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Mixture_Word_Problems/396940: the sum of the digits of a two digit number is 10.if 18 is added to the number.the digits will be reversed.find the number.check your answer 1 solutions Answer 281429 by solver91311(16897)   on 2011-01-19 18:59:34 (Show Source): You can put this solution on YOUR website! Let represent the 10s digit. Let represent the 1s digit. The actual number would then be . Reversing the digits gives . We are given that And From which we get and then Now we have: and Just solve the system for and . John My calculator said it, I believe it, that settles it

Graphs/396931: I'm working on the Linear Equations in my Alegbra book. I have a graph with a horizontal X line and a vertical Y line. There is a line that slopes down from left to right. My problem is asking me to find the slope, the y-intercept, and write the equation. The line intercepts the Y line at 1, then the X line at 2. I figured the slope is -1/2 since {delta y = -2} & {delta x = 4}. I believe the y-intercept is just 2, but I'm totally questioning myself on this & have no idea how to write the equation. Can you help me please? 1 solutions Answer 281425 by solver91311(16897)   on 2011-01-19 18:51:07 (Show Source): You can put this solution on YOUR website! Let's start by using the correct words to describe things. Not the X-line or Y-line, it is the x-axis and the y-axis. If the line crosses the y-axis at 1, then the coordinates of that point are (0,1). If the line crosses the x-axis at 2, then the coordinates of that point are (2,0). The slope of your line is indeed . Use the slope formula: where and are the coordinates of two points on your line. We determined the coordinates of two points by using the intercept values, so: I'm not sure where you got the idea that and unless there is another point or two defined on your line that you didn't tell us about. Using the coordinate differences on the two intercepts (reading left to right), and Once you have the slope and the y-coordinate value of the y-intercept, writing an equation that represents the line is easy. You have the information to write your equation in slope-intercept form, namely where is the slope number and is the y-coordinate of the y-intercept. For your problem, that is and , hence: From there you can use a little algebra to put the equation into Standard form, namely: For you: John My calculator said it, I believe it, that settles it

Equations/396799: A student scored 71, 83, and 96 on three algebra tests. What must he score on the fourth test in order to have an average of at least 85? 1 solutions Answer 281411 by solver91311(16897)   on 2011-01-19 17:02:55 (Show Source): You can put this solution on YOUR website! If you want the average of 4 numbers, you add the numbers and divide by 4. So if you have the average of 4 numbers, the sum of those numbers must be the average multiplied by 4. Add the three scores already received. Multiply 85 by 4. Subtract the sum of the first three scores. The result will be the score required to achieve the stated average. You might want to compare the score required to the maximum score possible on the last test, if you know it. After all, it is possible that the stated average cannot be achieved. John My calculator said it, I believe it, that settles it

Angles/396797: If angle 1 is 6 more than 3 times its supplement(angle 2), then what is angle 1 and angle 2? I have a big test on questions like this tommorow and I don't really know how to solve them. If you could help that would be great! 1 solutions Answer 281384 by solver91311(16897)   on 2011-01-19 15:32:09 (Show Source): You can put this solution on YOUR website! Let represent the measure of angle 2. Then angle 1 is represented by . The sum of two supplementary angles is , so: Solve for to get the measure of angle 2. Multiply by 3 and add 6 to get the measure of angle 1. John My calculator said it, I believe it, that settles it

Travel_Word_Problems/396790: two trains travel in the same direction on parallel tracks. train A starts out 50 kilometers ahead of train B. train A travels 90 kilometers per hour and train B travels 100 kilometers per hour. In how many hours will the trains be in the same place? 1 solutions Answer 281383 by solver91311(16897)   on 2011-01-19 15:26:37 (Show Source): You can put this solution on YOUR website! B is traveling 10 km/hr faster than A. B has to cover 50 km at 10km/hr because the other 90 km/hour of B's speed is being used up keeping up with A. John My calculator said it, I believe it, that settles it

Rectangles/396789: The length of a rectangle is 12 cm more than it's width. Find the area of the rectangle if its perimeter is 100 cm. 1 solutions Answer 281380 by solver91311(16897)   on 2011-01-19 15:20:55 (Show Source): You can put this solution on YOUR website! Let represent the width of the rectangle. Then represents the length. The perimeter of a rectangle is given by 2 times the length plus 2 times the width, so: Solve for to get the width. Add 12 to get the length. Multiply the length times the width to get the area. John My calculator said it, I believe it, that settles it

test/396772: Write and equation of the line that passes through the given point and is parallel to the given line. 1 solutions Answer 281378 by solver91311(16897)   on 2011-01-19 15:17:36 (Show Source): You can put this solution on YOUR website! Step 1: Determine the slope of the line represented by the given equation. Step 2: Determine the slope of the desired line. Parallel lines have equal slopes, so the desired line will have a slope equal to the slope determined in step 1. Step 3: Use the point-slope form of an equation of a line: where are the coordinates of the given point and is the given/calculated slope. John My calculator said it, I believe it, that settles it

Functions/396780: I am being told to verify that a function is the inverse of function The first step reads "The function notation f(x) can be rewritten as____________. Choose x or y." Then we are to "Rewrite the equation you wrote in Step One with the variables reversed. Solve for y." 1 solutions Answer 281375 by solver91311(16897)   on 2011-01-19 15:06:02 (Show Source): You can put this solution on YOUR website! I'm not sure what your book is looking for. All I can do is show you how I would do the problem. Substitute for Solve for in terms of Swap positions of and Substitute for but your given is that represents the inverse function, hence: Please note that you rendered your inverse function incorrectly. You should have written g(x)=(x-2)/5 which would have rendered John My calculator said it, I believe it, that settles it

Volume/396372: a box measures 7 inches by 6 inches by 4 inches. calculate its volume in cubic centimeters 1 solutions Answer 281201 by solver91311(16897)   on 2011-01-18 19:17:27 (Show Source): You can put this solution on YOUR website! Calculate the volume in cubic inches. Multiply by the number of cubic centimeters in one cubic inch, namely 16.387064. Round to the nearest WHOLE cubic centimeter. Round to the nearest whole because your input measurements are in whole numbers. It is an error to make the results of a calculation of measurements more precise than the least precise given measurement. John My calculator said it, I believe it, that settles it

Rational-functions/396393: 4a + a __ __ 7 21 that is 4a over 7 + a over 21 It is adding and subtracting Rational expressions. 1 solutions Answer 281200 by solver91311(16897)   on 2011-01-18 19:11:59 (Show Source): You can put this solution on YOUR website! Just like adding any other fractions. Find and apply the LCD and then add the numerators. Hint: 7 X 3 = 21. John My calculator said it, I believe it, that settles it

expressions/396395: 2/9n-5=2+5/9n I came up with -3/9n=-3. Is that correct? 1 solutions Answer 281199 by solver91311(16897)   on 2011-01-18 19:08:07 (Show Source): You can put this solution on YOUR website! In a word, no. Presuming you meant: (and not , which is an equally valid interpretation of what you wrote) Add to both sides: Add 5 to both sides Reduce the fraction: Multiply both sides by -3: John My calculator said it, I believe it, that settles it

absolute-value/396394: the opposite of the absolute value of the sum negative five and negative three 1 solutions Answer 281197 by solver91311(16897)   on 2011-01-18 18:59:07 (Show Source): You can put this solution on YOUR website! What about it? John My calculator said it, I believe it, that settles it

Complex_Numbers/396389: Find all real values of K for which 3t^2-4t+k=0 has imaginary roots 1 solutions Answer 281196 by solver91311(16897)   on 2011-01-18 18:58:02 (Show Source): You can put this solution on YOUR website! Quadratics don't have imaginary roots, they have complex roots -- when they don't have real roots, that is. When the discriminant is less than zero, the roots of a quadratic are a conjugate pair of complex roots. The discriminant of is: So for your problem, the discriminant is: If the roots are to be complex: Just solve the inequality. Any value of k in the solution set will result in complex roots for your quadratic. John My calculator said it, I believe it, that settles it

Geometry_Word_Problems/396380: The measures of two complementary angles are (14q+8)and 8q-6). Find the measures of the angles. 1 solutions Answer 281194 by solver91311(16897)   on 2011-01-18 18:51:27 (Show Source): You can put this solution on YOUR website! The sum of two complementary angles is Just solve for and then plug that value back into the expressions for the two angles. Add your results to check, you should get 90. John My calculator said it, I believe it, that settles it

Travel_Word_Problems/396384: 6 hours at the average rate of 49 miles per hour how far he can travel 1 solutions Answer 281190 by solver91311(16897)   on 2011-01-18 18:47:28 (Show Source): You can put this solution on YOUR website! Distance equals rate times time. John My calculator said it, I believe it, that settles it

Geometry_Word_Problems/396162: you want to tile your kitchen floor. the floor measures 15ft by 9ft. how many tiles, each a square with side 1 1/2 ft, should you purchase for the job? 1 solutions Answer 281105 by solver91311(16897)   on 2011-01-18 12:42:46 (Show Source): You can put this solution on YOUR website! Adding a 1/4 inch grout line to each of your tiles makes each tile cover 1.52 X 1.52 = 2.31 square feet. You have 15 X 9 = 135 square feet to cover. 135 divided by 2.31 is nearly 58.5 tiles. Round up to the next whole tile AND then add 10%. 59 plus 6 = 65 tiles. John My calculator said it, I believe it, that settles it

Proportions/395977: PLEASE HELP ME TO SOLVE AND UNDERSTAND THE FOLLOWING PROPORTIONS;SOLVE FOR X IN THE FOLLOWING PROPORTIONS 3OVERX =20OVER7 AND 7OVER12=XOVER30. THANK YOU MUCH FOR YOUR HELP, I AM STUMPED AND DO NOT UNDERSTAND 1 solutions Answer 280984 by solver91311(16897)   on 2011-01-17 21:10:30 (Show Source): You can put this solution on YOUR website! Just cross-multiply. The numerator of the right-hand fraction times the denominator of the left hand fraction is equal to the denominator of the right-hand fraction times the numerator of the left-hand fraction. Then divide both sides by the coefficient on x. And stop typing in all caps. It is the equivalent of shouting and is therefore both annoying and rude. John My calculator said it, I believe it, that settles it

Rate-of-work-word-problems/395976: the sum of two numbers is 180. if one number is 40% more than the other,find the number? what number increased by 3.5% of itslf equals 621? one man received 15% more than another man when they shared an inheritance of $4,300.how much did each man receive? a dress is prices at $21.42 the store is having a 30% off sale what was the original price of the dress? 1 solutions Answer 280983 by solver91311(16897)   on 2011-01-17 21:06:49 (Show Source): You can put this solution on YOUR website! What part of "One question per post" don't you understand? John My calculator said it, I believe it, that settles it

absolute-value/395956: Does this have a solution? Why or why not? 6|x|+22=4 1 solutions Answer 280982 by solver91311(16897)   on 2011-01-17 21:04:39 (Show Source): You can put this solution on YOUR website! Add -22 to both sides Multiply both sides by Now you have something in the LHS that is always positive or zero and something in the RHS that is clearly less than zero. No solution. John My calculator said it, I believe it, that settles it

Quadratic_Equations/395574: A carpenter is building a rectangular room with a fixed perimeter of 304 ft. What dimensions would yield the maximum area? What is the maximum area? The length that would yield the maximum area is ___ ft. 1 solutions Answer 280824 by solver91311(16897)   on 2011-01-17 13:10:14 (Show Source): You can put this solution on YOUR website! The dimensions of a rectangle that give the maximum area for a given perimeter are , that is to say it is a square whose side measure is one fourth of the given perimeter. Proof: Let represent the length of the rectangle and let represent the width. The perimeter of a rectangle that measures by is . A little algebra: The area of the rectangle is given by . Substituting: Which can be re-written: From here you can either use the formula for the x-coordinate of the vertex of: Which is: since we know that with a negative lead coefficient, the parbola opens down and thus the vertex is a function maximum. meaning that the area is maximum when the width (and therefore the length as well) is one-fourth of the perimeter. Or you can set the first derivative equal to zero: And then evaluate the second derivative at : Since in the domain of , the value of is a local maximum. John My calculator said it, I believe it, that settles it

Polynomials-and-rational-expressions/395675: 2x^2+14x+24 1 solutions Answer 280793 by solver91311(16897)   on 2011-01-17 11:33:26 (Show Source): You can put this solution on YOUR website! What a cute little quadratic trinomial. Look! All of the coefficients are even numbers. So, -- what did you have in mind to do with it? John My calculator said it, I believe it, that settles it

Probability-and-statistics/395677: what's the probability of pulling a heart or a queen from a standard deck of a cards? 1 solutions Answer 280790 by solver91311(16897)   on 2011-01-17 11:31:26 (Show Source): You can put this solution on YOUR website! Your denominator is 52 because there are 52 cards in the deck. There are 13 hearts and 4 queens, but one of the queens is a heart, so there are a total of 13 + 3 (or 12 + 4) = 16 in your numerator. Just reduce the fraction. John My calculator said it, I believe it, that settles it

Functions/395658: I would greatly appreciate any help with this problem! Find f(g(x)) and g(f(x)) and determine if f and g are inverses. f(x)= 2/x-5 g(x)= 2/x +5 Thank you very much! 1 solutions Answer 280788 by solver91311(16897)   on 2011-01-17 11:28:56 (Show Source): You can put this solution on YOUR website! You have to clarify. Do you mean: and Or do you mean and It makes a big difference and I'm not doing it both ways. John My calculator said it, I believe it, that settles it

Travel_Word_Problems/395669: please show me the steps in solving the following problem: You are in a biathalon which totals 62 miles, and you includes a run and a bike race. You finish in 4 hours and average 8 mi/hr on the run and 20 mi/hr on the bike. What is the distance of each? 1 solutions Answer 280779 by solver91311(16897)   on 2011-01-17 11:13:08 (Show Source): You can put this solution on YOUR website! Let represent the time running at 8 mph. Then, since the total time was 4 hours, the time spent bicycling must have been Running rate times running time plus bicycling rate times bicycling time is equal to running distance plus bicycling distance is equal to total distance, hence: Solve for and Once you have the times for each leg, the distances follow directly. John My calculator said it, I believe it, that settles it

Graphs/394799: Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic fuction, and graph the function. The vertex is ___ (Type an ordered pair.) The line of symmetry is: A. y=4 B. x=2 C. x=-2 D. y=-4 The maximum/minimum of f(x) is ___. Is the value, f(2)=4 a minimum or a maximum? Graph. 1 solutions Answer 280127 by solver91311(16897)   on 2011-01-14 15:53:12 (Show Source): You can put this solution on YOUR website! Given The -coordinate of the vertex is given by: The -coordinate of the vertex is given by: Hence the vertex is: The line of symmetry is: The maximum or minimum value is If then the parabola opens upward and is a minimum. If then the parabola opens upward and is a maximum. John My calculator said it, I believe it, that settles it

Linear-equations/394785: How might you interpret the solution of a system of linear equations based on the corresponding graph of the system? Thanks so much for the help 1 solutions Answer 280117 by solver91311(16897)   on 2011-01-14 15:39:46 (Show Source): You can put this solution on YOUR website! The point where the lines intersect is the solution, because the coordinates of that point will satisfy (read: make true) both of your equations. You need to determine, by inspection of the graph, what the coordinates of that point are and report your answer as an ordered pair, (x,y), using those coordinates. To check your answer, you should substitute this set of coordinates into each of your original equations and verify that you have a true statement for each of the equations. If both lines graph to the same line, then the solution set is infinite, i.e. every ordered pair that satisfies one equation will satisfy the other. If the lines are parallel, then the solution set is empty. A consistent system has at least one solution. An inconsistent system has no solutions. An independent system has exactly one solution. A dependent system has infinitely many solutions. Therefore a system can be either consistent and independent, consistent and dependent, or inconsistent. John My calculator said it, I believe it, that settles it

Systems-of-equations/394796: I'm having such a hard time understanding this Algebra course. Can you please help me with this question? Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm. Set up an equation for the perimeter involving only W, the width of the rectangle. 1 solutions Answer 280116 by solver91311(16897)   on 2011-01-14 15:37:53 (Show Source): You can put this solution on YOUR website! Let represent the width. Then the length is . The perimeter is 2 times the length plus 2 times the width. You will need to simplify and collect terms to finish the problem. John My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/394776: Using only 4 fours and any mathematical signs or symbols (EX. +, -, Sq. root, /, *, i) write an equation that equals 33. 1 solutions Answer 280115 by solver91311(16897)   on 2011-01-14 15:34:11 (Show Source): You can put this solution on YOUR website! An equation can't "equal" something. An equation is two things that are equal to each other. What you really want is an EXPRESSION that equals 33, right? or John My calculator said it, I believe it, that settles it

Age_Word_Problems/394782: If leah is 6 years older than sue, and jhon is 5 years older than leah and the total of their ages is 41 how old is sue? 1 solutions Answer 280110 by solver91311(16897)   on 2011-01-14 15:14:21 (Show Source): You can put this solution on YOUR website! I did this one yesterday, but here it is again. Let represent Sue's age. Then represents Leah's age and represents John's age, so: Solve for John My calculator said it, I believe it, that settles it

Divisibility_and_Prime_Numbers/394789: what is letter x divide 3 takeaway 1 1 solutions Answer 280108 by solver91311(16897)   on 2011-01-14 15:08:09 (Show Source): You can put this solution on YOUR website! A mathematical expression meaning "take some number and multiply it by and then add -1 to the product". John My calculator said it, I believe it, that settles it

Travel_Word_Problems/394790: Two trains leave different terminals heading towards each other. One train is traveling at a rate of speed of 50mph, while the other train is traveling at a rate of 60 mph.They are 90 miles apart. What is the formula for figuring out when they would meet? 1 solutions Answer 280106 by solver91311(16897)   on 2011-01-14 15:06:00 (Show Source): You can put this solution on YOUR website! The situation would be the same if one train remained stationary and the other was going 50 + 60 = 110 miles per hour. How long would it take a vehicle going 110 miles per hour to travel 90 miles? John My calculator said it, I believe it, that settles it