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# Recent problems solved by 'richard1234'

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 Quadratic_Equations/465855: solve 3x & -3x1 solutions Answer 319613 by richard1234(5390)   on 2011-07-01 02:30:24 (Show Source): You can put this solution on YOUR website!You'll have to explain what the & symbol represents. In logic and computer science there is a binary operator denoted & but I highly doubt it would be used with 3x and -3x.
 Exponents/465771: I'm studying, "Zero and Negative Integral Exponents". I have a couple of excericses to do with these insructions: Simplify and write each expression with postive exponents. y^c-d (if: c < d < 0) -> I kinda understand the range but I don't know how to use it in the exponent, do I evaluate the numbers and then substitute? 1 solutions Answer 319612 by richard1234(5390)   on 2011-07-01 02:26:25 (Show Source): You can put this solution on YOUR website! Since c < d, it follows c-d < 0, regardless of whether c and d are positive or negative. To rewrite with a positive exponent, we reciprocate it, yielding
 Polynomials-and-rational-expressions/466182: This is the last question I'll need help with for this week! Find all numbers for which the rational expression is undefined: r^3-7r/r^2-64 Thanks!1 solutions Answer 319610 by richard1234(5390)   on 2011-07-01 02:20:37 (Show Source): You can put this solution on YOUR website!The rational expression is undefined when the denominator is zero and the numerator is non-zero (if we get 0/0 we say the expression is indeterminate). Here, we set r^2 - 64 equal to 0, which implies r^2 = 64, r = 8 or -8. In either case, the numerator is non-zero.
 real-numbers/466271: hi tutor please help me in solving this problem find three irrational numbers between the rational numbers 5/7and9/11 I thank you very much1 solutions Answer 319609 by richard1234(5390)   on 2011-07-01 02:19:07 (Show Source): You can put this solution on YOUR website!5/7 = .7142857... 9/11 = .81818181... We could just think of a random string of numbers and claim it is irrational. For example, we could say that .76395882019... is irrational because it is assumed to be non-repeating, and cannot be expressed as a ratio of integers.
 Equations/466186: the half-life of the radioactive element unobtanium-47 is 5 seconds. If 80 grams of this are initially present, how many grams are present after 5 seconds?1 solutions Answer 319608 by richard1234(5390)   on 2011-07-01 02:16:51 (Show Source): You can put this solution on YOUR website!40 grams (after five seconds, one half-life has elapsed). Fortunately, the half-life of unobtanium is longer than 5 seconds. Otherwise, Avatar's Hallelujah Mountains would become lose its magnetic fields (as unobtanium is theoretically a superconductor) and crash to the ground.
 Money_Word_Problems/466157: The bus fare in a city is $1.75. People who use the bus have the option of purchasing a monthly coupon book for$26.00. With the coupon book, the fare is reduced to $0.75. Determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book.1 solutions Answer 319503 by richard1234(5390) on 2011-06-30 17:10:13 (Show Source): You can put this solution on YOUR website!If you buy the coupon book, you pay$26 but you save $1 for each ride. Hence, after 26 rides you will pay$26 and save \$26, in which the total is the same. You can also set it up as an algebraic equation, with "r" being the number of rides: 1.75r = 26 + .75r r = 26
 Reduction-of-unit-multipliers/466156: if you are 162 pounds, how many kilograms are you and how do you do it 1 solutions Answer 319502 by richard1234(5390)   on 2011-06-30 17:08:32 (Show Source): You can put this solution on YOUR website!Just use a unit multiplier. There are roughly 2.2 lb in one kilogram, so
 Angles/465968: three times the measure of a compliment of a certain angel is 30 more than the measure of a supplement of that angle.find the measure of each angle.1 solutions Answer 319501 by richard1234(5390)   on 2011-06-30 17:07:26 (Show Source): You can put this solution on YOUR website!See my lesson on complementary and supplementary angles here: http://www.algebra.com/algebra/homework/Angles/change-this-name27510.lesson
 Angles/465565: determine the measure of the complement of an angle whose measure is 20?1 solutions Answer 319480 by richard1234(5390)   on 2011-06-30 15:54:47 (Show Source): You can put this solution on YOUR website!90 - 20 = 70 degrees, the complement.
 Polynomials-and-rational-expressions/466091: Consider the graph to the right to complete the following: a. Find the zeros and state the multiplicity of each zero. b. Write an equation, expressed as the product of factors, of a polynomial function for the graph. Use a leading coefficient of 1 or -1 and make the degree of f as small as possible. c. Use the equation to find the y-intercept. The graph may not be exact. 1 solutions Answer 319476 by richard1234(5390)   on 2011-06-30 15:51:43 (Show Source): You can put this solution on YOUR website!What is "the graph to the right?"
 Linear_Equations_And_Systems_Word_Problems/466037: I need to solve the following equation using the graphing method: The perimeter of a soccer field is 340m. The lenght exceeds the width by 50m. I have the the problem solved by using P=2l+2w. How can i solve by using x and Y?1 solutions Answer 319404 by richard1234(5390)   on 2011-06-30 11:52:06 (Show Source): You can put this solution on YOUR website!If you are talking about 340 = 2x + 2y, the problem won't be any different. Other than the fact that the variables are changed.
 Angles/466036: Find the measure of an angle who supplement measures 39 more than twice its complement. Like to know if I am setting up the equation properly? Angle = x Supplement = 180-x Complement = 90-x 180-x = 2(90-x)+39 180 = 219 x= 39 Can I also say the supplement is 141 degrees and the complement is 56 degrees even though the problem is not requesting to find them? 1 solutions Answer 319399 by richard1234(5390)   on 2011-06-30 11:44:34 (Show Source): You can put this solution on YOUR website!You are correct in setting up the equation, and your final answer is correct; you probably typoed when you wrote "180 = 219" when it should be "180 = 219 - x." And the complement of 39 degrees is 90 - 39 = 51 degrees. You do not have to state the supplement or the complement for this problem.
 Equations/465947: A particle is projected from ground level so that its height above the ground after t seconds is given by 20t-5t^2 m. After how many seconds is it 15 m above the ground? Can you explain briefly why there are two possible answers?1 solutions Answer 319396 by richard1234(5390)   on 2011-06-30 11:37:03 (Show Source): You can put this solution on YOUR website!Because the height as a function of time is a quadratic, there can be two answers. The graph of the quadratic and the height h = 15 m intersect at two places, as shown: Note that the height vs. time graph is quadratic because acceleration due to gravity is constant (ignoring air resistance) and from this we can show that the position vs. time graph is quadratic using introductory physics and calculus.
 test/466028: I'm in intermediate algebra. I'm in the chapter about quadratic functions and equations. So how do you find the domain? The problem I have is: F(x)=2x+3 / x-7 and it asks to state the domain of the given function. Please help!!1 solutions Answer 319395 by richard1234(5390)   on 2011-06-30 11:32:58 (Show Source): You can put this solution on YOUR website!The function is undefined or indeterminate when the denominator is equal to zero; i.e. x-7 = 0, x = 7. Hence the domain is
 Probability-and-statistics/465983: Can someone answer this question for me step by step or in a broken down manner Determine the number of permutations of the letters of the word "sedlection." thanks....I saw it answered as 9![2!]=181,440 i was just wonder how you came up with this answer i looked at similar questions and determined that there are 1s,2e's,1L,1c,1t,1i,1o,and 1n...but after this i am lost what do you do from here thanks1 solutions Answer 319394 by richard1234(5390)   on 2011-06-30 11:31:22 (Show Source): You can put this solution on YOUR website!"Selection" not "sedlection." There are 9! ways to arrange nine distinct letters. However we divide by 2! because of the E's. If we were to treat the E's as distinct there would be 9! ways but here, we can arrange the E's themselves in 2! ways, leaving 9!/2! = 181440.
 Angles/466034: If angle r and s are supplemental angles and r = 50 and s = 2x + 30, what is the value of x?1 solutions Answer 319392 by richard1234(5390)   on 2011-06-30 11:29:38 (Show Source): You can put this solution on YOUR website!s is supplementary to r, meaning that r+s = 180, s = 130. This is equal to 2x+30 so we set up an equation 2x+30 = 130 2x = 100 x = 50
 Numbers_Word_Problems/465807: In the first 99 natural numbers, digit 4 comes how many times? I got 4,14,24,34,40,41,42,43,44,45,46,47,48,49,54,64,74,84,94 (19 times) But the answer written in my book is 20 times. Which number am i missing?1 solutions Answer 319308 by richard1234(5390)   on 2011-06-30 02:28:32 (Show Source): You can put this solution on YOUR website!44 has two fours. There are 19 numbers, but 20 4's. An easier way to count them is to list the numbers by unit digit and by tens digit, and always use the ellipsis (...) if necessary. You can organize them into sets like {4, 14, ...,94} and {40, 41, ..., 49}. Without writing every term you can easily count the number of elements by doing certain transformations like {4, 14, ..., 94} --> {0, 1, ..., 9} (removed 4's) --> {1, 2, ..., 10} (added 1), 10 elements.
 Geometric_formulas/465856: Hi Everyone :) I am taking a math class and our first thing we are doing is geometry, can someone please help me with his problem, I have never done geomery so any assistance will be greatly appreciated!!! Thank you :) find the complementary angle of the given angle. 89°1 solutions Answer 319307 by richard1234(5390)   on 2011-06-30 02:24:28 (Show Source): You can put this solution on YOUR website!Complementary angles, by definition, add up to 90 degrees, so the complement of 89 degrees is 90 - 89 = 1 degree. Similarly, you'll see the other definition, supplementary angles. They are similar, except that the two angles sum up to 180, not 90. The concept of complementary and supplementary angles is extremely useful in geometry. However I rarely see these words in advanced geometry problems, mainly because the question will be worded something like "Prove that ABC + CBD = 90" instead of "Prove that ABC and CBD are complementary" (possibly because foreign students might not know the terminology). But on certain problems involving parallel lines or right angles, this concept is crucial.
 Mixture_Word_Problems/465899: JIM NEEDS TO PREPARE ONE LITER OF A 4% NACL SOLUTION. HOW MUCH NACL SHOULD HE WEIGH OUT?1 solutions Answer 319306 by richard1234(5390)   on 2011-06-30 02:16:29 (Show Source): You can put this solution on YOUR website!4% of a 1 L NaCl solution is .04 L = 40 mL = 40 cm^3. However we want to find the mass of the salt by doing a unit conversion (had to look up the density online): (40 cm^3)(2.165 g/cm^3) = 86.6 g
 Graphs/465806: ok, here's another question with fraction involved. graph the equation using the slope and the y-intercept. y=7/5x+6 help!!1 solutions Answer 319305 by richard1234(5390)   on 2011-06-30 02:11:35 (Show Source): You can put this solution on YOUR website!Note that the y-intercept is 6, so the graph will go through the point (0,6). It has a slope 7/5, which is slightly higher than 1, so if you draw it by hand draw it a little steeper than a line with a slope of 1. It should look something like this: The fact that fractions are involved shouldn't make it any harder than if it was with integers.
 Numbers_Word_Problems/465939: five times an integer plus three times the square of the integer is 22. find the integer.1 solutions Answer 319304 by richard1234(5390)   on 2011-06-30 02:09:05 (Show Source): You can put this solution on YOUR website!Given the fact that the number is an integer, we can guess and check by inputting small integer values. Here we will get 2 as our answer. To show that it is the only answer, we can write a quadratic: where C is the other root. Here, we expect the constant term, 3(-2)(-C) to equal -22 --> 6C = -22. This implies C = -11/3, not an integer, so 2 is the only integer root.
 Word_Problems_With_Coins/465888: What is the smallest number that increases its value by 12 when the number's order of the digits is reversed?1 solutions Answer 319302 by richard1234(5390)   on 2011-06-30 02:03:22 (Show Source): You can put this solution on YOUR website!I think I've already solved this problem; there is no such positive integer. This is because the digit sum remains the same, so the remainder upon dividing by 9 will be the same. To see this, take some random numbers like 583, 79, and 1056. Reversing their digits we get 385, 97, and 6501. If we take their differences we get 583 - 385 = 198 = 22*9 79 - 97 = -18 = -2*9 1056 - 6501 = -5445 = -605*9 In all these cases we are essentially adding or subtracting multiples of 9, and since 12 is not a multiple of 9 we cannot make a number increase by 12. However this is entirely possible in other bases. If we have (12 in base 13 = 15) and we reverse the digits we get , and See if you can find the smallest base-10 number that, when written in a different base, the property holds (here the base-10 number was 15).
 Triangles/465853: A proof should always begin with stating the given information1 solutions Answer 319299 by richard1234(5390)   on 2011-06-30 01:54:48 (Show Source): You can put this solution on YOUR website!Usually, but not always true. Sometimes a proof might begin by introducing an entirely new concept and showing how it relates to and supports the original proof.
 Linear_Algebra/464826: 5y=2x+3x1 solutions Answer 319193 by richard1234(5390)   on 2011-06-29 18:03:39 (Show Source): You can put this solution on YOUR website!5y = 2x + 3x 5y = 5x y = x? Also that doesn't look like linear algebra to me...linear algebra is a completely different subject.
 Trigonometry-basics/465740: On a graph they want me to find y=A sin 0 (with a dash in the middle) for 0 (with a dash in the middle) between 0 and 6.28 radians, where A is constant. Which one?1 solutions Answer 319192 by richard1234(5390)   on 2011-06-29 18:00:56 (Show Source): You can put this solution on YOUR website! (the symbol is the Greek letter theta) It might look something like this (copy and paste link): http://www.wolframalpha.com/input/?i=y+%3D+3+sin+x%2C+0+%3C+x+%3C+2pi
 Linear-equations/465790: What is the equation of the line that passes through the point (3, 2) and has a slope of 4?1 solutions Answer 319191 by richard1234(5390)   on 2011-06-29 17:54:28 (Show Source): You can put this solution on YOUR website!Use the point-slope form: This is also equivalent to its slope-intercept form, y = 4x - 10.
 Equations/465787: please help! solve for the indicated letter. b = 6c, for c1 solutions Answer 319187 by richard1234(5390)   on 2011-06-29 17:38:43 (Show Source): You can put this solution on YOUR website!You have two expressions that are equal, so you can manipulate them the same way and still get an equality. Here if we divide both sides by 6 we will get b/6 = 6c/6 c = b/6
 Graphs/465746: If you are given an ordered pair (for example 1,4) and a shaded graph that shows a system of inequalities, how do you tell if the coordinates are SOLUTIONS of that shaded graph? I don't have anything to plug the coordinates into and I'm trying to see if they are solutions or not.1 solutions Answer 319153 by richard1234(5390)   on 2011-06-29 15:47:21 (Show Source): You can put this solution on YOUR website!You will have to determine graphically whether that point lies within the shaded boundaries of each inequality.
 Age_Word_Problems/465744: John is older than Sue. Sue is at least as old as Carrie. Which of the following is true?1 solutions Answer 319150 by richard1234(5390)   on 2011-06-29 15:45:30 (Show Source): You can put this solution on YOUR website!What is "the following?"
 Triangles/465642: how can i find the answer to a triangle has sides of length 4 inches and 7.5 inches. Which of the following cannot be the length of the third side: 3.5 inches, 4.0 inches, 5.0 inches, 5.5 inches, 9.5 inches1 solutions Answer 319075 by richard1234(5390)   on 2011-06-29 11:22:14 (Show Source): You can put this solution on YOUR website!3.5 inches, because 3.5 + 4 = 7.5, and the triangle inequality says that the sum of any two sides must be strictly greater than the third side.
 Miscellaneous_Word_Problems/465654: A gram of fat contains about 9 calories. If a quarter pound hamburger is made tha is 85% lean (15% fat), how many calories from fat will a person consume by eating just the meat.1 solutions Answer 319074 by richard1234(5390)   on 2011-06-29 11:21:01 (Show Source): You can put this solution on YOUR website!A quarter pound is roughly 113.4 grams. 15% of this is fat, so (113.4 g)(.15) = 17.01 grams of fat in this burger. There are 9 calories per gram of fat, so in 17.01 calories there are (17.01 g)(9 Cal/g) = 153.09 Calories. 153 Calories is a good approximate answer.