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# Recent problems solved by 'mmm4444bot'

 Equations/22903: (y-8)/2=(y+10)/51 solutions Answer 11466 by mmm4444bot(95)   on 2005-12-20 21:22:41 (Show Source): You can put this solution on YOUR website!Hello There: (y - 8)/2 = (y + 10)/5 Clear the fractions by multiplying both sides of this equation by 10 (the LCM of 2 and 5). 5*(y - 8) = 2*(y + 10) Use the distributive property to get rid of the parentheses. 5*y - 40 = 2*y + 20 Combine like terms; subtract 2*y from both sides and add 40 to both sides. 5*y - 2*y = 20 + 40 3*y = 60 Solve for y by dividing both sides by 3. y = 60/3 y = 20 Check the answer by substituting 20 for y in the original equation, and then simplify to see if you end up with a true statement. (20 - 8)/2 = (20 + 10)/5 12/2 = 30/5 6 = 6 Our solutions checks out. ~ Mark
 Graphs/23053: i need help to figue out what is? can you help me? thank you.1 solutions Answer 11464 by mmm4444bot(95)   on 2005-12-20 21:15:59 (Show Source): You can put this solution on YOUR website!Hello There: 3*a + b = 8 is an equation. We cannot solve this equation because there are two variables (a and b). Did you get any instructions for this equation? ~ Mark
 Graphs/21495: the instructions say, write an equation of the line that passes through the point and has the given slope. write the equation in slope-intercept form. the problem is (-3,-5),m=-2 i do not get how to do this at all. Can you teach me and walk me through the steps? thank you so much, melinda 1 solutions Answer 10381 by mmm4444bot(95)   on 2005-12-03 21:45:06 (Show Source): You can put this solution on YOUR website!Hello There: There are many different forms for writing the equation of a line. For this problem, we need to know two of them: y = m*x + b This is the "slope-intercept" form where m is the slope and b is the y-intercept. They call it the slope-intercept form because you can see at a glance what the slope and y-intercept are when looking at the equation. For example, y = -7*x + 13 We can see that this line has a slope of -7 and crosses the y-axis at (0,13). The other form that we need to know is the "point-slope" form. We use this form when we know the slope of the line and the coordinates of one point on the line. This is the information that you've been given. The slope is -2, and the known point is (-3, -5). If the known point is (a, b), and the slope is m, then the point-slope form is: y - b = m*(x - a) So, substituting the known coordinates for a and b, and the slope, we get: y - (-5) = (-2)*(x - [-3]) y + 5 = -2*(x + 3) y + 5 = -2*x - 6 y = -2*x - 6 - 5 y = -2*x - 11 So, as you see, by solving the point-slope form for y, we get the slope-intercept equation of the line. This line has a slope of -2, and it crosses the y-axis at (0, -11). ~ Mark
 Radicals/21479: Hello i ned help solving this equation: (^2-3)(^2+3) THANK YOU SOOO MUCH!!1 solutions Answer 10379 by mmm4444bot(95)   on 2005-12-03 21:37:16 (Show Source): You can put this solution on YOUR website!Hello There: (^2-3)(^2+3) This is not an equation. An equation always contains an equals sign. Additionally, these expressions do not make sense because you cannot begin with the ^symbol. If you mean: (x^2 - 3)*(x^2 + 3) and the instructions are to simplify, then this is the factorization of a "difference of squares" -- which should be discussed in your text. The pattern is: (a^2 - b^2) = (a + b)*(a - b) In your problem, a = x^2 and b = 3. Squaring both and taking their difference gives us: x^4 - 9 ~ Mark
 Radicals/21491: fill in the blank Between every two rational numbers there is another _________ number. Thank you sooo much for all your help!!1 solutions Answer 10378 by mmm4444bot(95)   on 2005-12-03 21:28:11 (Show Source): You can put this solution on YOUR website!Hello There: Consider these two rational numbers: 0 and 1. (We can think of them as rational numbers because they can be expressed as 0/1 and 1/1. Between them is the rational number 1/10. Between them is the rational number 1/100. And so it goes; all of these numbers are between 0/1 and 1/1: 1/1000 1/10000 1/100000 1/1000000 Since this goes on forever, we can say that there is a rational number between every two rational numbers. ~ Mark
 Radicals/21489: HOW MANY RATIONAL NUMBERS ARE THERE BETWEEN 5 AND 14? PLEASE I NEED HELP WITH THIS THANK YOU SO MUCH I REALLY APPRECIATE ALL UR HELP! :)1 solutions Answer 10376 by mmm4444bot(95)   on 2005-12-03 21:06:47 (Show Source): You can put this solution on YOUR website!Hello There: If we add 1/10 to 5, we get 5 + 1/10 which equals 51/10 (a rational number with a decimal representation of 5.1). If we add 1/100, we get 501/100 which equals 5.01. If we add 1/1000, we get 5001/1000 which equals 5.001. We can continue this forever: 50001/10000 = 5.0001 500001/100000 = 5.00001 5000001/1000000 = 5.00001 Since this process can go on forever, and each time we are adding a smaller and smaller amount to 5, there are an infinite number of rational numbers between 5 and 14. ~ Mark
 Radicals/21490: FILL IN THE BLANK: BETWEEN EVERY TWO RATIONAL NUMBERS THERE IS ANOTHER NUMBER. WHAT IS THE BLANK? THANK YOU GUYS SO MUCH YOU ALL ARE SO HELPFULL1 solutions Answer 10374 by mmm4444bot(95)   on 2005-12-03 20:54:36 (Show Source): You can put this solution on YOUR website!Hello There: What blank? ~ Mark
 Coordinate-system/21487: how do you graph it?1 solutions Answer 10373 by mmm4444bot(95)   on 2005-12-03 20:53:41 (Show Source): You can put this solution on YOUR website!Hello There: What are you trying to graph? ~ Mark
 Polynomials-and-rational-expressions/21012: x^2-14x+49 is this problem factorable? 1 solutions Answer 10081 by mmm4444bot(95)   on 2005-11-29 21:25:30 (Show Source): You can put this solution on YOUR website!Hello There: x^2 - 14*x + 49 is factorable if we can find two numbers that multiply to make 49 and add to make -7. With a little thought, you should realize that these two numbers are -7 and -7. (-7)*(-7) = 49 -7 - 7 = -14 So, the factorization is: (x - 7)*(x - 7) = (x - 7)^2 ~ Mark
 Systems-of-equations/21018: in class we're learning about system of equations and i don't really understand it so what is the coordinate for x-4y=15 and 2x+5y=4. could you explain it?1 solutions Answer 10080 by mmm4444bot(95)   on 2005-11-29 21:21:16 (Show Source): You can put this solution on YOUR website!Hello There: Off the top of my head, I can think of five different ways to solve this problem. I don't know which method(s) you've studied, so I have to guess. I'll use the "substitution method". The strategy in this method is to solve one of the equations for one of the variables. You'll end up with an expression that contains the other variable. Substitute this expression into the other equation, and that will give you an equation that contains only one variable. Solve it in the normal way. Once you have the value of that variable, substitute it into the expression you got from solving the first equation. Here goes: I choose to solve the first equation for 'y'. x - 4*y = 15 -4*y = 15 - x y = (15 - x)/(-4) Now I substitute this expression for y in the second equation. 2*x + 5*y = 4 2*x + 5 = 4 I'll clear the fraction by multiplying both sides by -4. -8*x + 5*(15 - x) = -16 -8*x + 75 - 5*x = -16 -13*x = -91 x = -91/(-13) x = 7 Now that we know x is 7, we substitute it for x in our formula for y above. y = (15 - x)/(-4) y = (15 - 7)/(-4) y = 8/(-4) y = -2 The solution is x = 7 and y = -2. You can verify this solution by substituting 7 for x and -2 for y into both of the original equations to see that it yields true statements. ~ Mark
 Functions/20574: What does it mean to make y a function of X. For example y=x-3. This is one of my problems. So far this is what I came up with. y=x-3 I added 3 to both sides of the equation. Then I got the answer y+3=x and I wanted to know weather or not I changed y into a function of x.1 solutions Answer 9917 by mmm4444bot(95)   on 2005-11-25 21:48:51 (Show Source): You can put this solution on YOUR website!Hello There: To make y a function of x, you need to have y all by itself on one side of the equals sign and then an expression containing x on the other side. So, your example of y = x - 3 is already in the correct form. ~ Mark
 Geometry_Word_Problems/20577: could someone please help me with this problem? a room 12ft by 16ft is carpeted. at \$18.00 per square yard, how much does it cost to carpet the room? use (9ft^2 = 1yd^2) to solve. thank-you!!!!!!1 solutions Answer 9916 by mmm4444bot(95)   on 2005-11-25 21:42:19 (Show Source): You can put this solution on YOUR website!Hello There: I just responded to this problem. See question 20587. ~ Mark
 Geometry_Word_Problems/20578: how many gallons of water will fill a fish tank that is 18in long 10in wide and 9in high? round to the nearest tenth. thanks!1 solutions Answer 9915 by mmm4444bot(95)   on 2005-11-25 21:41:22 (Show Source): You can put this solution on YOUR website!Hello There: I just responded to this question. See problem 20588. ~ Mark
 percentage/20583: Cellophane tape 2 rolls for \$1.28 Notepads 3pads for \$.87 Highlighters 1 for \$1.59 Ink cartridges 2 boxes for \$1.98 How much would you pay for one roll of tape, two note pads, two highlighters, and two boxes of ink cartridges?1 solutions Answer 9914 by mmm4444bot(95)   on 2005-11-25 21:32:32 (Show Source): You can put this solution on YOUR website!Hello There: To find the cost of one roll of tape, we divide the given price by 2 because the given price is for twice the number of rolls that we want. \$1.28/2 = \$0.64 ---------------- To find the cost of two note pads, we first divide the given price by 3 because we want to know how much one note pad costs. \$0.87/3 = \$0.29 Each note pad is 29 cents. Since we want to note pads, we double this amount. \$0.29*2 = \$0.58 ---------------- One highlighter costs \$1.59. We want two of them, so we double this amount. \$1.59*2 = \$3.18 ---------------- We want two boxes of ink catridges, and we are told that two boxes cost \$1.98. ---------------- Let's total the amounts: \$0.64 + \$0.58 + \$3.18 + \$1.98 = \$6.38 We would pay \$6.38 for these seven items. ~ Mark
 absolute-value/20584: Paul can type 60 words per minute and Jennifer can type 80 words per mute. How does Paul's tying speed compare to Jennifer?1 solutions Answer 9913 by mmm4444bot(95)   on 2005-11-25 21:21:41 (Show Source): You can put this solution on YOUR website!Hello There: In one minute, Paul types 60 words and Jennifer types 80 words. 80 - 60 = 20 Paul types 20 words per minute slower than Jennifer. ~ Mark
 Numeric_Fractions/20585: A certain alloy contains 5.25% copper. How much copper is there in a piece weighing 200 pounds?1 solutions Answer 9912 by mmm4444bot(95)   on 2005-11-25 21:19:12 (Show Source): You can put this solution on YOUR website!Hello There: This question wants to know what 5.25% of 200 is. Remember, the percent sign (%) means divide by one hundred. Dividing a decimal number by one hundred is easy; we just move the decimal point two places to the left. So, 5.25% = 0.0525 To find the percentage, we multiply this 'decimal' form of the percent by 200. 0.0525*200 = 10.5 The 200-pound piece of alloy contains 10-1/2 pounds of copper. ~ Mark
 Geometry_Word_Problems/20587: please help me out!!!!!!!! A room 12ft by 16ft is carpeted. At \$18.00 per square yard how much does it cost to carpet the room? thank-you for your help!1 solutions Answer 9911 by mmm4444bot(95)   on 2005-11-25 21:14:33 (Show Source): You can put this solution on YOUR website!Hello There: A square yard is a measure of area. To answer this question, we need to know two things. 1) How to calculate the total area carpeted (this will be the number of square feet). 2) How to convert square feet into square yards. To find the area, we use the simple formula: A = Length times Width A = 12*16 A = 192 The room is carpeted with 192 square feet of carpet. A square yard is a square that measures 3 feet by 3 feet because there are 3 feet in one yard. Therefore: 1 square yard = 3*3 square feet 1 square yard = 9 square feet To find the square yards, we divide 192 square feet by 9 to find out how many squares there are that measure 3 feet by 3 feet. 192/3 = 21-1/3 There are 21 and 1/3rd square yards of carpet. Each of these cost \$18. 18*21-1/3 = 384 It costs \$384 to carpet this room. ~ Mark
 Geometry_Word_Problems/20588: please help me out! how many gallons of water will fill a fish tank that is 18in long, 10in wide and 9in high? thank-you for your help!!1 solutions Answer 9910 by mmm4444bot(95)   on 2005-11-25 21:04:36 (Show Source): You can put this solution on YOUR website!Hello There: We need to know two things to answer this question. 1) How to calculate the volume of the tank in cubic inches (we use inches because that's the unit of measurement we are given). 2) Finding out how many cubic inches there are in one gallon of water. Let's do #1 first. The volume of a rectangular container is Length times Width times Height. V = 18*10*9 V = 1620 The fish tank holds 1,620 cubic inches of water. Now we do #2. I did not know how to convert gallons into cubic inches, so I went to the following site: http://www.onlineconversion.com/volume.htm Here, I found out that 231 cubic inches equals 1 U.S. liquid gallon. Now it's just a matter of finding out how many 231 cubic inch amounts there are in the fish tank. 1620/231 = 7.01 The fish tank holds 7 gallons of water. ~ Mark
 Linear_Equations_And_Systems_Word_Problems/20529: Claire has a small personal business making scented candles. Her startup costs are \$200. Her cost to make each cangle is \$1.50. She sells each candle for \$4.00. Use a system of equations to determine the number of candles she must sell to break even. (Write one equation for her prodction costs and one for her sales revenue.)=1 solutions Answer 9886 by mmm4444bot(95)   on 2005-11-24 21:28:14 (Show Source): You can put this solution on YOUR website!Hello There: Let x = the number of candles produced and sold. The costs are modeled by this equation: C = 200 + 1.5*x because each x costs \$1.50, and there is the startup costs (which is fixed one time only) of \$200. The revenue is modeled by this equation: R = 4*x because they collect \$4 for each x. To break even means that the costs equal the revenue (i.e., there is no profit, but there is no loss either). We find this number of candles by setting the costs equal to the revenue. 200 + 1.5*x = 4*x Subtract 1.5*x from both sides so that we can combine the x-terms together on the right side. 200 = 4*x - 1.5*x 200 = 2.5*x Solve for x by dividing both sides by 2.5: x = 200/2.5 x = 80 ~ Mark
 Linear-systems/20532: Hello, I have a list of equations below theres suppose to be two sets of parallel lines which one are ? also there are suppose to be 3 pairs of perpindicular lines as well i'm suppose to identify the perpindicular equations by letters and equations and for the parallel i'm suppose to criss cross by connecting each parallel line: heres the list:: correct me if i'm wrong x = 3 y = 2x-1 y/2 = x+3 y = -7 2y = -x x = -2 I know -2 and -7 are horizontial x=3 i think is perpindicular and 2x-1 is parallel so how can answer this problem logically to supply the answers that are needed thanks for looking and trying to help! 1 solutions Answer 9885 by mmm4444bot(95)   on 2005-11-24 21:20:15 (Show Source): You can put this solution on YOUR website!Hello There: Here is the information that you need to answer these questions. An equation of the form x = c, where c is a real number, has a graph that's a vertical line. Your two equations x = -2 and x = 3 are vertical lines that intersect the x-axis at (-2, 0) and (3, 0). An equation of the form y = c, where c is a real number, has a graph that's a horizontal line. Your equation y = -7 is a horizontal line that intersects the y-axis at (0, -7) When two lines have the same slope, they are parallel. When two lines have slopes that are negative reciprocals of each other, they aer perpendicular. Solving for y shows us the slope. This equation is already solved for y: y = 2*x - 1 Solving this equation: y/2 = x + 3 gives us: y = 2*x + 6 Both of these lines have slope 2, so they are parallel. Solving 2*y = -x leads to: y = -(1/2)*x This slope is -1/2; so it's the negative reciprocal of 2 (the slope of the parallel lines). So, 2*y = -x is the line that is perpendicular to y/2 = x + 3 and y = 2*x - 1. ~ Mark