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# Recent problems solved by 'drk'

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 Graphs/263441: how do you graph the equation y = -8/5 using the slope and y-intercept method?1 solutions Answer 194137 by drk(1908)   on 2010-01-31 14:29:49 (Show Source): You can put this solution on YOUR website!Normally we want where m = slope and b = y-intercept. in our example we have which means or m = 0 and b = -8/5. to graph first plot -8/5 on the y-axis. second move up 0 and over 1 (rise / run) and place a dot. connect the dots to find a long horizontal line.
 Evaluation_Word_Problems/263438: Given G(t) = 4 − 7t, write G( 5 + h) − G(5) in simplest form.1 solutions Answer 194132 by drk(1908)   on 2010-01-31 14:26:33 (Show Source): You can put this solution on YOUR website!the problem is Given G(t) = 4 − 7t, write G(5 + h) − G(5) in simplest form. step 1 - replace t with 5+h to get G(5+h) = 4 - 7(5+h) distribute to get G(5+h) = 4 - 35 -7h combine like terms to get G(5+h) = -7h - 31 --- G(5) = 4 - 7*5 = 4 - 35 = -31 --- G(5+h) - G(5) = -7h - 31 - (-31) = -7h
 Evaluation_Word_Problems/263440: The sum of two numbers is 39. The greater number is 5 less than 3 times the smaller number. What are the two numbers?1 solutions Answer 194131 by drk(1908)   on 2010-01-31 14:23:47 (Show Source): You can put this solution on YOUR website!We (i) a + b = 35 (ii) a = 3b - 5 substituting (ii) into (i), we get (iii) 3b-5 + b = 35 combine like terms to get (iv) 4b - 5 = 35 adding 5 we get (v) 4b = 40 dividing, we get b = 10 so a = 25
 Mixture_Word_Problems/263434: A silversmith mixed 30 g of a 70% silver alloy with 50 g of a 15% silver alloy. What is the percent concentration of the resulting alloy? (Round your answer to the nearest tenth of a percent.)1 solutions Answer 194129 by drk(1908)   on 2010-01-31 14:21:43 (Show Source): You can put this solution on YOUR website!This is a mixture problem with out mixture information. Here is a table based on the given information alloy . . . . . .% . . . . . .g . . . . . . .%g 70 . . . . . . . 70 . . . . 30 . . . . . .2100 15 . . . . . . .15 . . . . .50 . . . . . .750 mix . . . . . . x . . . . . .80 . . . . . .80x looking at the third column, we get adding we get dividing, we get x = 35.625 which is 35.63% = 35.6%
 Age_Word_Problems/263432: In 1992 the life expectancy of males in a certain country was 66.2 years in 1997 it was 69.9 years let E represent the life expectancy in year t and let t represent the number of years since 1992?1 solutions Answer 194127 by drk(1908)   on 2010-01-31 14:16:48 (Show Source): You can put this solution on YOUR website!I think you are looking for a linear equation to model this data. We have two coordinates here (0, 66.2) and (5, 69.9). Let 1992 = 0 and 1997 = 5. step 1 - find the slope using to get which is --- step 2 - using y = mx + b, and a coordinate, we get so, --- we have our answer as
 Linear-systems/263429: Determine whether the system is consistent, inconsistent, or dependent. 3x - 3y = -9 9x - 9y = -27 Determine whether the system is consistent, inconsistent, or dependent. 2x + 2y = 2 6x + 6y = 61 solutions Answer 194125 by drk(1908)   on 2010-01-31 14:12:57 (Show Source): You can put this solution on YOUR website!Lets take these one at a time: Determine whether the system is consistent, inconsistent, or dependent. (i) (ii) step 1 - multiply (i) by -3 to get (iii) step 2 - add (ii) and (iii) to get (iv) Here we have dependent , consistent Determine whether the system is consistent, inconsistent, or dependent. (i) (ii) step 1 - multiply (i) by -3 to get (iii) step 2 - add (ii) and (iii) to get (iv) Here we have dependent , consistent
 Mixture_Word_Problems/263426: A butcher has some hamburger that is 29% fat and some that is 15% fat. How many pounds of each should be mixed to make 63 lb of hamburger that is 17% fat?1 solutions Answer 194124 by drk(1908)   on 2010-01-31 14:07:35 (Show Source): You can put this solution on YOUR website!This is a mixture problem. Here is a table based on the given information fat . . . . . . .% . . . . . . pounds . . . . . . . . %-pounds 29. . . . . . . 29 . . . . . . . .p . . . . . . . . . . .29p 15 . . . . . . .15 . . . . . . . .63-p. . . . . . . . .945 -15p 17 . . . . . . .17 . . . . . . . .63. . . . . . . . . . .1071 set the third column equal to get combine like terms to get subtract 945 to get p = 9 pounds @ 29 % 63-p = 54 pounds @ 15%
 Mixture_Word_Problems/263420: A ferry leaves a harbor and travels to a resort island at an average speed of 22 mph. On the return trip, the ferry travels at an average speed of 10 mph because of fog. The total time for the trip is 4 h. How far is the island from the harbor?1 solutions Answer 194122 by drk(1908)   on 2010-01-31 14:01:23 (Show Source): You can put this solution on YOUR website!This is an RTD problem. Here is a table based on the given information location . . . . . rate . . . . .time . . . . . distance resort . . . . . . . .22 . . . . .t. . . . . . . . . . 22t harbor . . . . . . .10 . . . . .4-t. . . . . . . . . 40-10t total. . . . . . . . . . . . . . . . 4 since distances are =, set add 10t to get divide by 32 to get hours we want distance, so 22*1.25 = 27.5 miles
 Travel_Word_Problems/263413: Henry can ride his horse at 4 miles per hour and get to the battlefield on time. If he stops for 1 hour to make a speech to his troups, he must ride 5 miles per hour for the whole trip to get to the battlefield on time. How far is it to the battlefield?1 solutions Answer 194119 by drk(1908)   on 2010-01-31 13:56:55 (Show Source): You can put this solution on YOUR website!This is an RTD problem. Here is a table based on the given information travel . . . . . rate . . . . . .time . . . . . .distance horse . . . . . . 4 . . . . . . . .t . . . . . . . . .4t speech . . . . . 5 . . . . . . . t-1 . . . . . . . 5t - 5 set subtract 5t to get so t = 5. distance = 4t = 20 miles
 Polynomials-and-rational-expressions/263411: Factor the expression on the left side of each equation. Then solve the equation 4x³-32=01 solutions Answer 194116 by drk(1908)   on 2010-01-31 13:30:49 (Show Source): You can put this solution on YOUR website!The original equation was step 1 - rewrite the left side as and then using difference of cubes, we get set each part = 0 and solve to get add 2^(5/3) to get divide by 4^(1/3) to get the other parentheses, trinomial, will generate imaginary answers. so we get x = 2.
 Rate-of-work-word-problems/263393: An 8 hp pump can fill a tank in 8 hours. A smaller 3 hp pump fills the same tank in 12 hours. The pumps are used together to begin filling this tank. After four hours, the 8 hp pump breaks down. How long will it take the smaller pump to fill the tank?1 solutions Answer 194114 by drk(1908)   on 2010-01-31 13:20:30 (Show Source): You can put this solution on YOUR website!This is a working together problem. The rate of the 8 hp pump = 1/8 the rate of the 3 hp pump is 1/12 The time together will be 4 hours. The time that the 3 hp pump works alone is x hrs. We want to fill only 1 tank ----- we use the formula we get adding the fractions, we get subtract 5/6 to get multiply by 12 to get So, the 3 hp pump must work and additional 2 hours.
 Quadratic-relations-and-conic-sections/263410: How do you tell which way a parabola will open by their equation?1 solutions Answer 194110 by drk(1908)   on 2010-01-31 13:16:10 (Show Source): You can put this solution on YOUR website!The general parabola formula is or in either case to determine up or down, look at the "a" value If "a' is positive, then it opens up if "a" is negative, then it opens down
 Rectangles/263394: What is the perimeter and area of the rectangle that is 33 m wide and 2 m long?1 solutions Answer 194109 by drk(1908)   on 2010-01-31 13:14:20 (Show Source): You can put this solution on YOUR website!Perimeter formula is area formula is --- from the given information, we get } P = 70 m --- from the given information, we get A = 66 meters squared.
 Miscellaneous_Word_Problems/263404: If the patterns of the fines continue at the same rate of increase at what speed will the fines be the same? Given: County A rate is +15, County B rate is +10; at 60mph fine for County A is \$0 and the fine for County B is \$40.1 solutions Answer 194107 by drk(1908)   on 2010-01-31 13:11:30 (Show Source): You can put this solution on YOUR website!If I understand the question correctly, we have two equations (i) (ii) setting them equal, we get distribute to get combine like terms to get subtract 10m and add 900 to get divide to get So, at 68 mph, city A fine will be \$120 city B fine will be \$120
 Polynomials-and-rational-expressions/263409: 2x³-250=01 solutions Answer 194104 by drk(1908)   on 2010-01-31 13:03:41 (Show Source): You can put this solution on YOUR website!Here is the given equation step 1 - add 250 to get step 2 - divide by 2 to get step 3 - take a cube root of both sides to get
 Linear-equations/263407: Solve the following system of linear equations. If possible, express your answer as an ordered pair (x,y). Also, tell whether the system of equations is “independent”, “inconsistent”, or “dependent”. 2x-4y=8 x-2y=4 1 solutions Answer 194103 by drk(1908)   on 2010-01-31 13:02:09 (Show Source): You can put this solution on YOUR website!Here is our original system (i) (ii) step 1 - multiply (ii) by -2 to get (iii) add (ii) and (iii) to get (iv) this mans that we have the same equations but in disguise. These equations are "dependent"
 Polynomials-and-rational-expressions/263408: X³+64=01 solutions Answer 194102 by drk(1908)   on 2010-01-31 12:59:46 (Show Source): You can put this solution on YOUR website!here is the given equation step 1 - subtract 64 to get step 2 - take a cube root of both sides to get this is the only "real" solution. There are 2 imaginary solutions.
 Permutations/263406: How many six-letter permutations can be formed from the first nine letters of the alphabet? 1 solutions Answer 194101 by drk(1908)   on 2010-01-31 12:58:01 (Show Source): You can put this solution on YOUR website!We use the permutation formula: nPr and get 9P6 = 60,480
 Reduction-of-unit-multipliers/263405: Name the period of the first three digits: 234,837,925.001 solutions Answer 194100 by drk(1908)   on 2010-01-31 12:56:50 (Show Source): You can put this solution on YOUR website!The 234 occur in the millions period.
 Number-Line/263397: cant seem to solve this one.. i have to put it on a number line too x^2 + 2x > 3 Thanks!1 solutions Answer 194099 by drk(1908)   on 2010-01-31 12:55:55 (Show Source): You can put this solution on YOUR website!here is the original question step 1 - subtract 3 to get step 2 -factor to get step 3 we need to create 3 number line graphs. Make sure the 0 marker is aligned in all three. number line graph #1: x+3> 0 this means open circle above -3 and then + signs to the right and - signs to the left. number line graph #2: x-1> 0 this means open circle above +1 and then + signs to the right and - signs to the left. number line graph #3: (x+3)(x-1) > 0 we place open circles above -3 and then +1. To the left of -3, we have - signs for both lines. - x - = + so in the third number line place a + to the left of -3. Between -3 and +1 we have different signs, so place a - sign on the third number line between -3 and +1. To the right of +1, we have + signs for both lines. + x + = +, so in the third number line place a + to the right of +1. we want where the signs are > 0 or the + regions. Our final answer is open circles above -3 and +1 and then arrow from the -3 to the left and arrow from the +1 to the right.
 Travel_Word_Problems/263398: A cylindrical drum has a diameter of 3 yards and a volume of 65 cubic yards. What is the height of the drum? (Hint: Use V = пr2h)1 solutions Answer 194098 by drk(1908)   on 2010-01-31 12:46:11 (Show Source): You can put this solution on YOUR website!Using our volume formula as and our given information, we get notice I didn't use 3. D = 3, so r = 1.5 by division, we get yrds
 Triangles/263396: Two sides of a triangle have the same length. The third side measures 4 m less than twice that length. The perimeter of the traiangle is 24 m. Find the lengths of the 3 sides.1 solutions Answer 194097 by drk(1908)   on 2010-01-31 12:43:13 (Show Source): You can put this solution on YOUR website!Let x be the length of each equal side and then 2x - 4 is the length of the base. p = a + b + c 24 = a + b + c step 1 - combine like terms to get step 2 - add 4 to get step 3 - divide by 4 to get the three sides are {7, 7, 10}
 Number-Line/263392: please help me solve this equation... 1 solutions Answer 194096 by drk(1908)   on 2010-01-31 12:40:36 (Show Source): You can put this solution on YOUR website!here is the original equation step 1 - multiply by the common denominator of (x+1)(x+2) to get step 2 - combine like terms to get step 3 - subtract 3 to get step 4 - divide to get
 Mixture_Word_Problems/263387: What values are excluded from the domain of the function? (Separate multiple answers with commas. Enter NONE if there are none.) F(x) = (3 x - 9)/(x - 8) 1 solutions Answer 194093 by drk(1908)   on 2010-01-31 12:31:45 (Show Source): You can put this solution on YOUR website!To determine the domain of any function, we ask 2 questions (1) is the variable in a square root of any type? if "yes" set the stuff under the root >= 0 and solve for x. if "no" go to question 2. (2) is the variable information in the denominator? if "yes" set the denominator stuff not = 0 and solve for x. if "no" then you say "all reals" ----- Using these questions on the given problem., we get (1) NO (2) YES so solving for x, we get x = 8. This means we cannot use x = 8 as a domain number.
 Quadratic_Equations/263376: can any quadratic function of the form y=ax^2+bx+c be changed into a quadratic function in vertex form by completing a square?1 solutions Answer 194092 by drk(1908)   on 2010-01-31 12:26:59 (Show Source): You can put this solution on YOUR website!The answer is yes. By completing the square you convert the quadratic equation into the vertex form of a parabola. After the process is done you end up with the following:
 Square-cubic-other-roots/263378: Verify that -2 is a root of the equation Find the other two roots, correct to 2 decimal places.1 solutions Answer 194089 by drk(1908)   on 2010-01-31 12:20:15 (Show Source): You can put this solution on YOUR website!we can use synthetic division to verify. This will generate another equation that we will factor. -2 // . . . 2 . . . . 1 . . . . -10 . . . . . -8 . . . . . . . . . . . . -4 . . . . .6 . . . . . . .8 . . . . . . . 2 . . . . -3 . . . . -4 . . . // . 0 So, we have verified by getting a 0 remainder. We now have a new equation of the form By quadratic, we get and then we have two answers and rounded, we get x ~ 2.35 x ~ -0.85
 Number-Line/263375: (1/x)/(x-3) can you break this down for me step by step? Thanks1 solutions Answer 194088 by drk(1908)   on 2010-01-31 12:15:10 (Show Source): You can put this solution on YOUR website!here is the original problem / step 1 - multiply by 1/(x-3) to get / notice the denominator x-3 parts drop out, so we get which is
 real-numbers/263369: Cant seem to figure this one out :/ Find all solutions of the equation and express them in the form (a+bi) 2x^2 - 2x + 3 = 01 solutions Answer 194086 by drk(1908)   on 2010-01-31 12:12:06 (Show Source): You can put this solution on YOUR website!here is the original equation step 1 - using quadratic, we get and then simplifying the radical, we get and canceling, we get
 Functions/263371: 5/x+3 - 1/x = 1/21 solutions Answer 194085 by drk(1908)   on 2010-01-31 12:09:43 (Show Source): You can put this solution on YOUR website!here is the original equation step 1 - multiply by 2x to get step 2 - subtract x and subtract 8 to get by division, we get
 real-numbers/263370: Find all solutions of the equation and express them in the form (a+bi) z + 4 + 12/z = 0 Thanks :) 1 solutions Answer 194083 by drk(1908)   on 2010-01-31 12:07:18 (Show Source): You can put this solution on YOUR website!here is our original equation: step 1 - multiply by z to get using the quadratic, we get which becomes and then canceling, we get
 logarithm/263191: Evaluate the expression: e^In(x+1)^21 solutions Answer 193953 by drk(1908)   on 2010-01-30 20:03:20 (Show Source): You can put this solution on YOUR website! the e and ln drop out and we are left with