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Miscellaneous_Word_Problems/238679: Use inductive reasoning to predict the next complete line in the pattern. 55 - 6 = 49 565 - 67 = 498 5665 - 678 = 4987 Please help me. I have no idea where to even being 1 solutions Answer 175382 by solver91311(16897)   on 2009-11-13 22:14:17 (Show Source): You can put this solution on YOUR website! First number, first calculation, zero 6s. First number, second calculation, one 6 First number, third calculation, two 6s. First number, fourth calculation, hmmm, what do you think? Second number, first calculation, 6 Second number, second calculation, 67 Second number, third calculation, 678 So what do you think for this one? Last pattern 49 498 4987 4987? What do you think replaces the (?)? John

Equations/238685: I am trying to figure out how to elimination problems.... Not having much luck....can someone help me, point me in the right direction? 6x+2y-4=0 and 10x+7y=-8 1 solutions Answer 175380 by solver91311(16897)   on 2009-11-13 22:07:39 (Show Source): You can put this solution on YOUR website! Step 1: multiply one of the equations by a constant that will make the coefficient on one of the variables the additive inverse of the coefficient on that same variable in the other equation. Frequently, as in this case, you need to find multipliers for both equations to create the additive inverse relationship. In this case, you need to find the Least Common Multiple. LCM for 10 and 6 is 30, or the LCM for 2 and 7 is 14. So you can either multiply equation 1 by 5 and equation 2 by -3, or you can multiply equation 1 by 7 and equation 2 by -2. Step 2: add like terms in the two equations. the result will be one equation with one of the variables having a zero coefficient -- therefore eliminated. You are left with one equation in one variable that can be solved by ordinary means. John

Linear_Equations_And_Systems_Word_Problems/238683: Find the slope and the y-intercept f(x)= -9-8 what is the slope? what is the y-intercept? 1 solutions Answer 175375 by solver91311(16897)   on 2009-11-13 21:54:10 (Show Source): You can put this solution on YOUR website! As written, since you have no independent variable in the definition of your function, the slope is 0 and the y-intercept is -17. If you wrote the function incorrectly, then just use the slope intercept form: The slope is the coefficient on and the constant term is the -coordinate of the -intercept. John

Linear-equations/238667: Marginal Cost of Coffee. The manager of a restaurant found that the cost to produce 100 cups of coffee is $11.02, while the cost to produce 400 cups is $40.12. Assume the cost C(x) is a linear function of x, the number of cups produced. a. Find a formula for C(x). b. What is the fixed cost? c.Find the total cost of producing 1000 cups. d. Find the total cost of producing 1001 cups. e. Find the marginal cost of the 1001st cup. f. What is the marginal cost of any cup and what does this mean to the manager? I would appreciate any help at all if possible. This is really getting on my nerves. Thanks to who may help me. 1 solutions Answer 175372 by solver91311(16897)   on 2009-11-13 21:49:44 (Show Source): You can put this solution on YOUR website! Since it is given that is linear, and you are given two points on the Cups(x) vs. Cost(y) graph, use the two-point form of the equation of a line and then put it into slope-intercept form to derive the definition of Where and are the coordinates of the given points. For this problem and You can do your own arithmetic to verify, but the slope is 0.097 and the y-intercept, which is equal to the fixed cost in this example is 1.32. So the slope-intercept, or function of form is: Substitute 1000 for and calculate, then substitute 1001 for and calculate, then calculate the difference. Given proper arithmetic since this is a linear function, the marginal value at 1001 will be the same as the marginal value at any other value of the independent variable, namely the value of the slope. Marginal value is generally defined as the first derivative of the total cost function. But in the case of a linear function, the first derivative and the slope are the same thing. It means that it costs him less than a penny for each cup of coffee he serves after he as recouped the fixed cost of $1.32. John

Geometry_Word_Problems/238598: Given a rectagular Prism With dimesions w=3 , l=4, and h=6. If you created a second rectangular prism with the lenght double but the hieght halved( and the width stays the same), which would be the relation of the second volume to the first volume? 1 solutions Answer 175366 by solver91311(16897)   on 2009-11-13 20:49:13 (Show Source): You can put this solution on YOUR website! One volume is , the other volume is They are the same. John

Equations/238661: I am trying to figure out how to elimination problems.... Not having much luck....can someone help me, point me in the right direction? 6x+2y-4=0 and 10x+7y=-8 1 solutions Answer 175363 by solver91311(16897)   on 2009-11-13 20:34:13 (Show Source): You can put this solution on YOUR website! Step 1: multiply one of the equations by a constant that will make the coefficient on one of the variables the additive inverse of the coefficient on that same variable in the other equation. Frequently, as in this case, you need to find multipliers for both equations to create the additive inverse relationship. In this case, you need to find the Least Common Multiple. LCM for 10 and 6 is 30, or the LCM for 2 and 7 is 14. So you can either multiply equation 1 by 5 and equation 2 by -3, or you can multiply equation 1 by 7 and equation 2 by -2. Step 2: add like terms in the two equations. the result will be one equation with one of the variables having a zero coefficient -- therefore eliminated. You are left with one equation in one variable that can be solved by ordinary means. John

Travel_Word_Problems/238635: please help me solve this problem. A Police heliciopteris above the freeway watching traffic when it spots a speeding car.Thelicopter knows that the next four off ramps are exactly one mile apart if the car that is speeding passes one off ramp 30seconds how fast is the speeding traveling in miles per hour? HINT-a car traveling at 60 miles per hour will travel 1 mile in 60 seconds. 1 solutions Answer 175358 by solver91311(16897)   on 2009-11-13 20:24:18 (Show Source): You can put this solution on YOUR website! If it takes half the time, he has to be going twice as fast. 30 seconds is half of 60 seconds, so 2 times 60 = ? John

Pythagorean-theorem/238643: One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides? 1 solutions Answer 175347 by solver91311(16897)   on 2009-11-13 19:40:26 (Show Source): You can put this solution on YOUR website! Solve for John

Matrices-and-determiminant/238536: Use Gauss-Jordan elmination to solve the following augmented Matrix: 3 -4 2 0 -1 7 3/2 -2 1 1 solutions Answer 175270 by solver91311(16897)   on 2009-11-13 11:49:25 (Show Source): You can put this solution on YOUR website! An augmented matrix representing a system of two 2-variable equations would have two rows and three columns. If this is your representation, you have an extraneous row. An augmented matrix representing a system of three 3-variable equations would have three rows and four columns. If this is your representation, you are missing the augmentation column. Re-post presenting the correct matrix. John

Trigonometry-basics/238528: what quadrant is 11pie divided by 8 1 solutions Answer 175269 by solver91311(16897)   on 2009-11-13 11:44:18 (Show Source): You can put this solution on YOUR website! 11/8 is larger than 1 and smaller than 1.5. Quadrant III starts at and ends at . And by the way, "pie" is a dessert item, generally round in shape with a flaky crust and some sort of generally sweet but sometimes savory filling, often made of fruit. "pi" is the commonly accepted English language representation of the lower-case Greek letter that represents the ratio of a circle's circumference to its diameter. John

Trigonometry-basics/238531: PLEASE HELP ME SOLVE THIS TRIGONOMETRIC FUNCTIONS: Name the quadrant in which sin(theta)<0 and cos(thta)>0. a)l b)ll c)lll d)lV 1 solutions Answer 175267 by solver91311(16897)   on 2009-11-13 11:25:48 (Show Source): You can put this solution on YOUR website! On the unit circle, and . is positive above the -axis, and is positive to the right of the -axis. John

Rational-functions/238497: f(x)=x^2+4x-45 Does the graph of f open up or down. What is the vertex (h,k) of f What is the axis of symmetry What are the intercepts What is the domain of f What is the range of f on what interval f is decreasing On what interval f is increasing 1 solutions Answer 175266 by solver91311(16897)   on 2009-11-13 11:21:40 (Show Source): You can put this solution on YOUR website! is a parabola of the form The lead coefficient is positive so the parabola opens upward. The -coordinate of the vertex is given by Then obviously the -coordinate of the vertex must be The axis of symmetry is the vertical line The -intercepts, if any exist, are the values of that satisfy The -intercept is found by evaluating The domain of any polynomial function is all real numbers. The range of a quadratic polynomial in the form that opens upward is A parabola that opens upward is increasing to the right of the vertex, that is to say the interval [) Quite obviously the decreasing interval is (] John

Polynomials-and-rational-expressions/238518: Find all integers b for which a^2 + ba - 50 can be factored. 1 solutions Answer 175260 by solver91311(16897)   on 2009-11-13 10:46:48 (Show Source): You can put this solution on YOUR website! -1 + 50 = 49 1 - 50 = -49 -2 + 25 = 23 and so on until you have considered all of the integer factors of -50 John

Triangles/238420: An obelisk is a tall, thin, four-sided monument that tapers to a pyramidal top. The most well-known obelisk to Americans is the Washington Monument on the National Mall in Washington, D.C. Each face of the pyramidal top of the Washington Monument is an isosceles triangle. The height of each triangle is 55.5 feet, and the base of each triangle measures 34.4 feet. Find the length, to the nearest tenth of a foot, of one of the two equal legs of the triangle. I'm not sure how you calculate the length of a leg when they give you the length of the base, and the height of the triangle. I'm sure it's in the back of my head somewhere. I just need help getting it out of there and onto the paper. Do I use the Pythagorean Theorem? Like, a+b=c but with the squares in position? THANKS! (: - Kendall 9th Grader 1 solutions Answer 175167 by solver91311(16897)   on 2009-11-13 01:01:13 (Show Source): You can put this solution on YOUR website! Yes, Pythagoras is the one to use. But remember, when you construct the altitude of the isosceles triangle, it bisects the base. So the right triangle you want to calculate has legs that are the slant height of the pyramid which is the height of the isosceles triangle face, and one-half of the base measurement. Then the hypotenuse is one of the equal legs of the isosceles triangle. John

Linear_Algebra/238271: Planning a fundraiser your club plans to raise money by selling two sizes of fruit baskets. The plan is to buy small baskets for $10, and sell them for $16 and to buy large baskets for $15 and sell them for $25. The club president estimates that you will not sell more than 100 baskets. Your club can afford to spend up to 1200 dollars to buy the baskets. Find the number of small and large fruit baskets you should buy in order to maximize profit. Let x be small baskets and y be large. Objective function: P= _x+_y Constraints: (really need help with) 1 solutions Answer 175133 by solver91311(16897)   on 2009-11-12 20:25:31 (Show Source): You can put this solution on YOUR website! Your objective function is not quite right. Since you want to maximize profit, the profit on a small basket is 16 - 10 = 6, and on a large basket is 25 - 15 = 10, so your objective function needs to be: You won't sell more than 100 baskets, per Pres. estimate so: You can't spend more than $1200 procuring the baskets, and smalls cost 10 and larges cost 15, so: You can't sell less than zero of either kind of basket, so: and And, since it is highly unlikely that anyone will buy a fractional part of a basket of either size both quantities must be integers: Your area of feasibility, based on the above constraints is integer values where the ordered pair (x, y) is in the region bounded by the quadrilateral with vertices (0, 0), (100,0), (60, 80), and (0,80). You need to graph all of the constraints and solve the system: to find these points for yourself. There is an operations research theorem that says the optimum point will be at a vertex of the area of feasibility. So, just plug the vertex values into the objective function and see which one gives you the biggest answer. John

Linear-systems/238306: how can you solve the problem (8,3) m=4 and make it to standard form 1 solutions Answer 175127 by solver91311(16897)   on 2009-11-12 19:40:53 (Show Source): You can put this solution on YOUR website! Use the point-slope form of the equation of a line: where is the given slope and are the coordinates of the given point. Then put it into standard form which looks like: Some texts require A, B, and C to be integers. Check with your instructor about this requirement. John

Equations/238289: 2x + 9y = 19 what is the solution when I subtracted 9 from both sides I got 10 as an answer and then I divided by 2 and got 5. and my solution set is ( 0,5) am I right 1 solutions Answer 175124 by solver91311(16897)   on 2009-11-12 19:34:20 (Show Source): You can put this solution on YOUR website! No. The solution set is the set of all ordered pairs such that . That is all you can say about the solution set of one linear equation in two variables. In fact, despite the fact that the solution set does have an infinite number of elements, the ordered pair that you gave is NOT one of them. I think where you erred is when you subtracted 9 from the LHS, you said . And that is only true in the case where , an assertion that you cannot support with any evidence given so far. John

Numeric_Fractions/238294: whut is the lcm fo 30 1 solutions Answer 175118 by solver91311(16897)   on 2009-11-12 19:18:09 (Show Source): You can put this solution on YOUR website! What? Please express the complete problem. Your question makes no sense. And, please, if you are unable to spell properly on your own, invest in a dictionary. John

Equations/238299: I Dont understand this 4h+5=11 I have to solve this equation 1 solutions Answer 175115 by solver91311(16897)   on 2009-11-12 19:16:19 (Show Source): You can put this solution on YOUR website! Add -5 to both sides Multiply both sides by Check: Yep. Checks. John

Proportions/238298: 15% of what number is 150? 1 solutions Answer 175112 by solver91311(16897)   on 2009-11-12 19:10:03 (Show Source): You can put this solution on YOUR website! Solve for John

Rational-functions/238296: how can hiking, shopping, architecture, and stock markets be used in rational functions and expressions? 1 solutions Answer 175111 by solver91311(16897)   on 2009-11-12 19:09:00 (Show Source): You can put this solution on YOUR website! A rational expression is some function of a variable divided by some other (or could be the same) function of a variable, like this: A rational function is a function that is defined by a rational expression, like this: How that relates to the disciplines/interest areas you mentioned is for you to invent. John

Equations/238290: solve using the multipication principle. 11x= -99 I don't know what to do or where to begin a few hints can help me. Thanks 1 solutions Answer 175108 by solver91311(16897)   on 2009-11-12 19:03:59 (Show Source): You can put this solution on YOUR website! Any time you have something that looks like: Multiply by the reciprocal of the coefficient on , in this case so you end up with: Then reduce if possible. Your problem: Multiply by John

Rational-functions/238261: Please help me solve this equation: 6x/x+2-6= x-18/x-2 1 solutions Answer 175106 by solver91311(16897)   on 2009-11-12 18:59:01 (Show Source): You can put this solution on YOUR website! I'm reasonably certain you mean: Although there is at least two other interpretations possible. Be that as it may, you are going to get an answer to what I think it means. None of the denominators have any factors in common, so the LCD is just the product of all the denominators: Apply the common denominator: Multiply by the common denominator: Distribute to remove the parentheses and combine like terms. (verification of this next step is left as an exercise for the student) Solve for . Hint: It factors. Remember to check both roots for validity and for inclusion in the domain of the original equation. John

Inequalities/238254: Tell whether the given number is a solution of 5x–10 > 2x+4. The numbers are... 8, 5, 4, -2 Tell yes or no and graph. 1 solutions Answer 175078 by solver91311(16897)   on 2009-11-12 17:51:59 (Show Source): You can put this solution on YOUR website! Substitute the given numbers one at a time for the variable every place the variable appears. Then do the arithmetic. If you have a true statement, then the given number is a solution. If you have a false statement, then the given number is not a solution. For example: Is the answer to the question statement a yes or no? John

Points-lines-and-rays/238246: write the slope intercept form of the equation of the line passing through the point (-1,2) and perpendicular to the line y= -5/6x + 2 A] y= -6/5x - 16/5 c] y= 6/5x + 18/5 b] y= -1/6x - 18/5 d] y= 6/5x + 16/5 1 solutions Answer 175077 by solver91311(16897)   on 2009-11-12 17:47:05 (Show Source): You can put this solution on YOUR website! 1: Determine the slope of the given line by inspection of the coefficient on (The given equation is already in slope intercept form.) 2: Use To determine the slope of the perpendicular. The slopes of perpendicular lines are negative reciprocals. 3: Use the point-slope form of the equation of a line: Where is the slope value calculated in step 2 and are the coordinates of the given point to write an equation of the desired line. 4: Solve the equation derived in step 3 for in terms of to put the equation into slope-intercept form. John

Functions/238247: find domain for function h h(x) =15/x^2+6x+5 1 solutions Answer 175074 by solver91311(16897)   on 2009-11-12 17:39:16 (Show Source): You can put this solution on YOUR website! It depends. Do you mean: or Either way, set the denominator equal to zero and solve. The roots of this equation will be the values excluded from the rational function. The domain is all other real numbers. John

Numeric_Fractions/238233: what is the slope perpindicular to 7x-3y=6? 1 solutions Answer 175072 by solver91311(16897)   on 2009-11-12 17:35:22 (Show Source): You can put this solution on YOUR website! Step 1: Put the given equation into slope-intercept form by solving the equation for in terms of . Step 2: Determine the slope of the given equation by inspection of the coefficient on in the slope-intercept form derived in Step 1. Step 3: Use to find the slope of the perpendicular. Which is to say, compute the negative reciprocal of the value discovered in Step 2. John

Expressions-with-variables/238239: 2x+1y =7 - 3 1 solutions Answer 175071 by solver91311(16897)   on 2009-11-12 17:29:21 (Show Source): You can put this solution on YOUR website! Now that is a very handsome little 2-variable linear equation. What was it you wanted to do with it besides share it with us? John

Functions/238207: Find the domain and range of the inverse of the function f(x)= 7 + 3e^x. I found the inverse to be y =ln(x-7)/3. I do not know how to find the domain and range of the equation. I know that the range of the original function is the domain of the invrse function, but that is it. 1 solutions Answer 175066 by solver91311(16897)   on 2009-11-12 17:23:55 (Show Source): You can put this solution on YOUR website! The domain of is So if the function argument is , we need to describe the set of all such that is greater than zero. Hence the domain of your function is: If you graph you will see that the range is also . This makes sense because the range of is and you have just moved everything up 7 units. John

Human-and-algebraic-language/238204: Mr. Jacobs is four times as old as his son. Five years ago, he was nine times as old as his son. What is Mr. Jacob's age? 1 solutions Answer 175048 by solver91311(16897)   on 2009-11-12 16:35:23 (Show Source): You can put this solution on YOUR website! Let represent the son's age. Then the father's age is Five years ago the son was and the father was And we know that Solve for to get the son's age and then multiply by 4. The reason that I didn't set it up so that represented the father's age is that the son's age would have to be a fraction, -- messy. John

Equations/238201: 5/4x + 1/8= 7/8 solve the solution is x= I came up with subtract 1/8 from both sides = 7/8 -1/8= 6/8 reduced x= 1/2 am I right 1 solutions Answer 175044 by solver91311(16897)   on 2009-11-12 16:28:39 (Show Source): You can put this solution on YOUR website! You were on the right track but got derailed somewhere in the middle. Adding to both sides was the correct thing to do, but you didn't finish the simplification. Now I don't know where you went. You have a coefficient on , so you need to multiply both sides by the reciprocal of that coefficient: And simplify: John