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# Recent problems solved by 'oberobic'

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 Linear-equations/249978: Im no good at these word problems can someone help me? The function H described by H(x)=2.75x+71.48 can be used to predict the height in centimeters, of a womans whos humerus is x cm long Predict the height of a woman whos humerus is 33 cm long? Any help is appreciated thanks.1 solutions Answer 181996 by oberobic(2304)   on 2009-12-14 21:38:31 (Show Source): You can put this solution on YOUR website!The function H(x) defines the height of a woman based on the length of her humerus. H(x) = 2.75x + 71.48 . x=33 is given. . H(x) = 2.75(33) + 71.48 H(x) = 90.75 + 71.48 H(x) = 162.23 . Done
 Equations/249989: An apple costs the same as 2oranges. Together, an orange and a banana cost .10 more than an apple. Two oranges cost .15 more than a banana. what is the cost for one of each fruit?1 solutions Answer 181993 by oberobic(2304)   on 2009-12-14 21:34:35 (Show Source): You can put this solution on YOUR website!A = cost of an apple O = cost of an orange B = cost of a banana . The apple costs the same as 2 oranges... A = 2*O or O = A/2 . An orange and a banana costs 10 cents more than an apple... A + 10 = O + B so A = O + B - 10 and O = A + 10 - B and B = A + 10 - O . Two oranges cost 15 cents more than a banana 2*O = B + 15 so O = (B+15)/2 and B = 2*O - 15 . Now we solve these equations. The key strategy is to get all of the costs in terms of the same fruit... Since we have 3 equations that can be defined in terms of O, we can start with that. . O = A/2 O = A + 10 - B O = (B+15)/2 . If a=b and b=c, then a=c. So we know: A/2 = A+10 - B A = 2A + 20 - 2B 2B = A + 20 . A/2 = (B+15)/2 A = B+15 B = A - 15 2B = 2A - 30 . A+20 = 2A - 30 . A = 50 . Using A = 50 cents, we are able to find the other values by substituting back into the original equations. . A = 2*O so O = 25 . B = A + 10 - O B = 50 + 10 - 25 B = 35 . Substituting back into the initial equations, we are able to check these values. . The apple costs the same as 2 oranges... This statement was used to calculate the value of the oranges, so of course it checks. . An orange and a banana costs 10 cents more than an apple... O + B = 25 + 35 = 60 That is 10 cents more than an apple, so it checks. . Two oranges cost 15 cents more than a banana 2*25 = 50, which is 15 cents more than a banaa. . These all check. So we can conclude that in this case: Apples cost 50 cents. Oranges cost 25 cents. Bananas cost 35 cents. , Done
 Travel_Word_Problems/249957: A boat can travel 9mph in still water. It travels 7 miles downstream in the same time that it travels only 3 miles upstream. Find the rate of the current.1 solutions Answer 181967 by oberobic(2304)   on 2009-12-14 20:50:21 (Show Source): You can put this solution on YOUR website!Start by setting up the variables you will need. s = speed in still water = 9 mph c = current d = rt is the basic distance formula, where d=distance, r=rate, and t=time . Now translate the English into math. . Traveling downstream: r = s+c The current adds to the boat's speed. d=7 in time t . Traveling upstream: r = s - c The current subtracts from the boat's speed. d =3 in time t . We are told t=t so we can rearrange both equation to define 't'. . 7 = (s+c) * t . Divide both sides by (s+c) 7/(s+c) = t . The other equation is: 3 = (s-c) * t . Divide both sides by (s-c) 3/(s-c) = t . Since both equations = t, we can use this fact to set them equal to one another . 7/(s+c) = 3/(s-c) . Cross multiply 7(s-c) = 3(s+c) . 7s - 7c = 3s + 3c . 4s = 10c . Recall s = 9 . 4(9) = 36 = 10c . c = 3.6 The current runs at 3.6 mph . Next substitute back into the original equations to see if this answer is correct. . How long does it take to go 7 miles downstream? 7 = (9+3.6)t = 12.6t t = 7/12.6 = .555555556 . 3 = (9-3.6)t = 5.4t t = 3/5.4 = .555555556 , So we can conclude the current of the river is 3.6 mph. . Done
 Linear_Equations_And_Systems_Word_Problems/249946: write a system of equations that could be used to solve the following problem. solve using elmination. jana opened her coin purse and found dimes, quarters and nickels with a total value of \$1.90. there are twice as many dimes as quarters and half as many nickels as quarters. how many coins of each type did Jana have in her purse?1 solutions Answer 181958 by oberobic(2304)   on 2009-12-14 20:21:47 (Show Source): You can put this solution on YOUR website!With coin problems you have to keep track of the number of coins and the value of the coins. Usually these create two linear equations. . Jana found she had nickels, dimes, and quarters with a total value of \$1.90 = 190 cents. The total value obviously is a value problem, so: 5n + 10d + 25q = 190 , where n = number of nickels d = number of dimes q = number of quarters . But we need to figure out the number of coins, n, d, and q. . We are told in the problem: d = 2q twice as many dimes as quarters n = 1/2q half as many nickels as quarters . Substituting into the value equation, we have . 5(1/2q) + 10(2q) + 25q = 190 . Multiply by 2 to eliminate the fraction 5q + 40q + 50q = 380 . 95q = 380 . q = 4 . She has 4 quarters = 100 cents = \$1.00 . d = 2q = 2(4) = 8 . She has 8 dimes = 80 cents = \$.80 . n = 1/2q = 1/2(4) = 2 . She has 2 nickels = 10 cents = \$.10 . Adding up the dollar amounts, she has \$1.90. . That checks. Done.
 Age_Word_Problems/249488: Mary's father is four times as old as Mary. Five years ago he was seven times as old. How old is each now? Use the five step method to solve using algebra only.1 solutions Answer 181722 by oberobic(2304)   on 2009-12-13 22:58:13 (Show Source): You can put this solution on YOUR website!Step 1. Use some letter to represent the unknown quantity. Step 2. Translate the English into mathematics and create an equation. Step 3. Solve this equation. Step 4. Check your work by substituting your results back into the original problem statement. Step 5. Write your conclusion being sure answer the question asked. . STEP 1. F = Father's age M = Mary's age . STEP 2. Father is 4 times as old as Mary: F = 4*M, where F=Father's age, and M=Mary's age. Five years ago F was 7 times older than M. F-5 = 7(M-5) F-5 = 7M - 35 . STEP 3. substituting F = 4M 4M - 5 = 7M - 35 . adding 5 to both sides 4M = 7M - 30 . subtracting 7M from both sides -3M = -30 . dividing both sides by -3 M = 10 . STEP 4. Mary is 10 now. Father is 4*10 = 40 now. . Five years ago: Mary was 5. Father was 35. Was Father 7 times as old as Mary then? Yes. . Checks. STEP 5. Mary is 10 years old now. Father is 40 years old now.
 Age_Word_Problems/249525: Five years ago, Brad was two years older than 5/6 of his age today. What is his age today1 solutions Answer 181718 by oberobic(2304)   on 2009-12-13 22:41:48 (Show Source): You can put this solution on YOUR website!Brad's current age is: x 5 years ago, Brad's age was: x-5 At that time, his age was 2 more than 5/6*x. What is x? . x-5 = 5/6*x + 2 . Multiply through by 6 to eliminate the fraction 6x - 30 = 5x + 12 . Subtract 5x from both sides x - 30 = 12 . Add 30 to both sides . x = 42 . Five years ago, Brade's age was: x-5 = 37 5/6 of his current age is: 5/6x = 35 which is 2 less than 37. Done
 Linear-equations/249494: State wether the equation y=12x-6 is linear.1 solutions Answer 181716 by oberobic(2304)   on 2009-12-13 22:36:29 (Show Source): You can put this solution on YOUR website!Yes. There is no exponent involved. You can show by graphing it that it is a straight line (linear). To draw a straight line you only need two points and a straight edge to draw the line. . When x=0, y=-6. (0, -6) . When x=1/2, y=0. (1/2, 0) .
 Linear-equations/249529: trying to find slope and y integer for this problem -3x -5y = -25 please help also need to know the parallel slope and perpendicular slope1 solutions Answer 181714 by oberobic(2304)   on 2009-12-13 22:31:27 (Show Source): You can put this solution on YOUR website!Work the algebra to get the equation into slope-intercept form: y = mx + b. -3x -5y = -25 . Add 3x to both sides -5y = 3x -25 . Divide both sides by -5. y = -3/5x + 5 . Slope is -3/5 so any line with slope -3/5 will be parallel. y = -3/5x for example. . Any perpendicular will have negative inverse slope: 5/3. y = 5/3x for example . The following graph illustrates: red line: y=-3/5x+5 green line: y=-3/5x blue line: y = 5/3x .
 Linear-equations/249498: Write th slope intercept form of an equation of the line that passes through the point (4,4) and has the slope m=5.1 solutions Answer 181709 by oberobic(2304)   on 2009-12-13 21:35:15 (Show Source): You can put this solution on YOUR website!Slope-intercept form is: y = mx+b m = 5 (given) Since the slope = rise/run = change in 'y' divided by change in 'x', m=5 tells us that for a change of 1 in x we have a change of 5 in y. . One point is given: (4,4) . Substituting back into the equation, we have... 4 = 5(4) + b 4 = 20 + b -16 = b . So the intercept appears to be -16. . The resulting equation is: y = 5x - 16 . Is it true for (4,4)? Yes. . Is it true for another point? . Well, we can define another point based on knowing the slope. . m=5 means when we add 1 to x, the result is 5 being added to y. Let's do just that: (4+1, 4+5) would do so. . Now we have two points: (4,4) and (5,9). . Does y= 5x -16 work for the point (5,9)? . 9 = 5(5) - 16 9 = 25 - 16 True. . We also are informed by graphing the line. . Looking at the graph reminds us to check the point ( ?, 0). 0 = 5x - 16 5x = 16 x = 3.2 . Inspecting the graph shows that looks right. Done.
 Linear_Equations_And_Systems_Word_Problems/249485: larry takes 1 1/2 times as long to go 72 miles upstream as he takes to go 72 miles downstream. if the speed of his boat in still water is 30 mph, what is the speed of the current?1 solutions Answer 181708 by oberobic(2304)   on 2009-12-13 21:22:33 (Show Source): You can put this solution on YOUR website!time going upstream = 1.5 * time going downstream distance = 72 miles rate in still water (no current) = 30 mph What is the current? . Recall d=rt, where d=distance, r=rate, and t=time. . We can set the upstream leg of the trip as: 72 = (30-x)*1.5 . The downstream leg of the trip is: 72 = (30+x)*1 . Since the distances are equal, we can set the right-hand sides to equal each other. . (30-x)*1.5 = 30+x 45 - 1.5x = 30 + x . Subtracting adding 1.5x to both sides... 45 = 30 + 2.5x . Subtracting 30 from both sides... 15 = 2.5x so 2.5x = 15 . Divide both sides by 2.5... x = 15/2.5 = 6 . So our proposed speed of the current = 6 mph. . Checking our work . The upstream leg would have a speed against the current of 24 mph. Traveling 72 miles would take 72/24 = 3 hr. . The downstream leg would have a speed assisted by the current of 36 mph. Traveling the 72 miles would take 72/36 = 2 hr. . Thus the roundtrip would be 5 hrs. The total distance traveled would be 144 miles. So the average speed would be be 144/5 = 28.8 mph . Done.
 Numbers_Word_Problems/249475: the sum of 2 consecutive integers is 27 more than 5 times the larger integer find the integers1 solutions Answer 181706 by oberobic(2304)   on 2009-12-13 20:57:57 (Show Source): You can put this solution on YOUR website!We always seek ways to use the fewest unknowns when solving word problems. . We could call the two integers 'x' and 'y'. But we are told they are consecutive, so we can say: x = x y = x+1 That gives us only one unknown, 'x'. . We also are given some relationships: the sum of two consecutive integers: x + x+1 is 27 more than 5 times the larger integer: 5(x+1) + 27 . So, x + x+1 = 5(x+1) + 27 . Collecting and simplifying terms 2x + 1 = 5x + 5 + 27 2x + 1 = 5x + 32 . Subtracting 1 from both sides 2x = 5x + 31 . Subtracting 5x from both sides -3x = 31 . Dividing both sides by -3 shows that 'x' is NOT an integer, so there is no solution... . If only the setup had been 26 more instead of 27. (Or is that a typo?) Then we would have had: . 2x + 1 = 5x + 5 + 26 2x + 1 = 5x + 31 2x = 5x + 30 -3x = 30 x = -10 . Then the two consecutive integers would have been: -10 and -9. -10 + (-9) = -19 . 5*(-9) = -45 -45 + 26 = -19 . Done.
 Proportions/249470: if one painter can paint a house in 6 hours, and another painter paints a house in 9 hours. How long will it take them to paint the house working together1 solutions Answer 181695 by oberobic(2304)   on 2009-12-13 20:39:02 (Show Source): You can put this solution on YOUR website!The key to solving "job" problems is to realize the job is 1 whole job that is divided into components that people do at different rates. . One painter paints the house in 6 hours, so his rate is 1/6 of the house per hour. The other painter takes 9 hrs, so his rate is 1/9 of the house per hour. . Since we are not told otherwise, we assume they are working simultaneously: we assume they start and stop at the same time. So each of them works the same amount of time, which we will call 'x' hours. . First we set up time/rate for both painters: painter 1 works 'x' hrs at 1/6 of the whole job per hr; painter two works 'x' hrs at 1/9 of the whole job per hr: . The least common denominator is 54: . Cross multiply . Divide both sides by 15 Working together it takes them 3.6 hrs to paint the house. . Check by substituting back into the painter's rates to see if they total 1. So working together they complete 1 whole job in 3.6 hr = 3 hr 36 min = 216 minutes, depending on the units the answer should be in. . Done.
 Exponents-negative-and-fractional/249473: what is the algebraic expression to m to the 8th power multiplied by n to the negative 3rd power?1 solutions Answer 181686 by oberobic(2304)   on 2009-12-13 20:24:25 (Show Source):
 Money_Word_Problems/249469: Factor 1 solutions Answer 181680 by oberobic(2304)   on 2009-12-13 20:15:31 (Show Source): You can put this solution on YOUR website!The cubic root of The cubic root of . You can check by doing repeated multiplication: .
 Rectangles/249465: please guide me on how to solve this problem: the length of a rectangle is 5cm. more than twice the width. the perimeter of the rectangle is 34 cm. find the dimensions of the rectangle. 1 solutions Answer 181678 by oberobic(2304)   on 2009-12-13 20:11:01 (Show Source): You can put this solution on YOUR website!Turn each statement into an equation using the fewest possible unknowns. . L = length of the rectangle . Length is twice the width plus 5. L = 2W + 5 . P = perimeter of a rectangle. P = 2L + 2W = 2(L + W) P = 34 (given) . Substituting what we know... 34 = 2(L + W) . Divide both sides by 2... 17 = L + W . Substituting L = 2W+5... 17 = 2W + 5 + W . Collecting terms and subtracting 5 from both sides 12 = 3W so 3W = 12 . Dividing both sides by 3 W = 4 . L = 2W+5 L = 2(4)+5 L = 8+5 L = 13 . Checking the perimeter P = 2(L+W) = 2(13+4) = 2(17) = 34 . Checks.
 Travel_Word_Problems/249444: Mrs. Smith drove at a rate of 45 mph from her home to her sisters house. she spent 1.5 hrs having lunch with her sister. She then drove back home at a rate of 55 mph. The entire trip, including lunch, took 4 hrs. How far does Mrs. Smith live from her sister? 1 solutions Answer 181676 by oberobic(2304)   on 2009-12-13 20:04:51 (Show Source): You can put this solution on YOUR website!The elapsed time is 4 hr of which 2.5 hr was driving time. The distance formula is d = rt, where d=distance, r=rate, t=time We assume the distance to her sister's is the same as it is home (or she drives the same path both ways without any detours). . We can define the equation for driving to her sister's house: d = 45(t) . Then the equation for driving home from her sister's house is: d = 55(2.5-t) . In this way, we have defined the two unknown times in terms of a single unknown variable 't' and '2.5-t'. . Since d = d, we can say: 45t = 55(2.5-t) 45t = 137.5 - 55t . Adding 55t to both sides 100t = 137.5 . Dividing both sides by 100 t = 1.375 . So the time spend driving to her sister's house at 45 mph = 1.375 hr The time spend driving home at 55 mph = 2.5 - 1.375 = 1.125 hr . How far does she travel at 45 mph? d = 45 mph * 1.375 hr = 61.875 miles. How far does she travel at 55 mph? d = 55 mph * 1.125 hr = 61.875 miles. . So we've checked our work and are confident the distance is 61.875 = 61 7/8 miles. . We could be asked what her average speed was, too. Was it simply (45+55)/2? . Well, we see that 2d = 2*61.875 = 123.75 miles And it took 2.5 hr, so t = d/r = 123.75/2.5 = 49.5. So her average speed was 49.5. . Done.
 Travel_Word_Problems/249429: A man drives from home to work at a speed of 50mi/h. The return trip from work to home is traveled at the more leisurely pace of 30 mi/h. What is the man's average speed for the round trip? (I know the answer is not 40mi/h though)1 solutions Answer 181672 by oberobic(2304)   on 2009-12-13 19:43:39 (Show Source): You can put this solution on YOUR website!We know the basic formula for distance problems is: d = rt, where d=distance, r=rate, t=time. We know the man drives to work at 50 mph. We know he drives home at 30 mph. We know the distance is the same both ways. What we do not know are the times involved. . Let's assume he drives 30 miles to and from work. At 50 mph it takes him 30/50 or .6 of an hour to drive to work. .6*60 = 36 minutes At 30 mph it takes him 30/30 or 1 hr to drive home = 60 minutes . So the total elapsed time is 96 minutes to drive 60 miles. 96 minutes = 1.6 hr . Going back to d=rt . 60 miles = r mph * 1.6 hr = 1.6r . Dividing both sides by 1.6 37.5 = r r = 37.5 . Checking our work... How far will the car go in 1.6 hr at 37.5 mph? 60 miles OK.
 Quadratic_Equations/249403: The diagonal of a television set is 52 inches long. Its length is 28 inches more than its height. Find the dimensions of the television set.1 solutions Answer 181666 by oberobic(2304)   on 2009-12-13 19:12:21 (Show Source): You can put this solution on YOUR website!The diagonal of the TV can be considered the hypotenuse of a right triangle. It can be solved using the Pythagorean formula: . Assuming L is the width of the TV set, which the problem calls "length", and H is the height of the screen. . Returning to the Pythagorean formula... . . Substituting L = H+28 . Squaring 52 . Dividing both sides by 2 . Subtracting 1352 from both sides . Simplifying . Can 960 be factored such that the two terms are 28 apart? Yes. 48*20 = 960 and 48-20=28 . . So we have two candidate solutions: H= -48 and H = 20. Since a negative height is nonsense, then our suggested answer is: . Looking back to our defined equations, . Checking by using the Pythagorean formula: . So that checks just fine. . But is it an analog TV or an HDTV? . Analog TV has a ratio of width to height of 4:3. The picture is 4 units wide by 3 units high. HDTV has a ration of 16:9. The picture is 16 units wide by 9 units high. . Our proposed TV set has a picture that is 48 wide by 20 high. That is a ratio of 48:20, or 24:10, or 12:5. This does not correspond to any real TV set. So perhaps a negative height would work when solving an "imaginary" TV problem. Hmmm...
 Geometry_Word_Problems/249398: The length of a rectangle is 4 inches more than its width. It 2 inches are taken from the length and added to the width, the figure becomes a square with an area of 196 square inches. What are the dimensions of the original figure?1 solutions Answer 181642 by oberobic(2304)   on 2009-12-13 18:27:57 (Show Source): You can put this solution on YOUR website!Setting up the equations is the key to solving word problems. Drawing a diagram is helpful, too. . L = W+4 (the length is 4 inches more than length (given)) . L-2 (if 2 inches are taken from L) and added to the width (W+2) the figure becomes a square. A square has 4 equal sides. L-2 = W+2 . We are told the area of the square is 196. (L-2)(W+2) = 196 . Substituting from L = W+4 (W+4 -2)(W + 2) = 196 (W+2)(W+2) = 196 . Taking the square root (W+2) = sqrt(196) = 14 . Subtracting 2 from both sides W = 12 and L = W+4 = 16 . Is the length 4 more than width? Yes. If you subtract 2 from length and add 2 to width, and then multiply them, is the result 196? Yes. Done.
 real-numbers/249379: Solve the problem. Clearwater Community College had 1242 students enrolled in 1998 and 980 students enrolled in 1999. Find the percent of decrease in the number of students from 1998 to 1999. Round to the nearest tenth of a percent.1 solutions Answer 181633 by oberobic(2304)   on 2009-12-13 18:16:20 (Show Source): You can put this solution on YOUR website!Percentage change is always calculated by . . multiply by 100 to get percent 26.7% rounded to tenths .
 Radicals/249392: how to simplify the expression (sqrt8) and write it in radical form.1 solutions Answer 181629 by oberobic(2304)   on 2009-12-13 18:08:45 (Show Source):
 Triangles/249228: two sides of a triangle have lengths 6 and 11. the third side has to be?1 solutions Answer 181569 by oberobic(2304)   on 2009-12-13 14:00:40 (Show Source): You can put this solution on YOUR website!Assuming it is a right triangle, the Pythagorean formula applies:
 Rectangles/249084: The width of a rectangle is 5 meters less than twice its length. If its area is 88 square meters, find the dimensions of the rectangle. I appreciate your help!1 solutions Answer 181481 by oberobic(2304)   on 2009-12-12 21:33:54 (Show Source): You can put this solution on YOUR website! . Substitute . Subtract 88 from both sides so . Can you factor this? Yes. . . So our candidate solutions are L = -5.5 and L = 8. . A negative number for the side of the rectangle is nonsense. So our answer is L = 8. . Recall so . With L = 8 and W = 11, the area = 88. So we're done.
Graphs/248955: Find the x- and y-intercepts. If no x-intercepts exist, state so.

1 solutions

Answer 181390 by oberobic(2304)   on 2009-12-12 11:33:59 (Show Source):
You can put this solution on YOUR website!

.
y-intercept is defined by f(0).
It is where the line crosses the y-axis.

.
x-intercept is defined by f(x) = 0.
It is where the line crosses the x-axis.
Recall

If x=4, then the entire right-hand side = 0, so that is an x-intercept.
If x=-3, then the entire right-hand side = 0, so that is another x-intercept.
.
The graph is useful to review. It is a parabola.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=196 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, -3. Here's your graph:

 Mixture_Word_Problems/248824: If to my age there added be; one half, one third and three times three six score and ten the sum what's my age1 solutions Answer 181339 by oberobic(2304)   on 2009-12-11 23:13:58 (Show Source): You can put this solution on YOUR website!There is something missing from your statement. Please try again.
 Linear_Equations_And_Systems_Word_Problems/248822: twice one number added to another number is 18. four times the first number minus the other number is 12. find the numbers.1 solutions Answer 181338 by oberobic(2304)   on 2009-12-11 23:12:54 (Show Source): You can put this solution on YOUR website!The statements become the following equations. 2x + y = 18 4x - y = 12 . 2x + y = 18 Subtract 2x from both sides y = -2x + 18 . Substitute into the 2nd equation 4x - (-2x + 18) = 12 4x +2x - 18 = 12 Combine terms 6x -18 = 12 Add 18 to both sides 6x = 30 Divide both sides by 6 x = 5 . Looking back, we recall: 2x + y = 18 4x - y = 12 . 2(5) + y = 18 10 + y = 18 Subtract 10 from both sides y = 8 . 4(5)-8 = 12 True . So the two numbers are: x = 5 y = 8
 Rate-of-work-word-problems/248810: Sam can mow a lawn in 20 minutes and Robert can mow the same lawn in 30 minutes. If they worked together, how long would it take them to do the work? I need the rate of work (R), the time of work (T) , and the work done (W) the equation is RT = W. It would help if I am provided a detailed explanation1 solutions Answer 181336 by oberobic(2304)   on 2009-12-11 23:07:46 (Show Source): You can put this solution on YOUR website!The critical insight is that you have to get the equations in terms of accomplishing 1 job. . Sam can do the job in 20 min. So he can do the whole job at the rate of 1 job in 20 minutes. So he does 1/20 of the job per minute. . Rob can do the job in 30 min. His rate is 1/30 of the job per minute. . Working together how does it take? . 1/20*x + 1/30*x = 1 job done , where x = minutes. . Multiply everything by 60 go get rid of the fractions. 3x + 2x = 60 5x = 60 . Divide both sides by 12 x = 12 . So our candidate answer is working together it will take them 12 minutes. . Let's check. In 12 minutes, Sam does 12/20 of the job and Rob does 12/30 of the job. 12/20 = .6 12/30 = .4 Total = 1 job done.
 Equations/248856: Determine where the two lines x+4y=3 and 2x-6y=8 intersect?1 solutions Answer 181334 by oberobic(2304)   on 2009-12-11 23:00:54 (Show Source): You can put this solution on YOUR website!Arrange both equations in slope-intercept form. . The first equation is: Subtract x from both sides Divide both sides by 4 . The second equation is: Subtract 2x from both sides Divide both sides by -6 . By inspection, we know the two lines are not parallel because they do not have the same slope. So they cannot be the same line. We also can tell they are not perpendicular. . The two equations will intersect the points will be the same. . Multiply both sides by 12 to remove the fractions Subtract 4x from both sides Subtract 9 from both sides Divide both sides by -7 . Graph
Quadratic_Equations/248831: 1. x2 - 8x + 16 = 36
2. use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions. 3 + 8z2 = -7z
1 solutions

Answer 181331 by oberobic(2304)   on 2009-12-11 22:37:06 (Show Source):
You can put this solution on YOUR website!
1.

subtract 36 from both sides

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=144 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 10, -2. Here's your graph:

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2.

Add 7z to both sides and rearrange

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . The discriminant -47 is less than zero. That means that there are no solutions among real numbers. If you are a student of advanced school algebra and are aware about imaginary numbers, read on. In the field of imaginary numbers, the square root of -47 is + or - . The solution is Here's your graph:

 Permutations/248855: how many ways can a committee of 3 men and 3 women be formed from a group of 9 men and women1 solutions Answer 181330 by oberobic(2304)   on 2009-12-11 22:31:29 (Show Source): You can put this solution on YOUR website!It depends on how men and women there are in the group of 9.