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# Recent problems solved by 'solver91311'

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 Linear-systems/616985: on a feasible region whose vertices ar{(0, 0), (1, 12), (5, 8), (8, 3), (9, 0) what is the maximum of the objective function p=6x+4y, and where does it occur?1 solutions Answer 388070 by solver91311(17074)   on 2012-06-01 18:29:31 (Show Source): You can put this solution on YOUR website! Substitute the coordinate values for each of your feasible region vertices and calculate the value of the objective function for each one. The largest one is the maximum of the objective. If two adjacent points have the same objective function value, then any point on the segment that joins those two points is an optimum. John My calculator said it, I believe it, that settles it
 Quadratic-relations-and-conic-sections/616987: All of the questions are based on the same ellipse... 1)An ellpise has foci at (-5,0)and (5,0). What is the value of c²? 2)If the sum of the focal radii of this ellpise is 12, what is the value of a²? 3)Using your conclusions, what is the value of b²? 4)What is the equation of the ellipes? 5)What are the x-intercepts of the ellipse? 6)What are the y-intercepts of this ellipse? 7) Graph the ellipse and plot the foci on a graph. 1 solutions Answer 388069 by solver91311(17074)   on 2012-06-01 18:23:04 (Show Source): You can put this solution on YOUR website! is the distance from the center to either of the foci. Since the foci are equidistant from the -axis and the -coordinates of the foci are both , we can conclude that the center of the ellipse is the origin, (0,0). Given that you should be able to determine the distance from the center to either focus by inspection and square that value to get . John My calculator said it, I believe it, that settles it
 Surface-area/616981: How many square feet is the surface area of the house. The house is 45' by 34'. Each corner is 10'high and the peak of the roof is 14'. I have a lot of questions that require the same formula but I can not figure out what the roof has to do with it. If i can get help on the formula i can do the rest. Thank you1 solutions Answer 388067 by solver91311(17074)   on 2012-06-01 18:17:11 (Show Source): You can put this solution on YOUR website! The roof is part of the outside surface of the house, the problem is you haven't provided enough information. Which side of the house (the 45' side or the 34' side) is parallel to the ridgeline of the roof? You have two rectangles that form the roof, each having a length that is either 34 or 45 feet and a width that you have to calculate using Pythagoras; that width being the hypotenuse of a right triangle with one leg of 4 feet (14 minus 10) and the other leg being either 17 feet (half of 34) or 22.5 feet (half of 14). Then you need to calculate the areas of the sides of the house. First you have two 10 by 34 rectangles and tow 10 by 45 rectangles. Then, depending on which dimension is parallel to the ridge line, you have two isosceles triangles with bases of 34 or 45 and a height of 4. John My calculator said it, I believe it, that settles it
 Geometry_Word_Problems/616959: a photographer has 2 photos, each with same area. One is a square, the other a rectangle. If the length of the rectangle is 3 inches greater and the width is 2 inches shorter than the length of one side of the square, what are the dimensions of each photo? 1 solutions Answer 388063 by solver91311(17074)   on 2012-06-01 17:56:35 (Show Source): You can put this solution on YOUR website! Let represent the measure of one side of the square, then the length of the rectangle is and the width of the rectangle is The area of the square is just And the area of the rectangle is And these two areas are the same, so: Expand the pair of binomials, collect like terms, and solve for John My calculator said it, I believe it, that settles it
 Human-and-algebraic-language/616979: 3. You recently started the paperwork to purchase your new home, and were just notified that you can move into the house in 2 weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested in contacting two companies, Heavy Lifting and Quick Move, to discuss their rates. Heavy Lifting charges an $80 fee plus$35 per hour. Quick Move charges $55 per hour with no additional fees. a. Which mover provides a better deal for 2 hours of work? How did you arrive at your answer? b. Which mover provides a better deal for 15 hours of work? How did you arrive at your answer? c. For what values h (hours) does Quick Move offer the better deal? Express your answer as an inequality. Explain how you reached your answer. 1 solutions Answer 388060 by solver91311(17074) on 2012-06-01 17:48:20 (Show Source): You can put this solution on YOUR website! Tell us what parts of this you don't understand. Explain what you have done so far. John My calculator said it, I believe it, that settles it  Human-and-algebraic-language/616976: The sales representative informs you that there are 56 houses for sale with two floor plans still available. Use x to represent floor plan one and y to represent floor plan two. Write an equation that illustrates the situation. b. The sales representative later indicates that there are three times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in Part a. c. Use the equations from Parts a. and b. of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem. d. What are the intercepts of the equation from Part a. of this problem? What are the intercepts from Part b. of this problem? Where would the lines intersect if you solved the system by graphing? 1 solutions Answer 388059 by solver91311(17074) on 2012-06-01 17:48:01 (Show Source): You can put this solution on YOUR website! Tell us what parts of this you don't understand. Explain what you have done so far. John My calculator said it, I believe it, that settles it  Circles/616977: Suppose the circumference of a circle is 15π. What is its diameter?1 solutions Answer 388057 by solver91311(17074) on 2012-06-01 17:45:53 (Show Source): You can put this solution on YOUR website! Where represents the circumference and represents the diameter. Substitute what you know and then solve for what you don't know. John My calculator said it, I believe it, that settles it  Human-and-algebraic-language/616978: 2. As you are leaving the community, you notice another new community just down the street. Because you are in the area, you decide to inquire about it. a. The sales representative here tells you they also have two floor plans available, but they only have 38 homes still for sale. Write an equation that illustrates the situation. Use x and y to denote floor plan one and floor plan two respectively. b. The representative tells you that floor plan one sells for$175,000 and floor plan two sells for $200,000. She also mentions that all the available houses combined are worth$7,200,000. Write an equation that illustrates this situation. Use the same variables you used in Part a. c. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer. 1 solutions Answer 388056 by solver91311(17074)   on 2012-06-01 17:39:49 (Show Source): You can put this solution on YOUR website! Tell us which part of this you don't know how to do. Explain what you have tried so far. John My calculator said it, I believe it, that settles it
 expressions/616964: Please solve and write the solution using set builder notation: x+3>-5/4 Thank you, Janice 1 solutions Answer 388053 by solver91311(17074)   on 2012-06-01 17:28:12 (Show Source): You can put this solution on YOUR website! Which is it that you don't know how to do: Solve the inequality or express the answer in set builder notation? To solve the inequality, add -3 to both sides then do the arithmetic to collect like terms in the RHS. See Set Builder Notation for the other part. John My calculator said it, I believe it, that settles it
 Polynomials-and-rational-expressions/616968: please help. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval. f(x) = 8x^3 - 10x^2 + 3x + 5; [-1, 0]1 solutions Answer 388050 by solver91311(17074)   on 2012-06-01 17:15:51 (Show Source): You can put this solution on YOUR website! If where, presuming real function values: $\sgn(x) = \begin{cases} -1 & \text{if } x < 0, \\ 0 & \text{if } x = 0, \\ 1 & \text{if } x > 0. \end{cases}$ then has a real zero on [] John My calculator said it, I believe it, that settles it
 Numeric_Fractions/616970: Can you please give me the answer to this equation, and explain how the answer was derived? If 5x + x² > 100, then x is not Thank you.1 solutions Answer 388044 by solver91311(17074)   on 2012-06-01 17:00:14 (Show Source): You can put this solution on YOUR website! It is impossible to do what you ask. You can't solve an equation that doesn't exist. What you have provided is an inequality, NOT an equation. On the other hand, you need to turn it into an equation in order to determine the solution set interval. Step 1: Replace the inequality sign with an equals sign. Step 2: Put the equation into standard quadratic form. Step 3: Evaluate the discriminant, i.e., , to determine that the quadratic does not factor over the rationals. Step 4: Use the quadratic equation to find the conjugate pair of irrational roots of the equation. Step 5: Divide the -axis into three regions, up to the smaller value root, the smaller value root to the larger value root, and the larger value root to . Step 6: Select any one of the three intervals, and select a value from that interval that is NOT an endpoint value. Substitute this value into the original inequality and do the arithmetic. Step 7: If the result of step 6 is a true statement, then the interval selected is contained in the solution set of the inequality. Otherwise not. Step 8: Repeat steps 6 and 7 for each of the other intervals. Use the results to fully describe the solution set. Generally, interval notation is best. John My calculator said it, I believe it, that settles it
 Coordinate-system/616972: graph the linear equation: -2x+5y=-10 1 solutions Answer 388039 by solver91311(17074)   on 2012-06-01 16:44:25 (Show Source): You can put this solution on YOUR website! Step 1. Pick a value for x. It can be anything you like, but 0, 1, or some other small integer usually works well and makes the arithmetic easier. Step 2. Substitute that value in place of x in your equation. Do the arithmetic and determine the value of y that results. Step 3. Take the value of x that you selected for step 1 and the value of y that you calculated in step 2 and form an ordered pair (x,y). Step 4. Plot the ordered pair from Step 3 on your graph. Remember that the x value is the distance right or left along the horizontal axis and the y value is the distance up or down along the vertical axis. Step 5. Repeat steps 1 through 4 with a different value for x. Step 6. Draw a line across your graph that passes through the two points that you plotted. John My calculator said it, I believe it, that settles it
 Square-cubic-other-roots/616973: Simplify the following expression; express in terms of i. sqrt sign then -16 1 solutions Answer 388038 by solver91311(17074)   on 2012-06-01 16:42:53 (Show Source): You can put this solution on YOUR website! so so John My calculator said it, I believe it, that settles it
 Mixture_Word_Problems/616946: A new lab technician, on his first day on the job, drops his lab key into a large bottle of concentrated nitric acid, and key begins to dissolve. the mass of the key is 2.03 oz (1 oz=28.35g) and has a density of 6.347 g/cm^3. The acid dissolves the key at a rate of 0.00235 g/s. By the time the lab tech gets the key out of acid, 10.0 minutes have passed.What is the volume of the key by then? I solved this then but I feel like the answer is wrong. 1 solutions Answer 388034 by solver91311(17074)   on 2012-06-01 16:38:46 (Show Source): You can put this solution on YOUR website! First calculate the number of grams of mass in the key before it went in the acid. Next, calculate the number of grams lost in 10 minutes: Next, calculate the mass remaining after 10 minutes, i.e. what it was minus what it lost: Then divide the final mass by the density to calculate the volume: John My calculator said it, I believe it, that settles it
 Miscellaneous_Word_Problems/616950: John rents a booth for $35.00 a day and sells ice cream cones. His cost for each cone is$2.00 and he sells the cones for $5.00 each. If John wants to make at least a$200.00 profit for the day, how many ice cream cones must he sell? a. 34 b. 78 c. 79 d. 118 Which would be the correct answer and please explain, the way to arrive at the answer... please..1 solutions Answer 388022 by solver91311(17074)   on 2012-06-01 15:26:46 (Show Source): You can put this solution on YOUR website! He sells them for $5 each, so his revenue function is where is the number sold. His cost function is because of the$2 per cone cost plus the $35 fixed rental cost. Profit is revenue minus cost, so: So if you want the value of to be at least$200, Solve for and round UP to the nearest whole number (because you can't sell a fraction of an ice cream cone). John My calculator said it, I believe it, that settles it
 Geometry_Word_Problems/616953: I am asked to draw a figure and then draw another one with a 3:5 ratio of the 1st figure. So I drew a 2 by 2 square. How big would the next figure be?1 solutions Answer 388021 by solver91311(17074)   on 2012-06-01 15:16:25 (Show Source): You can put this solution on YOUR website! Cross-multiply and solve for John My calculator said it, I believe it, that settles it
 test/616954: x/8=x/9-41 solutions Answer 388020 by solver91311(17074)   on 2012-06-01 15:14:11 (Show Source): You can put this solution on YOUR website! Multiply both sides by 72, then add to both sides. John My calculator said it, I believe it, that settles it
 Trigonometry-basics/616932: 1. Complete the last step to prove the following identity. Express answer in terms of sin and/or cos only. cot B sec B=csc B 2. Change this problem to an expression of sin and/or cos only. tan A - sec A = 3. Complete the last step to prove the following identity. Express answer in terms of tangent and/or cotangent only. (1+tan^(2)x)/(tan^(2)x)=csc^(2)x1 solutions Answer 388014 by solver91311(17074)   on 2012-06-01 12:43:34 (Show Source): You can put this solution on YOUR website! 2. John My calculator said it, I believe it, that settles it
 Polynomials-and-rational-expressions/616939: i need your help with adding and subtracting rational expressions. can you help me? 1 solutions Answer 388012 by solver91311(17074)   on 2012-06-01 12:36:50 (Show Source): You can put this solution on YOUR website! Only if you go back and read the rules for submission. Especially read the part that compares a bad question to a good question. Write back when you understand that your question is a poster child for a bad question. John My calculator said it, I believe it, that settles it
 Conjunction/616941: how do you solve -5<_ a+2<3?1 solutions Answer 388011 by solver91311(17074)   on 2012-06-01 12:36:09 (Show Source): You can put this solution on YOUR website! Add -2 to all three parts of your compound inequality. John My calculator said it, I believe it, that settles it
 Average/616940: if i get 94 on the last semester and i get a 62 on the last exam, whats my final average?1 solutions Answer 388009 by solver91311(17074)   on 2012-06-01 12:33:45 (Show Source): You can put this solution on YOUR website! Insufficient information. You haven't supplied the relative weight of the previous semester's work as compared to the final exam. Please describe your situation in more detail. Also remember that attention to detail regarding capitalization, punctuation, spelling, and the rules of good grammar tends to facilitate effective communication. What you did write makes it nearly impossible to comprehend what you want. John My calculator said it, I believe it, that settles it
 Triangles/616924: if one leg of a 30, 60 ,90 degree triangle has a length of 6 and the adjacent angel is 30 , what is the exact length of the hypotenuse in simplest radical form1 solutions Answer 388006 by solver91311(17074)   on 2012-06-01 12:28:03 (Show Source): You can put this solution on YOUR website! If you have a question that involves an "angel", adjacent or otherwise, please ask the local clergyperson or tribal shaman of your personal choice. In the event you actually meant "angle", read on: The short leg of a 30-60-90 right triangle always measures one-half the measure of the hypotenuse. C.f. . So if you have a right triangle where one leg measures 6, another leg measures and the hypotenuse measures , then, according to Mr. Pythagoras: Solve for . John My calculator said it, I believe it, that settles it
 Trigonometry-basics/616705: find the measure of angle x in the interval 180 is greater than or equal to x greater than or equal to 270 that satisfies the equation 2cosx+1=01 solutions Answer 387850 by solver91311(17074)   on 2012-05-31 17:47:56 (Show Source): You can put this solution on YOUR website! No such interval. No value of can satisfy . I'm pretty sure you meant , i.e. the third quadrant. Solve for Refer to the unit circle: Find a 3rd quadrant angle where the terminal ray intersects the unit circle in a point with an -coordinate. John My calculator said it, I believe it, that settles it
 Rectangles/616703: Question: Determine the dimension of a rectangle with a perimeter of 40cm and the greatest possible area. Book's answer is: 10cm by 10cm I do not get how can you get 10cm by 10cm, if it is a rectangle. Please help me! Thank you.1 solutions Answer 387847 by solver91311(17074)   on 2012-05-31 17:34:23 (Show Source): You can put this solution on YOUR website! A square is just a special case of a rectangle. There is nothing wrong with calling a square a rectangle any more than it is wrong to call a square a rhombus, parallelogram, or just a plain old quadrilateral. Having said that, given a rectangle with length , width , perimeter , and area , we can first describe the length in terms of the width and the perimeter: Substituting this into the area formula, we create a function for area in terms of width: Rearranging in to standard quadratic form: Recognizing that this second degree polynomial function in graphs to a parabola, opening downward because of the negative lead coefficient, that must have a vertex as a maximum function value. Using the fact that has a vertex at , we can find the vertex of our function: This means that the maximum of the function, that is to say the maximum area rectangle for any given perimeter is a rectangle with a width one-fourth of the perimeter. If the width is one-fourth, two times the width has to be one-half of the perimeter, leaving one-half of the perimeter to account for two times the length, hence the length must also be one-fourth of the perimeter. John My calculator said it, I believe it, that settles it
 Linear-equations/616676: Find the equation of the line that passes through the points (–4, -1) parallel to 6x-y=61 solutions Answer 387844 by solver91311(17074)   on 2012-05-31 17:13:14 (Show Source): You can put this solution on YOUR website! You cannot find "the" equation of any line. You can only write "an" equation of a line. In the first place, you could just substitute the values in the point-slope form and have an equation of the desired line, or you could solve for to put it into slope-intercept form, or you could rearrange it into standard form, namely . Furthermore, for a given , , and , where describes a set of equations with an infinite number of elements, each of which graphs to the same line in . First put your given equation into slope intercept form. Make sure that the coefficient on is reduced to lowest terms if necessary. Then, by inspection of the coefficient on you can determine the slope of the given line. Parallel lines have equal slopes. Use the point-slope form of an equation of a line, the given point and the slope determined as described to write an equation of your desired line. where are the coordinates of the given point and is the given/calculated slope. Follow your instructor's or textbook's instructions as to form of your answer. John My calculator said it, I believe it, that settles it
 Average/616693: A student scores 70 out of 100 on a test. If the maximum score on the next test is also 100 points, what score does the student need to maintain at least an average of 78?1 solutions Answer 387842 by solver91311(17074)   on 2012-05-31 17:03:37 (Show Source): You can put this solution on YOUR website! The average of a set of numbers is the sum of the numbers divided by the number of numbers. Here we will have two scores that when added together and then divided by 2 must equal 78. So when added together must be 2 times 78. So what score would you need to add to 70 so that the sum is equal to 2 times 78? John My calculator said it, I believe it, that settles it
 Linear_Equations_And_Systems_Word_Problems/616699: Fourteen oranges cost $2.00. How many oranges can be bought for$5.00? 1 solutions Answer 387840 by solver91311(17074)   on 2012-05-31 17:00:56 (Show Source): You can put this solution on YOUR website! $5 divided by$2 is a factor of 2.5. John My calculator said it, I believe it, that settles it
 Surface-area/616695: Matthew is in charge of registration for the science fair.Each science project is created by a team of three students.If there are 67 projects, how many students will Matthew register?1 solutions Answer 387839 by solver91311(17074)   on 2012-05-31 16:58:31 (Show Source): You can put this solution on YOUR website! Depends on whether any given student is allowed to be on more than one team. If that is possible, the question cannot be answered with the given information. But if such is not allowed there will be 3 students for each of the 67 projects. So you can add 3 + 3 + 3 + ... (67 times), or you could add 67 + 67 + 67, or you could just do it the simplest way: Multiply 3 times 67. John My calculator said it, I believe it, that settles it
 Triangles/616691: How to find the area of a parallelogram with the given vertices. P(1,3) Q(3,3) R(7,8) S(9,8). Please explain. 1 solutions Answer 387837 by solver91311(17074)   on 2012-05-31 16:53:40 (Show Source): You can put this solution on YOUR website! The difference in the x-coordinates of either of the bases is 2; 3 - 1 = 2 and 9 - 7 = 2, hence the measure of the base is 2. The difference in the y-coordinates is 8 - 3 = 5, so the altitude is 5. Use the formula for the area of a parallelogram. John My calculator said it, I believe it, that settles it
 Average/616679: if a student has scores of 76,95,71, and 72 and she wants to have 75% grade for the semister what would be the minuim grade she can get if she took her last quiz choices A-61 B-65 C-92 D-931 solutions Answer 387836 by solver91311(17074)   on 2012-05-31 16:41:12 (Show Source): You can put this solution on YOUR website! At the end of the semester, the average is going to be calculated by taking the sum of the 5 scores and dividing by 5. If you want the result to be at least 75, then the sum of all 5 scores has to be at least 75 times 5. John My calculator said it, I believe it, that settles it
 Surface-area/616688: the area of a rectangle is 120 square cm. If its width is 10cm, what is its length? 1 solutions Answer 387835 by solver91311(17074)   on 2012-05-31 16:37:08 (Show Source): You can put this solution on YOUR website! Since the area was calculated by length times width, divide the area by the width to get the length. John My calculator said it, I believe it, that settles it