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# Recent problems solved by 'richard1234'

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 Graphs/483506: an equation and two ordered pairs are given. Show that each pair is a solution of the equation. Then graph the two pairs to determine another solution. Answers may vary. y = x − 2; (3,1), (−2, −4) 1 solutions Answer 331041 by richard1234(5390)   on 2011-08-20 22:04:26 (Show Source): You can put this solution on YOUR website!x = 3, y = 1 satisfies y = x-2. Similarly, x = -2, y = -4. Or (10,8) or (485,483).
 test/483455: does this quote have allusion to naploen ?  i have to win this now ,an fora all time ,ill fight it everyday and it will get worse and worse.` - orsen scott 1 solutions Answer 331039 by richard1234(5390)   on 2011-08-20 21:56:34 (Show Source): You can put this solution on YOUR website!This is a math homework help site. Look up that quote online, and you should be able to find relevant search results relating that quote to Napoleon.
 Radicals/483716: I'm not sure what my reacher is asking she added this question that we did not cover. solve: v/14-v/49=1/14=1 solutions Answer 331038 by richard1234(5390)   on 2011-08-20 21:50:25 (Show Source): You can put this solution on YOUR website!Did she not cover the entire concept, or that one specific equation? There's a difference. We can multiply both sides by the LCM of the fractions, which is 98.
 Polynomials-and-rational-expressions/483748: does whole numbers a rational expression??how can i easily determine rational algebraic equation???? are those with radical sign an algebraic equation??? yhanks 1 solutions Answer 331037 by richard1234(5390)   on 2011-08-20 21:47:43 (Show Source): You can put this solution on YOUR website!Your first question grammatically makes no sense. Your second question, if you are talking about a "rational equation," it is simply an equation with one or more rational expressions. Your third question can be either yes or no.
 Pythagorean-theorem/483424: find the area of an equilateral triangle with altitude 1 unit, leave your answer in simplest radical form.1 solutions Answer 330829 by richard1234(5390)   on 2011-08-19 16:43:23 (Show Source): You can put this solution on YOUR website!Two ways to do this: You can draw an altitude and call it h. This splits the equilateral triangle into two 30-60-90 right triangles, each with a leg of 1/2 and the height is sqrt(3)/2. The area is (1/2)(sqrt(3)/2) = sqrt(3)/4. Or, you can say that the area of the triangle is 1*1*(sin 60)/2 = sqrt(3)/4, same result.
 test/483356: The perimeter of a right angled triangle is 60 cm and its hypotenuse is 26 cm. the other two sides of the triangle are a) 24 cm,10 cm b) 25 cm,9 cm c) 20 cm,14 cm d) 26 cm,8 cm1 solutions Answer 330828 by richard1234(5390)   on 2011-08-19 16:40:51 (Show Source): You can put this solution on YOUR website!a) is the only choice that satisfies the Pythagorean theorem, since 10^2 + 24^2 = 26^2.
 Numbers_Word_Problems/483423: the product of two consecutive positive integers is 240. what is the sum of the two integers1 solutions Answer 330827 by richard1234(5390)   on 2011-08-19 16:39:26 (Show Source): You can put this solution on YOUR website!240 = 15*16, 15+16 = 31 You could also do x(x+1) = 240, but given that the root is an integer, it is simply easier to look for factors of 240.
 Quadratic_Equations/483300: Quadratic equations, which are expressed in the form of ax2 + bx + c = 0, where a does not equal 0, may have how many solutions? Explain why? Think of a linear equation. How many solutions may that have? Can you extend this to a an n-degree equation? 1 solutions Answer 330826 by richard1234(5390)   on 2011-08-19 16:38:23 (Show Source): You can put this solution on YOUR website!Quadratic equations have two solutions. If you want to learn why, look up the proof of the fundamental theorem of algebra (most are quite advanced and use some complex analysis).
 Probability-and-statistics/482591: The probability that an event A occurs in one trial of an experiment is 0.4 Three independent trials of experiment are performed. The probability that A occurs at least once is1 solutions Answer 330806 by richard1234(5390)   on 2011-08-19 14:25:12 (Show Source): You can put this solution on YOUR website!P(A occurs >= 1) = 1 - P(A does not occur at all) = 1 - (0.6)^3 = 0.784
 real-numbers/483074: How do you express 2.135 repeating, the 35 is repeating, as a fraction1 solutions Answer 330804 by richard1234(5390)   on 2011-08-19 14:23:27 (Show Source): You can put this solution on YOUR website!2.1353535... = 2.1 + .0353535... = 2.1 + (35/99)/10 = 21/10 + 35/990 = 1057/495 You can check this with a calculator.
 Probability-and-statistics/483114: Into which range (Response 1, 2, or 3) does the following value fall: 3.51 solutions Answer 330802 by richard1234(5390)   on 2011-08-19 14:20:43 (Show Source): You can put this solution on YOUR website!What are responses 1,2,3?
 Age_Word_Problems/483338: Essay; show all work. Consider that the age, x, of a unicorn in human equivalent years can be given by the formula f(x) = - 0.001718x4 + 0.087326x3 – 1.3367x2 + 12.46x + 3.914. When a unicorn is 2.5 years old, what is its age in human equivalent years? What about when it is 12 years old?1 solutions Answer 330801 by richard1234(5390)   on 2011-08-19 14:20:06 (Show Source): You can put this solution on YOUR website!Somehow this is one of those overused problems that textbooks just like to throw in repeatedly. Solution is quite simple, to find f(2.5), just replace all occurrences of x with 2.5. Similarly, to find f(12), replace x with 12. f(2.5) = 28.007 years f(12) = 76.2241 years http://www.wolframalpha.com/input/?i=-+0.001718x^4+%2B+0.087326x^3+%E2%80%93+1.3367x^2+%2B+12.46x+%2B+3.914+where+x+%3D+12
 Polynomials-and-rational-expressions/483384: how do i factor a binomial like1 solutions Answer 330798 by richard1234(5390)   on 2011-08-19 14:14:25 (Show Source): You can put this solution on YOUR website!Difference of two squares x^2 - (5)^2 = (x-5)(x+5)
 Points-lines-and-rays/483235: are 3 points coplanar1 solutions Answer 330764 by richard1234(5390)   on 2011-08-19 09:36:16 (Show Source): You can put this solution on YOUR website!In 3-space, yes. Even if those three points are on the same line, they still lie on a plane, even though they do not uniquely determine a plane.
 real-numbers/483073: Explain why the sum, the difference, and the product of two rational numbers are rational numbers. Is the product of two irrational numbers necessarily irrational? What about the sum?1 solutions Answer 330712 by richard1234(5390)   on 2011-08-19 00:21:53 (Show Source): You can put this solution on YOUR website!Sum, difference, and product of two rational numbers is always rational, it can be shown similar to a way we add, subtract, and multiply fractions. If a/b, c/d are the two rational numbers then their sum is (ad + bc)/bd, their difference is (ad - bc)/bd, and their product is ac/bd, all of them rational because the numerator and denominator are always integers. The product and sum of two irrational numbers is not always irrational. For example,
 Angles/483230: If in a triangle, the sum of two angles is equal to the third angle then the triangle is called – what? Right/acute/obtuse? and How?1 solutions Answer 330711 by richard1234(5390)   on 2011-08-19 00:19:07 (Show Source): You can put this solution on YOUR website!If the sum of two of the angles is equal to the third angle, then the third angle must be 90 degrees. This is because if we let the angles be A,B,C with A+B = C, we have A+B+C = 180, replace A+B with C to get 2C = 180, C = 90. Hence the triangle is a right triangle.
 Angles/483153: i've got a triangel wich is equal-sided.Both are 5 cm long and i got alpha wich 45 degrees.the other two angles are missed.what should i do ? 1 solutions Answer 330709 by richard1234(5390)   on 2011-08-19 00:04:12 (Show Source): You can put this solution on YOUR website!Which angle is 45 degrees? The vertex angle or one of the base angles?
 Points-lines-and-rays/483157: Sketch and label the figure described. Use dashes for hidden parts. Point P is not in plane N. Three lines through point P intersect N in points A, B, and C.1 solutions Answer 330707 by richard1234(5390)   on 2011-08-18 23:55:33 (Show Source): You can put this solution on YOUR website!Can't really draw that online...I'll let you sketch it. Draw some arbitrary plane (label it N), draw a point in 3-dimensional space not on N and label it P. Choose three points A,B,C on the plane and connect each point to line P (so you will have three lines).
 real-numbers/483198: My homework said to write each number in the form a/b using integers to show that it is a rational number. One of the numbers was 0.2. If you could give me steps how to figure it out that would be great.:)1 solutions Answer 330706 by richard1234(5390)   on 2011-08-18 23:51:37 (Show Source): You can put this solution on YOUR website!0.2 = 2/10 = 1/5 It's a ratio of two integers, so 0.2 is rational.
 Distributive-associative-commutative-properties/483220: whats 3+4=? 1 solutions Answer 330705 by richard1234(5390)   on 2011-08-18 23:48:44 (Show Source):
 real-numbers/483221: Well, I am dealing with Properties of Real Numbers. It says: Name the sets of numbers to which each number belongs. I only got 2 down. 1. -4.55 I don't really know. 2. Square root of 10 - it's a Irrational number and Real Number, right? 3. -31 - I'm trying 4. 12 over 2 - I'm trying 5. 3 pie over 2 - Natural, Whole, Intergers, Rationals, and real numbers?1 solutions Answer 330704 by richard1234(5390)   on 2011-08-18 23:43:51 (Show Source): You can put this solution on YOUR website!-4.55 is a rational number because -4.55 = -455/100. sqrt(10) is irrational and real. -31 is rational, integer, but not a whole number (whole numbers are nonnegative). 12/2 = 6, rational, integer, whole, and natural number. 3pi/2 is irrational and real. Look in your textbook or online for definitions of these numbers.
 Triangles/482923: A triangle has angles labeled A, B,C. B is twice A. C is three times A. What type of triangle is this? evigiletti@aol.com1 solutions Answer 330553 by richard1234(5390)   on 2011-08-18 00:53:41 (Show Source): You can put this solution on YOUR website!B = 2A, C = 3A, sum of the angles A+B+C is A + 2A + 3A = 6A = 180 Since 6A = 180, A = 30, and B = 60, C = 90 Triangle is a 30-60-90 triangle.
 Volume/483007: for apositiv integer n,difine the d(n),the number of positive diviser of n what is the value on d(d(d(12)))?1 solutions Answer 330552 by richard1234(5390)   on 2011-08-18 00:52:03 (Show Source): You can put this solution on YOUR website!d(12) = 6 (1,2,3,4,6,12) d(d(12)) = d(6) = 4 (1,2,3,6) d(d(d(12))) = d(4) = 3 (1,2,4)
 Functions/482541: Find the domain of y=x/cosx I know that cos(x)can't equal zero and that means x can't be pi/2, 3pi/2, etc. Just not sure on how to notate the domain for this one.1 solutions Answer 330551 by richard1234(5390)   on 2011-08-18 00:50:48 (Show Source): You can put this solution on YOUR website!You could notate it something like (The () should be {}, LaTeX interprets curly braces differently so I could not type them without changing the {} to a string). This is set-builder notation representing "the set of all real x such that for all non-integer k, x = (2k+1)pi/2."
 Probability-and-statistics/482877: Choose a natural number between 1 and 23, inclusive. What is the probability that the number is a multiple of 3? I need someone to help me figure out which way to go with this one also. Will one of the tutors help me to get the correct answer for this problem? Thank you!1 solutions Answer 330548 by richard1234(5390)   on 2011-08-18 00:34:50 (Show Source): You can put this solution on YOUR website!There are 23 numbers, seven of them (3,6,9,...,21) being multiples of 3. The probability is 7/23.
 Square-cubic-other-roots/482981: How do I calculate the square root of a number without a calculator.1 solutions Answer 330547 by richard1234(5390)   on 2011-08-18 00:33:54 (Show Source): You can put this solution on YOUR website!If you can tell that the number is a perfect square, it should be pretty easy. There are several other algorithms (you can search online) used to find the square root of a non-perfect square, many of them using some sort of recursion.
 Geometry_Word_Problems/482883: Evaluate: 7C5 thank you.1 solutions Answer 330546 by richard1234(5390)   on 2011-08-18 00:29:57 (Show Source): You can put this solution on YOUR website!7C5 = 7!/(5!2!) = 21 Or, you could say 7C5 = 7C2 = (7*6)/2! = 21, same thing.
 Rectangles/482644: What are length of the two rectangles' dimensions, if one perimeter is measuring 28 inches and the other perimeter is measuring 60 inches ?1 solutions Answer 330545 by richard1234(5390)   on 2011-08-18 00:28:25 (Show Source): You can put this solution on YOUR website!Can't determine from the information given. Are the rectangles related/connected in some way?
 Distributive-associative-commutative-properties/482915: Expand (x+h)^31 solutions Answer 330544 by richard1234(5390)   on 2011-08-18 00:25:10 (Show Source): You can put this solution on YOUR website!Use binomial theorem:
 Inequalities/482948: Explain, in your own words, how to evaluate a polynomial for a given value of the variable. (Section 4.7). Demonstrate the process with an example.1 solutions Answer 330542 by richard1234(5390)   on 2011-08-18 00:18:58 (Show Source): You can put this solution on YOUR website!Just replace all occurrences of the variable (e.g. x, n) with that number and simplify. For example, Things get a little different when the function is not in terms of a simple "x." We can define a function g: Suppose we want to find the value of g(7). We do not plug in x = 7. Rather we plug in 2x + 1 = 7, which is the same as plugging in x = 3.
 Geometry_Word_Problems/482935: Points A, B, C, D, and E are coplanar and no three are collinear. In how many way can the plane be named using only these points?1 solutions Answer 330533 by richard1234(5390)   on 2011-08-17 23:05:33 (Show Source): You can put this solution on YOUR website!Remember that three or more coplanar points uniquely determine a plane. We can choose three points, or even four or all five points. The number of ways to do so is 5C3 + 5C4 + 5C5 = 10 + 5 + 1 = 16 ways.