If you factor it, you will end up with: (2p-3)(3p+2) = 0 p=3/2 or p=-2/3 If you use the Quadratic Formula: p=3/2 or p=-2/3 So as you can see, you get the same answer whether you factor it or use the quadratic formula. Check out this link for a graph of the function: http://www.wolframalpha.com/input/?i=6p^2-5p-6%3D0 Hope this helps!
 Travel_Word_Problems/403876: The distance from King Street to Prince Street is 21 km. It takes 30 minutes. What is the average speed of the bus between these two places?1 solutions Answer 285504 by texttutoring(324)   on 2011-02-03 15:12:11 (Show Source): You can put this solution on YOUR website!The relationship between Distance, Speed and Time is found in this formula: D=ST You have D at T, and you're looking for S. First, let's change T from 30 minutes to 0.5 hours, so that our speeed will be in km/h. D=ST 21 = S(0.5) S = 21/0.5 S = 42 km/h So the average speed is 42 km/h. Hope this helps!
 Polynomials-and-rational-expressions/389646: Solveby factoring when first coefficient is a negative number. please take me thru each step: -2x^2 + 13x - 21 they say the answer is 3, 7/21 solutions Answer 276159 by texttutoring(324)   on 2010-12-31 16:23:35 (Show Source): You can put this solution on YOUR website!Recall the general form for a quadratic equation: ax^2 + bx + c -2x^2 + 13x - 21 We will use the Decomposition Method for factoring. First, multiply a*c = (-2)(-21) = 42 So you need to find two numbers that multiply to 42 and add up to the b term, +13. This is pretty easy: the numbers are 7 and 6. Now the hard part is to decompose the b term, +13, into these two factors. Notice that I list 6x first, so that it pairs with the 2x^2, and the 7x second, so that it pairs with the 21 at the end. -2x^2 + 13x - 21 -2x^2 + 6x + 7x - 21 Next, factor out the -2x and 7 from each. Note that you are left with identical terms, (x-3) for each. -2x(x-3) + 7(x-3) Combine the -2x and 7 into one bracket: (-2x + 7)(x-3) This leaves you with two answers, which you can find by setting each bracket to zero, and solving for x: -2x+7 =0 7=2x x=7/2 x-3=0 x=3 Hope this helps! Let me know if you're confused by anything.
 Functions/388569: During a nine hour storm it snows at a rate of 1 inch per hour for the first two hours, at a rate of 2 inches per hour for the next six hours, and at a rate of 1 inch per hour for the final hour. Write and graph a compound function that gives the depth of snow during the snowstorm. Not sure which section this would be in... I know this says no graph but I can probably figure out the graph on my own anyways. Any help at all is appreciated greatly! Happy holidays :)1 solutions Answer 274932 by texttutoring(324)   on 2010-12-22 22:49:16 (Show Source): You can put this solution on YOUR website!Recall the equation of a line, y=mx+b. We will be using a similar equation, but with snow, S, and time, t instead of y and x. The rate of inches per hour represents the slope of the graph, m. The y-variable would be the amount of snow, S. The x-variable would be the time, t, in hours. The function has three pieces: i) S = t (slope = 1) ii) S = 2t (slope = 2) iii) S = t (slope = 1) For the first piece, i), t=2, so the amount of snow is 2 inches. For the second piece, ii) t=6, so the amount of snow is 12 inches. For the third piece, iii) t=1, so the amount of snow is 1 inch. In total, it snowed 15 inches. Hopefully this makes sense. The graph is just three lines. The first and third pieces are identical, while the middle piece is a bit steeper, with a slope of 2.
 Linear-systems/388586: Use the substitution method to solve the linear system given. Express the answer as an ordered pair of the form (x,y) x + y = 5 2x + y = 6 I need these answers to be as straightforward as possible. No shown work is needed. *Thank you for all simply put answers* 1 solutions Answer 274931 by texttutoring(324)   on 2010-12-22 22:43:42 (Show Source): You can put this solution on YOUR website!x+y=5 2x+y=6 Let`s isolate for x in equation 1: x = 5-y Now let`s substitute this value into 2x+y=6: 2(5-y) + y = 6 10 - 2y + y = 6 10 - y = 6 10 - 6 = y y = 4 Now find x: x=5-y x=5-4 x=1 So the answer, as an ordered pair is: (1,4)
 Linear-systems/388587: Ques 7. A music store is selling compact disks for \$11.50 and \$7.50. You buy 12 disks and spend a total of \$110. How many compact disks that cost \$11.50 did you buy? I need these answers to be as straightforward as possible. No shown work is needed. *Thank you for all simply put answers* 1 solutions Answer 274930 by texttutoring(324)   on 2010-12-22 22:41:04 (Show Source): You can put this solution on YOUR website!Let x = number of \$11.50 discs you bought let y = number of \$7.50 discs you bought Two equations: x+y=12 (because there are 12 disks bought in total) 11.50x + 7.50y = 110 (because the total cost is \$110) Use substitution or elimination to solve. I will use substitution. y = 12-x 11.50x +7.50(12-x) = 110 11.50x + 90 -7.5x = 110 4x = 20 x = 5 So there were five \$11.50 disks bought. This means there must have been seven \$7.50 disks bought.
 Trigonometry-basics/388313: Using f(x)=1sin x or f(x)=cos x as a guide,graph each function. Identify the amplitude and the period. f(x)=2 sin 1/2 x thnxs1 solutions Answer 274616 by texttutoring(324)   on 2010-12-21 16:32:00 (Show Source): You can put this solution on YOUR website!The sine graph will look like this: http://www.wolframalpha.com/input/?i=y%3D2+sin(x/2) (Copy and paste the URL if you can't click it.) In any sine curve, the general equation is: y=a*sinb(x-c) + d Where a=amplitude, b=compression (determines period), c=phase shift (left or right shift), and d=vertical displacement (up/down shift) In your question, a=2, b=1/2, and c=0, d=0. So the amplitude is 2. This means that the curve goes up to a max of y=2 and a min of y=-2. You can find the period by using this simple formula: P = 2Pi /b Your value of b is 1/2, so the period is: P = 2Pi / (1/2) P = 4Pi So the period of this function is 4Pi, which you should be able to see from the graph on the link. In essence, this means that the curve was stretched out in the x-direction by double. If b=2, it would be compressed to a period of 1Pi. Hope this helps!
 Polynomials-and-rational-expressions/385308: Use the “difference of squares” rule to factor the following expression: 36x^2-9y^2 1 solutions Answer 272632 by texttutoring(324)   on 2010-12-13 03:31:20 (Show Source): You can put this solution on YOUR website!The difference of squares rule is this: a^2 - b^2 = (a+b)(a-b) In your case, a^2=36x^2 and b^2=9y^2, therefore: 36x^2 - 9y^2 = (6x+3y)(6x-3y) That's it. It's factored!
 Miscellaneous_Word_Problems/385309: The length of a rectangle is 2in. less than 7 times its width. the area of the rectangle is 57 sq. in. What are the dimentions of the rectangle?1 solutions Answer 272630 by texttutoring(324)   on 2010-12-13 03:29:03 (Show Source): You can put this solution on YOUR website!Let w = width Let L = length Length is 2 less than 7 times the width: L = 7w - 2 Formula for area of a rectangle is A = w*L, and we know that A = 57 Substitute the formula for L into the equation, and solve for w: A= w*L 57 = w(7w-2) 57 = 7w^2 - 2w 0 = 7w^2 - 2w -57 Use the quadratic equation (or WolframAlpha.com) to solve. You should find that w=3 This means that L is: L=7w-2 L=7(3)-2 L=21-2 L=19 So the dimensions are w=3, L=19.
 Equations/385310: write an algebraic equation which could be used to solve the following problem. then find the solution: "A 40-inch rope is cut into three pieces so that the second piece is four times as long as the first and the third piece is three times as long as the first piece. Find the length of all three pieces." im so confused1 solutions Answer 272628 by texttutoring(324)   on 2010-12-13 03:20:53 (Show Source): You can put this solution on YOUR website!It appears as if you have three variables, but if you keep reading the question, you'll see you can actually express the three lengths in terms of the first. We know the 3 lengths add up to 40. Let's let x = the first length We also know the second length is 4 times the first, so the second length is 4x. That means the third length must be 3x. Putting it all together: x + 4x + 3x = 40 8x = 40 x = 40/8 x = 5 So the first length is 5 inches. The second length is 5*4 = 20 inches The third length is 3*5 = 15 inches. Check that the three lengths add up to 40: 5+15+20 = 40 Yes, it works! Good job you're done.
 Human-and-algebraic-language/385312: A book cost \$15 if bought online and \$22.50 if bought at the store. The bookstore sold 250 books and took in \$4995. How many books were bought online and how many were bought in the store?1 solutions Answer 272624 by texttutoring(324)   on 2010-12-13 03:08:04 (Show Source): You can put this solution on YOUR website!You have two variables, so you need to make two equations. Let x = number of books bought online Let y = number of books bought in store There were 250 books sold in total: x+y = 250 Their sales totaled \$4995: 15x + 22.50y = 4995 Use elimination or substitution with the two equations to solve for x and y. I will use elimination, by multiplying the first equation by 15, then subtracting. 15x + 22.50y = 4995 15x + 15y = 3750 ----------------- 0 + 7.50y = 1245 y = 1245/7.50 y= 166 Now find x: x+y=250 x+166=250 x=250-166 x=84 So there were 84 books sold online, and 166 sold in the store. Hope this helps! Let me know if you need any more help.
 Human-and-algebraic-language/385315: Peter is outside looking at pigs and chickens in the yard. He comes inside, tells Nadia that he counted 13 heads and 36 feet, and asks her how many pigs and chickens were in the yard. what should Nadia tell him?1 solutions Answer 272622 by texttutoring(324)   on 2010-12-13 03:03:23 (Show Source): You can put this solution on YOUR website!You have two variables, number of chickens and number of pigs. This means you need to algebra equations. Let c = number of chickens Let p = number of pigs We know that there are 13 heads in total, so that means that: c + p = 13 (Because each chicken and pig has one head each!) We also know that there are 36 feet. Chickens have 2 feet, while pigs have 4 feet: 2c + 4p = 36 Now you have your two equations. Solve them with elimination or substitution. c+p=13 2c+4p=36 Multiply the first equation by 2, then subtract: 2c+2p=26 2c+4p=36 --------- 0 - 2p = -10 p = 5 Now find c: c = 13 - p c= 13-5 c = 8 So there are 8 chickens and 5 pigs.
 Linear_Equations_And_Systems_Word_Problems/385316: roger studied for x hours. her sister studied five more than roger. between both of them, they studied 30 hours. how much did each study?1 solutions Answer 272620 by texttutoring(324)   on 2010-12-13 02:58:09 (Show Source): You can put this solution on YOUR website!Roger studied for x hours Her sister studied for (x+5) hours. Together, they studied for 30 hours in total. You need to set up an algebra equation to model this question: x + (x+5) = 30 Now collect like terms: 2x + 5 = 30 2x = 30 -5 2x = 25 x = 12.5 So Roger studied for 12.5 hours. That means his sister must have studied for 12.5+5 = 17.5 hours. Check your work. Does 12.5+17.5 = 30? Yes, it does! So that means this must be correct.
 Polygons/385321: What polygon, if any, has angle measures that add up to 5400 degrees?1 solutions Answer 272618 by texttutoring(324)   on 2010-12-13 02:55:22 (Show Source): You can put this solution on YOUR website!There's a formula to find the angle total of a polygon if you know n, the number of sides. Angle Total = (n-2) * 180 For this question, you know the angle total is 5400, so solve for n: 5400 = (n-2) * 180 5400 / 180 = n-2 30 = n-2 n = 32 So the polygon has 32 sides. It is called an Icosidodecagon, and you can view it here: http://mathworld.wolfram.com/Icosidodecagon.html
 Linear_Equations_And_Systems_Word_Problems/385320: solve x+4y=19 5x+y+0 solve a-b=25 3a+4b=41 solutions Answer 272616 by texttutoring(324)   on 2010-12-13 02:51:55 (Show Source): You can put this solution on YOUR website!x+4y=19 5x+y+0 Let's solve this one by elimination method. Multiply the second equation by 4, then subtract it from the first equation: x+4y = 19 20x +4y = 0 ----------- -19x = 19 x= -1 Plug this value into either equation to find y: 5x+y = 0 5(-1) + y = 0 -5 + y = 0 y = 5 So the solution is (-1,5) or x=-1, y=5. Second question is weird because it has no nice answers. Are you supposed to write your answers as fractions or as decimals? I did it with fractions: a-b=25 3a+4b=4 Multiply the first equation by 3, then subtract. 3a - 3b = 75 3a + 4b = 4 -------------- 0 - 7b = 71 b = -71/7 Plug this into either equation to find a: 3a - 3(-71/7) = 75 3a + 213/7 = 75 3a = 75- 213/7 3a = 312/7 a = 312/21 a = 104/7
 Graphs/384208: Translate to an equation: h \$100 bills and t \$20 bills total \$400 Graph the equation and use the graph to determine three different combinations of \$100 bills and \$20 bills that total \$400. (I have no idea how to do this please help me) 1 solutions Answer 271976 by texttutoring(324)   on 2010-12-10 14:57:12 (Show Source): You can put this solution on YOUR website!Let h = number of hundred dollar bills Let t = number of twenty dollar bills the equation is: 100h + 20t = 400 Image that h is like the y-variable, and t is like the x-variable. The graph would look like this: http://www.wolframalpha.com/input/?i=100y+%2B+20x+%3D+400 (copy this link into your web browser) Try plotting this graph yourself on graph paper, and you should see a variety of combinations that are possible. Anything that falls on the line is possible. For instance, if h=3, then t=5. This makes sense because 100(3) + 20(5) = 400 Another possibility is if h=2, then t=10. 100(2) + 20(10) = 400 I will leave it up to you to find the last combination. Hint... keep going down the line as I've done.
 Money_Word_Problems/384209: sandras monthly salary is 1500 2/3 is take home pay she spends 1/4 on car payments how much are her care payments. 1 solutions Answer 271975 by texttutoring(324)   on 2010-12-10 14:47:50 (Show Source): You can put this solution on YOUR website!2/3 of \$1500 is \$1000, so her take-home pay is \$1000. I found this by multiplying \$1500 * (2/3) She spends 1/4 of this take-home pay on car payments. \$1000 * (1/4) = \$250 Her car payments are \$250.
 Expressions-with-variables/384179: solve the following system of equations.. x + 5y =5 (1),.. x=3-5y (2)1 solutions Answer 271970 by texttutoring(324)   on 2010-12-10 14:28:27 (Show Source): You can put this solution on YOUR website!x + 5y =5 x=3-5y The second equation already has x isolated, so let's substitute that value of x into the first equation: x+5y=5 (3-5y) + 5y = 5 3 -5y + 5y = 5 3 + 0 = 5 3 = 5 This is not true, so it means there is no solution. This is because these two lines have identical slopes. They are parallel lines, so they never intersect.
 Probability-and-statistics/356703: A company manufactures calculators in batches of 64 and there is a 5% rate of defects. What is the mean number of defects per batch?1 solutions Answer 254607 by texttutoring(324)   on 2010-10-14 23:50:07 (Show Source): You can put this solution on YOUR website!Find 5 percent of 64: 64*0.05 = 3.2 So there would be 3.2 defective calculators per batch, on average. If you want a whole number answer, you could round it down to 3.
 Miscellaneous_Word_Problems/348273: Hello I am really stuck on this algebra word problem. Please assist me in solving this problem. The formula N=4x^2 + 5x +1 represents the number of households, N, in thousands, in a certain city tha have a computer x years after 1990. According to the formula, in what year were there 85,000 households with computers in this city? Thank you for your assistance in advance1 solutions Answer 248984 by texttutoring(324)   on 2010-09-26 15:06:12 (Show Source): You can put this solution on YOUR website!N=4x^2 + 5x +1 So they're telling you that N=85 because it says N is in thousands. You need to solve for x. Whatever number you get for x, add that to 1990 and you will find the year. N=4x^2 + 5x +1 85=4x^2 +5x + 1 0 = 4x^2 + 5x -84 You now have a quadratic equation. You can solve this using the quadratic formula. Where a = 4, b = 5 and c = -84 After doing the algebra for the quadratic formula (or using an online solver), you will find that there are two answers: x = -5.25 or x = 4 Choose the positive answer, x=4, because it wouldn't make sense to be negative. That means that there were 85,000 computers in this city in 1994. Hope this helps!