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# Recent problems solved by 'richard1234'

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 Circles/464099: what is the result when number of sides of a circle is multiplied by zero?1 solutions Answer 317907 by richard1234(5390)   on 2011-06-24 11:12:56 (Show Source): You can put this solution on YOUR website!The result is not really defined because you're taking an infinite (or undefined) number and multiplying it by zero, which does not necessarily result in 0. For example, if we try to evaluate the product Since and we might be tempted to say the answer is infinity times zero, when the answer is just 1.
 Rational-functions/464091: 61-(-7)1 solutions Answer 317906 by richard1234(5390)   on 2011-06-24 11:07:37 (Show Source): You can put this solution on YOUR website!61 - (-7) = 61 + 7 = 68
 Word_Problems_With_Coins/464101: I have 18 pesos money. How many stamps of 1.4 pesos each can I buy? how much is my change?1 solutions Answer 317905 by richard1234(5390)   on 2011-06-24 11:06:39 (Show Source): You can put this solution on YOUR website!18/1.4 = 12.85... but we round down to 12 because you cannot buy part of a stamp. So the maximum number of stamps you can buy is 12. If you buy 12 stamps you will spend 16.8 pesos, and the amount of change is 18 - 16.8 = 1.2 pesos.
 Miscellaneous_Word_Problems/464058: A 100kg Brick On The Moon. If The Moon Had 5x Less Gravity Than Earth, What Would The Weight Of The Brick Now?1 solutions Answer 317901 by richard1234(5390)   on 2011-06-24 10:17:29 (Show Source): You can put this solution on YOUR website!Technically, the kilogram is a unit of mass (not weight, the two are different), so the mass of the brick on Earth is 100 kg and the weight of the brick on Earth would be
 Quadratic_Equations/463888: p(x)=-2x^2+39x-132 find the maximun and minimum i belive the vertex is (9.75,566.65)1 solutions Answer 317746 by richard1234(5390)   on 2011-06-23 16:37:51 (Show Source): You can put this solution on YOUR website!I assumed you meant -2x^2 + 39x - 132 so I changed it. The x-coordinate of the vertex occurs at -39/(2*-2) = 9.75. Also, p(39/4) = 58.125, so the coordinate of the vertex is (9.75, 58.125). This vertex is the maximum of the parabola, because it opens downward. There is no minimum because the parabola goes to negative infinity as x gets really large (or small).
 Rectangles/463891: I just finished a math exam and theres one question that I just couldn't figure out. It went like this: "A rectangular field has an 800m long fence around the perimeter. The area of the field is 37500m^2. What are the diemensions of the field." I think im supposed to use Substitution so I wrote the formulas I know that relate to the question and I plugged in the information from the question into the equation so it was like this: "P(perimeter)=2*L(length)+2*width & A(area)=L*W. After this I dont know what to do. I can eliminate be the operations are different so the only option is to change an equation to isolate a variable to substitute it into the next equation but I don't know. No hurry gettin back to me the exams already done im just asking to ease my mind1 solutions Answer 317744 by richard1234(5390)   on 2011-06-23 16:36:36 (Show Source): You can put this solution on YOUR website!We know the perimeter is 800 m and the area is 37500m^2, so 800 = 2L + 2W --> L + W = 400 LW = 37500 From the equation L + W = 400 we can isolate L and say L = 400 - W. Plug this into the expression for area: (400-W)W = 37500 -W^2 + 400W - 37500 = 0 W^2 - 400W + 37500 = 0 By factoring or by the quadratic formula, we get W = 150 or W = 250. This implies the other dimension is 250 or 150 (order doesn't matter since we can choose a different L. The dimensions are basically 150x250).
 Linear-equations/463835: What is the slope of a line that is parallel to the line represented by the equation y-2x=7?1 solutions Answer 317722 by richard1234(5390)   on 2011-06-23 12:00:59 (Show Source): You can put this solution on YOUR website!y - 2x = 7 y = 2x + 7 This line, as well as all other lines parallel to this one, have a slope of 2.
 Points-lines-and-rays/463634: Find the midpoint coordinates of the segment that connects the following given points: (8, a + 7) and (5, a + 11)1 solutions Answer 317721 by richard1234(5390)   on 2011-06-23 11:58:24 (Show Source): You can put this solution on YOUR website!Just take the average of the x-coordinates and average of the y-coordinates.
 Trigonometry-basics/463788: What is the exact value of cos 0° as found on the unit circle?1 solutions Answer 317720 by richard1234(5390)   on 2011-06-23 11:56:26 (Show Source): You can put this solution on YOUR website!If you draw the angle 0 degrees on a unit circle, you will see the x-coordinate is 1. Hence cos(0) = 1.
 Numbers_Word_Problems/463816: The number 48 is divisible by its unit’s digit, 8. How many two digit numbers are divisible by their units’ digit? a) 31 b) 41 c) 50 d) 55 e) none of the above1 solutions Answer 317719 by richard1234(5390)   on 2011-06-23 11:54:06 (Show Source): You can put this solution on YOUR website!We go case by case, by units digit: 0 - Nothing is "divisible" by 0 since division by zero is undefined. 1 - Any number is divisible by 1, so all of the numbers {11, 21, ..., 91} (9 numbers) 2 - Any number ending in 2 is divisible by 2, {12, 22, ..., 92} (9 numbers) We continue to go case by case, up to 9: 3 - {33, 63, 93} (3 numbers) 4 - {24, 44, 64, 84} (4 numbers) 5 - {15, 25, ..., 95} (9 numbers) 6 - {36, 66, 96} (3 numbers) 7 - {77} (1 number) 8 - {48, 88} (2 numbers) 9 - {99} (1 numbers) The total number of numbers is 9+9+3+4+9+3+1+2+1 = 41, answer choice b). An easy way to generate all numbers is to start with the original number and add any multiple of the LCM of that number and 10. Here, if we use 4, we start with 4 and add multiples of LCM(4, 10). The LCM of 4 and 10 is 20, so we can add any multiple of 20 to get {24, 44, ...}. This would be particularly useful if we wanted to count all the numbers from 1 to 1000 that satisfied this property.
 Rectangles/463792: Can a Golden Rectangle have a shorter base than height?1 solutions Answer 317718 by richard1234(5390)   on 2011-06-23 11:42:50 (Show Source): You can put this solution on YOUR website!Yes, because you can label either side the base. Here, just label the shorter side the base.
 Subset/463808: Lessons Course Information Assessments Gradebook Email Discussion Groups ChatRoom Whiteboard My Folders Students Technical Support Announcements Other Courses Logoff Web 2.0 Tools User: esterlande prince In Course: EL Algebra I v10 ( 3092) Instructor: Deborah Stone WARNING: You must not leave this exam form! If you try to click back into this exam again prior to submitting, your access to it will be denied! 03.11 Module Three Test Warning: There is a checkbox at the bottom of the exam form that you MUST check prior to submitting this exam. Failure to do so may cause your work to be lost. Question 1 (Multiple Choice Worth 4 points) [3.06] If f(x) = x + 3, find the value of x if f(x) = 9. 6 12 3 9 Question 2 (Multiple Choice Worth 4 points) [3.06] If f(x) = −3x + 1, find f(−2). 7 −5 −4 6 Question 3 (Yes/No Worth 3 points) [3.05] Is the following relation a function? Yes No Question 4 (Multiple Choice Worth 3 points) [3.05] Which of the following does not represent a function? Question 5 (Multiple Choice Worth 3 points) [3.01] Choose the correct statement about the given Venn Diagram. A total of 17 people were surveyed. Everyone surveyed like cake and cookies. A total of 3 people surveyed like cookies. A total of 14 people surveyed like cake. Question 6 (Multiple Choice Worth 4 points) [3.06] If g(x) = x2 − 3, find g(4). 13 5 16 −3 Question 7 (Multiple Choice Worth 4 points) [3.03] If U = {all university students} and subset F = {the female students at the university}, what is F′? {seniors at the university that are female} {male university students} {female professors at the university} none of the above Question 8 (Multiple Choice Worth 4 points) [3.06] Given the function g(x) = 8x − 2, compare and contrast g(−2) and g(4). Choose the statement that is true concerning these two values. The value of g(−2) is larger than the value of g(4). The value of g(−2) is the same as the value of g(4). The value of g(−2) is smaller than the value of g(4). The values of g(−2) and g(4) cannot be compared. Question 9 (Multiple Choice Worth 4 points) [3.03] Let A = {red, blue, yellow} and let B = {1, 2}. Find A X B. {(red, 1), (red, 2), (blue, 1), (blue, 2), (yellow, 1), (yellow, 2)} {red, blue, yellow, 1, 2} { } {1, 2} Question 10 (Multiple Choice Worth 3 points) [3.01] Which of the following is a subset of the set A: {children between the ages of 3 and 7} {children over 7} {children under 3} {a 10 year old child} {children between the ages of 4 and 6} Question 11 (Multiple Choice Worth 3 points) [3.01] Which of the following does not represent the set of even integers from 1 to 20? {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} {2, 4, 6, …, 16, 18, 20 } {2, 4, 6, 8, …} {even integers from 1 to 20} Question 12 (Multiple Choice Worth 4 points) [3.05] Choose the relation with a range of {−2, −1, 2, 4, 5}. R = {(−2, −1), (2, 2), (4, 5)} R = {(5, 6), (−1, 3), (−2, 5), (4, 5), (2, 8)} R = {(5, 4), (2, 2), (−1, −2)} R = {(−3, 5), (−6, 4), (−2, 2), (5, −2) (0, −1)} Question 13 (Multiple Choice Worth 4 points) [3.06] If f(x) = 2x + 8, find f(9). 18 19 8 26 Question 14 (Multiple Choice Worth 4 points) [3.05] Which of the following does not represent a function? x 1 3 5 7 y 7 11 15 11 x −4 −2 0 2 y 3 −1 −5 −9 x −4 −3 −2 −1 y −32 −18 −8 −2 x −3 2 6 2 y 0 1 5 4 Question 15 (Multiple Choice Worth 4 points) [3.02] If A = {0, 1, 2, 3} and B = {integers}, what is A ∩ B? {…−3, −2, −1, 0, 1, 2, 3, …} { } {0} {0, 1, 2, 3} Question 16 (Multiple Choice Worth 4 points) [3.02] If A = {red, orange, black, grey} and B = {red, orange, yellow, green, blue, indigo, violet}, what is A B? {red, orange} {red, orange, black, grey} { } {red, orange, yellow, green, blue, indigo, violet, black, grey} Question 17 (Multiple Choice Worth 3 points) [3.05] The range of the relation below is x y −3 10 2 8 2 4 0 4 {4, 8, 10} {0, 2, −3} {4, 4, 8, 10} No range exists. Question 18 (Multiple Choice Worth 4 points) [3.05] Choose the relation with a domain of {−2, −1, 2, 4, 5}. R = {(−3, 5), (−6, 4), (−2, 2), (5, −2) (0, −1)} R = {(−2, 1), (2, 2), (4, 5)} R = {(5, −3), (4, −6), (2, −2), (−2, 5) (−1,0)} R = {(5, 4), (2, 2), (1, −2)} Question 19 (Multiple Choice Worth 3 points) [3.03] If N = {positive integers} and subset C = {positive even integers}, what is C′? {1, 3, 5, 7, …} { } {… −7, −5, −3, −1} {2, 4, 6, 8, …} Question 20 (Multiple Choice Worth 3 points) [3.05] The domain of the following relation: R: {(3, −3), (1, 6), (−5, −4), (−10, 6)} is {−10, −5, 1, 3} {−4, −3, 6} {6} No domain exists Question 21 (Multiple Choice Worth 4 points) [3.02] If C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} and D = {numbers divisible by 6 from 1 to 12}, what is C ∩ D? {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} {6} { } {6, 12} Question 22 (Essay Worth 6 points) [3.06] John is going to rent a tent to go camping. The cost to rent a camping tent from Woodland Outfitters is a flat rate of $12.00 plus$2.00 for each night the tent is rented. Part a. Let x represent the number of nights John keeps the tent and write a cost function, c(x), for the cost to rent a tent from Woodland Outfitters. Part b. How much will John owe if he uses the tent for three nights? Question 23 (Essay Worth 6 points) [3.05] In your own words, explain what the domain of a relation is and give an example. Question 24 (Essay Worth 6 points) [3.02] Create two sets A and B. State what each set is and find A B. Question 25 (Essay Worth 6 points) [3.03] Let A = {2, 4, 6} and let B = {circle, square}. Find A X B. YOU MUST CHECK THE BOX BELOW PRIOR TO SUBMITTING YOUR EXAM! Check this box to indicate you are ready to submit your exam You have 9 Unread E-Mail Messages Instructors monitor ALL areas of a student's account Student e-mail accounts are to be used for FLVS course-related email only and not for general introductions or spamming of people in your address book. Please remember to click the Logoff link when you have completed your work in the course. Related Help Center Topics Taking Exams Proctored Exams Question Types 1 solutions Answer 317716 by richard1234(5390)   on 2011-06-23 11:28:30 (Show Source): You can put this solution on YOUR website!The instructions that appear on this site before posting problems say "one question per post." I can quickly tell you copied and pasted this from some algebra site. Read up on the curriculum first (e.g. sets, functions) and try to solve as many questions as possible. Only post the ones you are having trouble with.
 Subset/463814: Without writing them all out, what is the number of subsets of set B = {3, 6, 9, 12, 15}?1 solutions Answer 317715 by richard1234(5390)   on 2011-06-23 11:26:34 (Show Source): You can put this solution on YOUR website!There are five elements, so the number of subsets is 2^5 = 32.
 Angles/463453: Question: Find the Complement of the angle measure ANGLE MEASURE 1.) 37 degrees 2.) 48 degrees 3.) 20 degrees 4.) x degrees 5.) (2x+ 10) degrees EQUATION 1.) 37+c=90 2.) 48+c=90 3.) 20+c=90 4.) x+c=90 5.) _______ COMPLEMENT 1.) 53 degrees 2.) 42 degrees 3.) 70 degrees 4.) ________ 5.) ________ In equation number 1, I just transposed 37 to the right and then I subtract 37 to 90 that's how I got 53 degrees as the complement of the angle measure. But I just couldn't figure out question number 4 and number 5. There are more Questions but I already answered them I just gave Numbers 1,2,and 3 as examples that you can base on.1 solutions Answer 317636 by richard1234(5390)   on 2011-06-22 19:52:12 (Show Source): You can put this solution on YOUR website!Just subtract each angle from 90. The fact that there are variables shouldn't make it any harder. 4: Complement = 90 - x 5: Complement = 90 - (2x + 10) = 80 - 2x
 Quadratic_Equations/463659: How is the zero product property used to solve a quadratic equations? What would be an good example of this?1 solutions Answer 317633 by richard1234(5390)   on 2011-06-22 19:46:13 (Show Source): You can put this solution on YOUR website!Sometimes if a quadratic, for example x^2 - 5x + 4 = 0 factors to (x-4)(x-1) = 0, we can deduce that the roots occur when x-4 = 0 or x-1 = 0, i.e. x = 4 or 1.
 Polynomials-and-rational-expressions/463155: multiply and simplify. assume variables represent nonzero real numbers. z^11*z^01 solutions Answer 317631 by richard1234(5390)   on 2011-06-22 19:34:06 (Show Source): You can put this solution on YOUR website!(z^11)(z^0) = z^11
 Travel_Word_Problems/463653: find the distance (d) traveled by a train moving at the rate (r) of 50mi/h for the time (t) of 3 hr using the formula d = rt.1 solutions Answer 317630 by richard1234(5390)   on 2011-06-22 19:32:56 (Show Source): You can put this solution on YOUR website!Replace r and t into the equation: d = (50 mi/hr)(3 hr) = 150 miles
 Equations/463547: If 7x^2 + 4x = 3 , which of the following is (are) true? I. The sum of the solutions is positive. II. The product of the solutions is negative. III. Both solutions are integers. a) I only b) II only c) III only d) I and II only e) II and III only1 solutions Answer 317629 by richard1234(5390)   on 2011-06-22 19:26:32 (Show Source): You can put this solution on YOUR website! Know Vieta's formulas, which say that if you have a polynomial Then the sum of the roots is and the product of the roots is (plus, a whole bunch of other identities can be derived but we won't need them here). Here, the sum of the solutions is -4/7, which is not positive, so I is not true. The product of the solutions is (-3)/7, negative, so II is true. We automatically know III cannot be true since if both solutions were integers, their sum would be an integer, but we already know I is not true. Hence, only II is true; answer is B. For certain math problems, it can help to find a slick, fast solution. Here we were able to do it without even finding the roots of the quadratic.
 Quadratic-relations-and-conic-sections/463573: The cardinal number of the set {rose, daisy, sunflower, marigold, azalea, orchid, lily, carnation, tulip, and violet} is _________.1 solutions Answer 317627 by richard1234(5390)   on 2011-06-22 19:19:59 (Show Source): You can put this solution on YOUR website!Count the number of elements in the set. That is the cardinal number (or cardinality).
 Surface-area/463612: A cube has an edge length represented by x - 3. Find the surface area of the cube.1 solutions Answer 317625 by richard1234(5390)   on 2011-06-22 19:18:52 (Show Source): You can put this solution on YOUR website!Other tutor did x-2, not x-3. The surface area of a rectangular prism is SA = 2LW + 2WH + 2LH, but in the case of a cube, it can be reduced to 6s^2, where s is the side length. Here, s = x-3, so SA = 6(x-3)^2 = 6(x^2 - 6x + 9) = 6x^2 - 36x + 54
 Graphs/463644: Find the slope of each of the three line segments in the graph below. Please show all of your work. Between which two points is the slope the largest? 1 solutions Answer 317624 by richard1234(5390)   on 2011-06-22 19:16:02 (Show Source): You can put this solution on YOUR website!You've basically given me the hamburger without the meat. In other words, you've given me the graphing question without the graph.
 Numbers_Word_Problems/463627: Find three positive numbers a, b, and c such that 18 times "a" plus 13 times "b" plus 8 times "c" equals 135, and such that the product of a, b and c is a maximum.1 solutions Answer 317623 by richard1234(5390)   on 2011-06-22 19:12:31 (Show Source): You can put this solution on YOUR website! By the AM-GM inequality, we can say that The AM-GM inequality states that equality occurs when all the "terms" (18a, 13b, 8c) are equal, i.e. 18a = 13b = 8c = 135/9 = 15. Hence, a = 5/6, b = 15/13, and c = 15/8.
 real-numbers/463475: Determine what is wrong with the following simplification. x^2+y^2/x =x+y^2 Give an example that shows why this is incorrect. What should x^2+y^2/x equal ??1 solutions Answer 317569 by richard1234(5390)   on 2011-06-22 12:47:46 (Show Source): You can put this solution on YOUR website!You need to divide the y^2 by x. Here,
 real-numbers/463472: Please help me solve the following problem: Given that a/a= a^0 = 1 where "a" is a real number. Does this hold for all real numbers or should we add a disclaimer about a? If a disclaimer is needed, what should it say?1 solutions Answer 317558 by richard1234(5390)   on 2011-06-22 12:06:43 (Show Source): You can put this solution on YOUR website!It doesn't hold when a = 0. In this case, we say that 0/0 is indeterminate (unlike "undefined," indeterminate means that 0/0 can equal any number such that it is impossible to determine a unique answer. "Undefined" means that there is no such possible finite answer, such as 1/0.).
 Volume/462794: The base of the cylinder has an area of 10 square inches. what is the volume of the cylinder in cubic inches. 1 solutions Answer 317385 by richard1234(5390)   on 2011-06-21 12:13:43 (Show Source): You can put this solution on YOUR website!Need to know the height of the cylinder. Once you know the height, multiply by 10 in^2 to find the volume.
 Equations/462556: Find the numbers preceding and succeeding the following number. EEE Base twelve The preceding number is ___ base twelve. The succeeding number is ___ base twelve. 1 solutions Answer 317383 by richard1234(5390)   on 2011-06-21 12:11:46 (Show Source): You can put this solution on YOUR website!EEE is not a base 12 number, unless you are using digits other than 1-9, A and B. In this case, know the digits immediately before and after E, and know when to regroup, similar to regrouping in base 10 addition.
 Linear-equations/463181: How do I Graph X + Y > 1? I have been trying for two days! Please show me.1 solutions Answer 317382 by richard1234(5390)   on 2011-06-21 12:05:12 (Show Source): You can put this solution on YOUR website!Two days? All you need to do is graph x+y = 1, then shade the area above it, since you want x+y to be greater than 1. To graph it more easily, write it as y > 1 - x, graph the equation y = 1 - x, then shade everything above it. It is sometimes conventional to draw a dashed line through y = 1 - x, indicating that it is not part of the function.
 Miscellaneous_Word_Problems/463076: A person Who can Appreciates art, music etc.?1 solutions Answer 317381 by richard1234(5390)   on 2011-06-21 12:01:19 (Show Source): You can put this solution on YOUR website!Is this person right-brained?
 test/463167: How many positive integers less than 1,000 are multiples of 5 and are equal to 3 times an even integer.1 solutions Answer 317380 by richard1234(5390)   on 2011-06-21 11:59:22 (Show Source): You can put this solution on YOUR website!"Equal to 3 times an even integer" is just a strange, tricky way of saying "is a multiple of 6." Also, if a number is a multiple of 5 and 6, it must be a multiple of 30. Here, all we have to do is count the multiples of 30 up to 1000, which are 30, 60, 90, ..., 990, or 33 numbers.
 test/463168: If notebooks cost $2 each and backpacks cost$32 each, which of the following represents the cost, in dollars, of n notebooks and b backpacks?1 solutions Answer 317378 by richard1234(5390)   on 2011-06-21 11:49:47 (Show Source): You can put this solution on YOUR website!2n + 32b
 real-numbers/463148: Which pair of equations does NOT have a common solution? a) x+y = -1; 4x-3y=24 b)4x+6y=12; 6x+9y=12 c) 2x-3y=-4; 2x+y=4 d) 5x-4y=9; x-2y=-3 Please Explain solution Thank you!1 solutions Answer 317372 by richard1234(5390)   on 2011-06-21 10:48:51 (Show Source): You can put this solution on YOUR website!Already posted. Even with the changes in C, B does not have a common solution.