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 Money_Word_Problems/400094: Write a word about money where each child in the problem ends up with $5. Make sure two operations must be used to solve the problem.1 solutions Answer 283297 by solver91311(16897) on 2011-01-26 13:52:12 (Show Source): You can put this solution on YOUR website! Impossible to do that in one word, which is what "write a word" means. Now if you meant "Write a word problem..." that is an entirely different story. But that isn't what you asked. John My calculator said it, I believe it, that settles it  Linear-equations/400092: what is the slope of the given points: (3,2) and (8,4)? 1 solutions Answer 283295 by solver91311(16897) on 2011-01-26 13:49:59 (Show Source): You can put this solution on YOUR website! Use the slope formula: where and are the coordinates of the given points. And by the way, your question is stated improperly. A pair of points does not have a slope. The line containing that pair of points has a slope. Hence, properly couched, your question is: "What is the slope of the line containing the given points?" John My calculator said it, I believe it, that settles it  Linear-equations/400093: What is the equation for a vertical line?1 solutions Answer 283292 by solver91311(16897) on 2011-01-26 13:47:21 (Show Source): You can put this solution on YOUR website! The equation for a vertical line that passes through the point is . Such an equation describes a set of points in such that all of the -coordinates are equal to and the -coordinates can be anything you like. John My calculator said it, I believe it, that settles it  Linear-equations/400087: what is the slope of the given pointts: (1,4) and (3,1)? 1 solutions Answer 283289 by solver91311(16897) on 2011-01-26 13:42:04 (Show Source): You can put this solution on YOUR website! Use the slope formula: where and are the coordinates of the given points. And by the way, your question is stated improperly. A pair of points does not have a slope. The line containing that pair of points has a slope. Hence, properly couched, your question is: "What is the slope of the line containing the given points?" John My calculator said it, I believe it, that settles it  Age_Word_Problems/400084: one number is 6 more than a second number. The sum of the two numbers is 92. Find the smallest number1 solutions Answer 283287 by solver91311(16897) on 2011-01-26 13:40:50 (Show Source): You can put this solution on YOUR website! Let represent the smaller number. Then represents the larger number. The sum is 92, so: Solve for . John My calculator said it, I believe it, that settles it  Quadratic_Equations/400026: We are studying Equations, Inequalities, and mathematical modeling. Question says to find ALL solutions of the equation. check your solution in original equation. I need help working this problem. Can you show me step-by-etep how to work and solve equation? equation: 6x^4-14x^2=01 solutions Answer 283244 by solver91311(16897) on 2011-01-26 11:57:24 (Show Source): You can put this solution on YOUR website! Factor out: Use the Zero Product Rule, if and only if or The factors of the LHS are: The first two are trivial, namely Set the third one equal to zero: Note rationalization of the denominator. That gives you a total of 4 roots (counting multiplicities) as is demanded of a 4th degree polynomial equation by the Fundamental Theorem of Algebra. (multiplicity of 2) John My calculator said it, I believe it, that settles it  Expressions-with-variables/400011: Could someone please explain how to do these problems, we are solving problems with two variables and I do not understand how to even start working on them, the directions state...Solve by the addition-or-subtraction method, if someone could explain how they are solved I think I could get it.... 3x-y=-5 2x+2y=-6 I would greatly appreciate it...thanks!!!!1 solutions Answer 283240 by solver91311(16897) on 2011-01-26 11:39:36 (Show Source): You can put this solution on YOUR website! Step 1: Determine a factor that will transform one of the coefficients on one of the variables into the additive inverse of the coefficient on that same variable in the other equation. For your example, note that multiplying the first equation by 2 would make the coefficient on in the first equation be -2 which is the additive inverse of 2, the coefficient on in the second equation. is the first equation after multiplying it by 2. is the original second equation. Step 2: Add the two equations, term-by-term to get: Did you notice how the contrivance to have the coefficients on be additive inverses caused the variable to disappear altogether? Step 3: Solve for the remaining variable: Step 4: Substitute the value of the variable you just determined back into either of the original equations: Step 5: Solve: Step 6: Specify the solution set: The solution set consists of a single element, namely the ordered pair Now that you are done with your example problem, a few general notes. 1. Sometimes you will have to find two multipliers, one for each equation in order to achieve the additive inverse relationship between coefficients in the two equations. For example: would require multiplication of the first equation by 3 and the second by 5 in order to eliminate the variable. 2. Cross out any reference to "addition-or-subtraction" method. Completely erase such a notion from your head. It is the Elimination method because the purpose of the method is to eliminate one of the variables. 3. While you are at it, eliminate the notions of "subtraction" and "division." You never have to do either. Always add. That is to say perform instead of . You will make orders of magnitude fewer sign errors if you do that. As for division, you multiply by the reciprocal instead. For example, the process instead of will save you lots of grief when you start working with rational functions later on. 4. You will encounter situations where the result of the elimination process will be a triviality, generally , or an absurdity, that is something that looks like . Every two-variable linear equation has a graph that is a straight line. For any given pair of equations there are three possibilities. One, they can be two lines that intersect in a single point. Such is the case with your example problem -- the solution set consists of a single ordered pair representing the single point of intersection of the graphs of the two lines. Two, they could be exactly the same line, such that any ordered pair that satisfies one of the equations also satisfies the other equation. Graphically, this is represented by the two equations having exactly the same graph, and this situation is indicated by arriving at the trivial result mentioned above. Three, they could be two different but parallel lines. They never intersect, and hence the solution set is the empty set. Such a situation is indicated by achiving an absurd result to the Elimination method. John My calculator said it, I believe it, that settles it  Word_Problems_With_Coins/400018: Please help me solve this: Zack has$20.25 in nickles and quaters. The number of nickels is 33 less than the number of quaters. How many of each does he have?1 solutions Answer 283227 by solver91311(16897)   on 2011-01-26 10:57:47 (Show Source): You can put this solution on YOUR website! Let represent the number of quarters. Then is the value of those quarters in cents. Since there are 33 less nickels than quarters, must represent the number of nickels. then represents the value of the nickels in cents. The value of the quarters plus the value of the nickels is $20.25, but that is the same as 2025 cents. Therefore: Solve for to get the number of quarters. Subtract 33 to find the number of nickels. Oh, by the way: would work just as well. It is just that I would rather work with integer coefficients given the choice. John My calculator said it, I believe it, that settles it  Equations/400016: Find an equation of the line. Write the equation using function notation. Through (10,-52) and (2,-4)1 solutions Answer 283223 by solver91311(16897) on 2011-01-26 10:45:35 (Show Source): You can put this solution on YOUR website! Use the two-point form of an equation of a line: where and are the coordinates of the given points. Do the indicated arithmetic and then solve the equation for in terms of everything else so that the equation is in the slope-intercept form, . Finally replace with John My calculator said it, I believe it, that settles it  Polygons/399886: as the number of sides of a regular polygon increases, What happens to the measure of each exterior angle? What is the least to the possible measure of an exterior angle of a polygon?1 solutions Answer 283139 by solver91311(16897) on 2011-01-26 00:18:06 (Show Source): You can put this solution on YOUR website! The sum of the measures of the exterior angles of a polygon is 360 degrees regardless of the number of sides. That means that the measure of each exterior angle must get smaller as the number of sides increases. There is no "least possible measure" because even though the limiting value is 0 you can never achieve a 0 degree exterior angle and still have a polygon. You can get as close to zero as you like, but as close as you get, someone else can always come along and get closer. Another way to look at it is that a zero degree exterior angle measure implies that there are an infinite number of sides. And an infinite number of sides implies a circle, not a polygon. John My calculator said it, I believe it, that settles it  Rational-functions/399727: Attempting to solve what looks like a simple problem, but keep coming up with the incorrect answer. 5/4z - 3/8z The problem is written as a fraction, with one term directly above the other. I've done the best I can to represent this here. I came up with 2/4z, which I simplify to 2z. Can you help?1 solutions Answer 283051 by solver91311(16897) on 2011-01-25 19:23:46 (Show Source): You can put this solution on YOUR website! Presuming you mean: rather than which is an equally valid interpretation of what you wrote, proceed as follows: Find the LCD of 4 and 8. Both 4 and 8 divide 8 evenly, so 8 is the LCD. Convert . You have to multiply the denominator by 2 to get from 4 to 8, so you have to multiply the numerator by 2 as well. Result: Now you can add the numerators. 10 plus -3 is 7, so: Now, for where I think you may have gone wrong. You added 5 and -3 to get 2 and then simply ignored the fact that you had a different denominator in the second fraction. Then, having erroneously decided that the sum was , you changed into 2. Let's see if your arithmetic makes any sense. I have one whole pizza and a quarter of a pizza. The whole pizza is sliced into 8 slices, and the quarter pizza is two slices. I give you the whole thing and tell you to eat what you want and calculate what you have when you are done. You eat 3 of the slices and then, according to your arithmetic, you have 2 whole pizzas left. I never believed that loaves and fishes story either. John My calculator said it, I believe it, that settles it  Numbers_Word_Problems/399736: twice an unknown number and 3 is 181 solutions Answer 283044 by solver91311(16897) on 2011-01-25 19:05:56 (Show Source): You can put this solution on YOUR website! Truly fascinating! Now, what was your question? John My calculator said it, I believe it, that settles it  Linear-systems/399731: I don't understand how to make a word problem into a linear system. This is an example in my Algebra I book: You are planning a party for a friend. You can have the party at a pizza place for$8 per person plus $30 for favors and a small cake, or at a taco place for$12 dollars per person plus \$14 for a large cake. Could you please create a linear system from this data?1 solutions Answer 283043 by solver91311(16897)   on 2011-01-25 19:05:12 (Show Source): You can put this solution on YOUR website! Where is the cost function for the pizza place, is the cost function for the taco place, and is the number of people attending the party (don't forget to count yourself -- and me. I am invited aren't I?) John My calculator said it, I believe it, that settles it
 Mixture_Word_Problems/399626: shad made 9 of the 25 free throws at basketball practice. what percent did he make?1 solutions Answer 282977 by solver91311(16897)   on 2011-01-25 16:55:07 (Show Source): You can put this solution on YOUR website! Divide 9 by 25, then move the decimal point two places to the right. John My calculator said it, I believe it, that settles it
 Linear_Algebra/399601: WHATS 2R+2=56-R1 solutions Answer 282975 by solver91311(16897)   on 2011-01-25 16:53:02 (Show Source): You can put this solution on YOUR website! Did you mean "What's" as in "What is"? is a single variable linear equation. John My calculator said it, I believe it, that settles it
 Mixture_Word_Problems/399624: two-fifths of the area of school parking lot can be used for a cultural festival. if the whole parking lot is 7800 square feet, how many square feet can be used for the festival?1 solutions Answer 282974 by solver91311(16897)   on 2011-01-25 16:50:17 (Show Source): You can put this solution on YOUR website! Either multiply 7800 by or convert to a decimal and then multiply. John My calculator said it, I believe it, that settles it
 Mixture_Word_Problems/399622: sandra spent 2/5 of an hour helping a customer extange an unwanted gift. then she spent 1/2 an hour giving a costumer a refund. what fraction of an hour did she spend helping both customer?1 solutions Answer 282972 by solver91311(16897)   on 2011-01-25 16:48:04 (Show Source): You can put this solution on YOUR website! Add John My calculator said it, I believe it, that settles it
 test/399599: I want to learn more.1 solutions Answer 282970 by solver91311(16897)   on 2011-01-25 16:46:39 (Show Source): You can put this solution on YOUR website! I applaud your desire. Start by reading the instructions for posting on this site. John My calculator said it, I believe it, that settles it
 Expressions-with-variables/399617: Can someone please help....don't know how to solve these problems...have to solve these using the addition or subtraction method.... x+y=8 x-y=21 solutions Answer 282969 by solver91311(16897)   on 2011-01-25 16:43:41 (Show Source): You can put this solution on YOUR website! You already have one of the variables with additive inverse coefficients -- the coefficient on y in the first equation is 1 and the coefficient on y in the second equation is -1, so just add the two equations, term by term, and the y variable will go away. x plus x is 2x, y plus -y is 0, and 8 plus 2 is 10. so 2x = 10. Solve for x. John My calculator said it, I believe it, that settles it