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# Recent problems solved by 'drk'

drk answered: 1901 problems
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 Triangles/252954: i am doing a project for school and i had to graph a triangle. After that i have to find the degrees and sides for the triangle. Can you help me find the degrees and sides 1 solutions Answer 185135 by drk(1908)   on 2010-01-01 18:56:06 (Show Source): You can put this solution on YOUR website!Since thee are 7 different triangles, I will need more information please. Is there a relationship between the angles, between the sides? Is it a right or not?
 Triangles/250318: If an isosceles triangle has a perimeter of 64. How many different triangles can this be, and what are the dimensions of each triangle?1 solutions Answer 185134 by drk(1908)   on 2010-01-01 18:54:11 (Show Source): You can put this solution on YOUR website!Let's start with the base. assume I can only use integers: base = 2, leg = 31, 31 base = 4, leg = 30, 30 base = 6, leg = 29, 29 base = 8, leg = 28, 28 base = 10, leg = 27, 27 base = 12, leg = 26, 26 base = 14, leg = 25, 25 base = 16, leg = 24, 24 base = 18, leg = 23, 23 base = 20, leg = 22, 22 base = 22, leg = 21, 21 base = 24, leg = 20, 20 base = 26, leg = 19, 19 base = 28, leg = 18, 18 base = 30, leg = 17, 17 There are 15 options.
 Probability-and-statistics/250323: eight boys & six girls in a class, if you randomly choose two students, one at a time, whats the probability that there girls?1 solutions Answer 185133 by drk(1908)   on 2010-01-01 18:47:11 (Show Source): You can put this solution on YOUR website!You want both girls, so of the 8 boys you choose 0 boys and of the 6 girls, you choose 2 girls. There are 14 kids and you are choosing 2. So,
 logarithm/250327: find the domain of f(x)=log [(x-2)/(x-1)]1 solutions Answer 185132 by drk(1908)   on 2010-01-01 18:44:28 (Show Source): You can put this solution on YOUR website!Here is the original problem. f(x)=log [(x-2)/(x-1)] The domain of any log >=0 Step 1 -set (x-2) / (x-1) >= 0 First notice that if x = 1, our fraction is undefined. * X cannot = 1 step 2 - multiply both sides by (x-1) to get (x-2) >= 0 solving for x, we see ** x cannot = 2. So it appears that x cannot equal 1 or 2.
 logarithm/250331: Hello, How would I do the following: 1. Express as a single logarithm and if possible, simplify. 2. Choose the expression or equation that is equivalent to the one given Logx 29=5 a. 29^x=5 b. X^29=5 c. 5^x=29 d. X^5=29 My answer is "d" is that right? 3. Express as a sum, difference, and product of logarithms, without using exponents. I am really lost, this is part of a test, and I can to figure them out, can you please help me. 1 solutions Answer 185131 by drk(1908)   on 2010-01-01 18:38:22 (Show Source): You can put this solution on YOUR website!Let's take this part by part: 1. Express as a single logarithm and if possible, simplify. Step 1 - use the power rule and bring the 2 up to the exponent: step 2 - rewrite the square root a 1/2 power and cancel with the 2. step 3 - since the bases are the same and we are subtracting, we can combine and make this division as step 4 - we can reduce by x; assuming x is not 0 as -- 2. Choose the expression or equation that is equivalent to the one given Log_x(29) = 5 a. 29^x=5 b. X^29=5 c. 5^x=29 d. X^5=29 My answer is "d" is that right? [D] is correct. -- 3. Express as a sum, difference, and product of logarithms, without using exponents: / step 1 - since 5y^8 is the big exponent, that comes out front using power rule step 2 - since we are multiplying 2 and x, we can split it using addition as
 Probability-and-statistics/250330: in the lottery there are 9 balls, numbered 1-9, in each of the three bins. one ball will be selected from each bin. what are the odds of the numbers 2,3, & 4 being pulled IN THAT ORDER?1 solutions Answer 185129 by drk(1908)   on 2010-01-01 18:24:30 (Show Source): You can put this solution on YOUR website!There is only 1 way to get 2,3,4 in that order. The total number of ways for the 3 balls is 9*8*7 = 504. So, success = 1, total = 504, fail = 503. odds = success / failure, so 1:503.
 Equations/252953: Find the solutions to the system of equations by the addition method. x-5y=-47 -4x-5y=-37 is the answer (-1,9)1 solutions Answer 185128 by drk(1908)   on 2010-01-01 18:21:53 (Show Source): You can put this solution on YOUR website!Here are the two equations: (i) 1x - 5y = -47 (ii) -4x - 5y = -37 multiply (i) by -1 to get (iii) -1x + 5y = +47 (ii) -4x - 5y = -37 add down and find x. (iv) -5x = 10 x = -2 solve for y. y = 9. (-2,9)
 Mixture_Word_Problems/250376: how many milligrams of metal that contains 45% nickel must be combined of 6 milligrams of 100% nickel to get 78% nickel1 solutions Answer 185127 by drk(1908)   on 2010-01-01 18:18:44 (Show Source): You can put this solution on YOUR website!This is a mixture problem. Here is the table: nickel . . . . . % . . . . .mg . . . . . %g 45 . . . . . . .45 . . . . .g . . . . . 45g 100 . . . . . . 100 . . . . 6 . . . . . 600 Mixture . . .. .78 . . . . g + 6 . . . .78g + 468 Now, in the right hand column, 45g + 600 = 78g + 468 33g = 132 g = 4. 4 mg of metal at 45%.
 test/250344: for the given value of a, find -a and |a| 1 solutions Answer 185126 by drk(1908)   on 2010-01-01 18:14:02 (Show Source): You can put this solution on YOUR website!If you are given a value called , -a = the opposite of what you were given. |a| is always the positive number a. hope that helps.
 Quadratic_Equations/250347: How would you write the equation of a parabola in vertex from that has the vertex (0,3) and a point (-4,-45)?1 solutions Answer 185125 by drk(1908)   on 2010-01-01 18:11:46 (Show Source): You can put this solution on YOUR website!Parabola have the equation: where h,k is the vertex. We are given (0,3) as well as (-4, -45). Putting all of this in, we can find a as: The equation is or simply
 Circles/252952: kevin designs a sprinkler system for his yard. one rotation of the sprinkler waters a circle with an area of 225π square feet. What is the radius,r,of the circle the rotating sprinkler waters?1 solutions Answer 185124 by drk(1908)   on 2010-01-01 18:07:50 (Show Source): You can put this solution on YOUR website!Area of circle has the formula: Your area was given as 225pi, so we have divide by pi to get take a square root and we get
 Quadratic-relations-and-conic-sections/250363: Complete the square in order to graph the conic section. x^2-6x+2y-1=0 1 solutions Answer 185123 by drk(1908)   on 2010-01-01 18:06:15 (Show Source): You can put this solution on YOUR website!Step 1 solve for y; y = -x^2 + 6x + 1 step 2: complete the square on the right side as: y = -(x^2 -6x + ___ ) + 1 + ___ y = -(x^2 - 6x + (-3)^2) + 1 + 9 y = -(x-3)^2 + 10. Now you are ready to graph
 Linear-equations/250348: rewrite the equation in standard form with integer coefficients. 2y=-2x+6 y=3/4x+1/21 solutions Answer 185121 by drk(1908)   on 2010-01-01 18:01:46 (Show Source): You can put this solution on YOUR website!Standard form requires two things: (1) all variable on the same side and (2) no fractions. -- 2y=-2x+6 Here we need variables on the same side so, we get 2x + 2y = 6. Since there are no fractions, we are done. -- y=3/4x+1/2 Here we have fractions. Multiply by 4, the common denominator. We get 4y = 3x + 2 Now put all variables on the same side. We get -3x + 4y = 2. Some teachers are picky about this and require x to be positive.
 Graphs/252951: graph 1 solutions Answer 185120 by drk(1908)   on 2010-01-01 17:58:14 (Show Source): You can put this solution on YOUR website!This is a quadratic opening down with vertex at(-1,-2)
 Graphs/252950: graph y=-3/4x+5 1 solutions Answer 185119 by drk(1908)   on 2010-01-01 17:56:18 (Show Source): You can put this solution on YOUR website!I assume x is in the numerator. This is a linear function with negative slope and a positive y-intercept.
 Equations/252949: If 3x - 7 = -4, then x = 1. Write the hypotheses of this statement1 solutions Answer 185118 by drk(1908)   on 2010-01-01 17:52:02 (Show Source): You can put this solution on YOUR website!The "if" part is the hypothesis, so we say: 3x - 7 = -4.
 Linear-systems/252948: Here is the problem. Find the missing co-efficient and write the completed equation Ax + 3y = 5 (2,1). We have answers from the teacher and our answer doesn't match1 solutions Answer 185116 by drk(1908)   on 2010-01-01 17:30:54 (Show Source): You can put this solution on YOUR website!Here is the original problem: with coordinate (2,1). substitute X and Y into the equation to get So, the equation should be: x + 3Y = 5. Hope that is what you were looking for.
 Angles/252947: what is the complement of an angle that measures 19 degrees 1 solutions Answer 185114 by drk(1908)   on 2010-01-01 17:28:29 (Show Source): You can put this solution on YOUR website!Complementary angles add to 180 degrees, or X + Y = 180. If one angle is 19, then the other is 180 - 19 or 161 degrees.
 Geometry_proofs/252943: Given: Angle AXY is congruent to Angle AYX, and Angle AXC is congruent to Angle AYB Prove:Segment BY is congruent to Segment CX1 solutions Answer 185113 by drk(1908)   on 2010-01-01 17:27:28 (Show Source): You can put this solution on YOUR website!Hope this idea works for you. Draw a diagram that meets the criteria. Notice it appears to be a trapezoid. STATEMENT 1: angle AXY congruent to angle AYX REASON 1: given STATEMENT 2: angle AXC congruent to angle AYB REASON 2: given STATEMENT 3: angle C congruent angle B. REASON 3: if the top leg angles of a trapezoid are congruent then there base angles are congruent. STATEMENT 4: triangle AXC congruent to triangle AYB REASON 4: AAS postulate STATEMENT 5: segment BY congruent segment CX REASON 5: CPCTC
 Evaluation_Word_Problems/250398: Peyton has 6 times as many pencils as paint brushes. He has a total of 63 pencils and paint brushes. How many does he have of each?1 solutions Answer 185110 by drk(1908)   on 2010-01-01 17:15:29 (Show Source): You can put this solution on YOUR website!Let A = paint brush and E = pencils. E = 6A A + E = 63 By substitution, we get a + 6A = 63 7A = 63 A = 9 E = 54 9 paint brushes and 54 pencils.
 Numbers_Word_Problems/252946: One number is five more than another. Five times the smaller equals four times the larger. Find the numbers1 solutions Answer 185108 by drk(1908)   on 2010-01-01 17:13:24 (Show Source): You can put this solution on YOUR website!Let X and Y be the numbers. X = Y + 5 5Y = 4X. By substitution, we get 5Y = 4(Y+5) 5Y = 4Y + 20 Y = 20. X = 25.
 Polynomials-and-rational-expressions/250404: I need help dividing the following using synthetic division. (x^2 - 6x - 6x^3 + x^4) / (6 + x)1 solutions Answer 185107 by drk(1908)   on 2010-01-01 17:11:40 (Show Source): You can put this solution on YOUR website!First thing is to write everything in descending order and not to skip any terms: we have: we solve X + 6 = 0 for x to get x = 6. Now we are ready. 6.// . 1 . . -6 . . 1 . . -6 . . . . . . 6 . . .0 . . 6 ______________________________ . . . 1. . 0 . . . 1 . . 0. So, if all of this works correctly, you will see X^2 + 1 with no remainder.
 test/252945: Write the equation for a horizontal line passing through the point (6,18)?1 solutions Answer 185106 by drk(1908)   on 2010-01-01 17:06:40 (Show Source): You can put this solution on YOUR website!A horizontal line has equation: Y = 0x + b. The coordinate was (6,18) 18 + 6*0 + b 18 = b So, we just have Y = 18.