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# Recent problems solved by 'nerdybill'

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 Angles/187738: Can someone help me with this please. If the measure of an angle is 23 degrees 17' 18", what is the measure of its supplement?1 solutions Answer 140786 by nerdybill(6951)   on 2009-03-22 17:18:31 (Show Source): You can put this solution on YOUR website! Can someone help me with this please. If the measure of an angle is 23 degrees 17' 18", what is the measure of its supplement? . Two angles are "supplementary" if the sum of the two angles equals 180. . 180 00' 00" 23 17' 18" . Borrowing from the 180 and then subtracting we have: 179 59' 60" 23 17' 18" ----------- 156 42' 42" . That is, 156 degrees 42 minutes and 42 seconds
 test/187730: Where will the line 3x+12y=24 cut the y-axis? Please put the solution.. thank you for being so nice and helpful tutors..^^1 solutions Answer 140750 by nerdybill(6951)   on 2009-03-22 10:57:54 (Show Source): You can put this solution on YOUR website!Where is "cuts the y-axis" is equivalent to the y-intercept. . To find it, set x = 0 and solve for y: 3x+12y=24 3(0)+12y=24 0+12y=24 12y=24 y = 2 . Therefore, it "cuts the y-axis" at (0, 2)
 Surface-area/187735: The radius of the circle x^2+y^2-2x-2y+2=0 Thanks for the big help.. Kindly put the solution..1 solutions Answer 140747 by nerdybill(6951)   on 2009-03-22 10:54:06 (Show Source): You can put this solution on YOUR website!Standard equation of a circle is: (x - h)^2 + (y - k)^2 = r^2 . We "complete the square" to put our equation into the standard form: x^2+y^2-2x-2y+2=0 x^2+y^2-2x-2y = -2 (x^2-2x)+(y^2-2y) = -2 (x^2-2x+1)+(y^2-2y+1) = -2+1+1 (x-1)^2+(y-1)^2 = 0 . Radius = 0
Equations/187699: This question is from textbook mathematical analysis
If Y= f(x)= 5-x-3x^2
Find
a) the Y-intercept
b) the X-intercept
c) th vertex
Thank you,,

1 solutions

Answer 140746 by nerdybill(6951)   on 2009-03-22 10:48:11 (Show Source):
You can put this solution on YOUR website!
If Y= f(x)= 5-x-3x^2
Find
a) the Y-intercept
y = -3x^2 - x + 5
Set x = 0 and solve for y:
y = -3(0)^2 - 0 + 5
y = -0 - 0 + 5
y = 5
So, y-intercept is at (0, 5)
.
b) the X-intercept
Set y = 0 and solve for x:
y = -3x^2 - x + 5
0 = -3x^2 - x + 5
Since we can't factor, we must use the quadratic equation.
Doing so yields:
x = {-1.468, 1.135}
Note: details at the end
.
c) the vertex
.
vertex form:
y= a(x-h)^2+k
.
Starting with:
y = -3x^2 - x + 5
y = -3(x^2 + (1/3)x) + 5
y = -3(x^2 + (1/3)x + 1/36) + 5 + 1/13
y = -3(x + 1/6)^2 + 66/13
y = -3(x - (-1/6))^2 + 66/13
.
Therefore, vertex is at (-1/6, 66/13)
.
.
.
Details of solving the quadratic for part b follows:
 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=61 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -1.46837494598444, 1.13504161265111. Here's your graph:

 Problems-with-consecutive-odd-even-integers/187711: 3 times the first three consecutive numbers is 4 more than 2 times the second 1 solutions Answer 140743 by nerdybill(6951)   on 2009-03-22 10:34:12 (Show Source): You can put this solution on YOUR website!Let x = first of three consecutive numbers x+1 = second of three consecutive numbers x+3 = third of three consecutive numbers . 3x = 2(x+1) + 4 3x = 2x + 2 + 4 3x = 2x + 6 x = 6 . Our three consecutive numbers are: 6, 7, and 8
 Miscellaneous_Word_Problems/187716: The width of a rectangle is fixed at 15cm. What lengths will make the permiter greater than 72 cm1 solutions Answer 140742 by nerdybill(6951)   on 2009-03-22 10:30:37 (Show Source): You can put this solution on YOUR website!Let x = length width is given as 15 cm . Perimeter = 2(width + length) . 72 < 2(15+x) dividing both sides by 2: 36 < 15+x subtracting both sides by 15: 21 < x . This says that the length has to be "greater than" 21 cm.
 Graphs/187705: What is the value of x when 8x-7=5x+2 ?1 solutions Answer 140740 by nerdybill(6951)   on 2009-03-22 10:26:48 (Show Source): You can put this solution on YOUR website!8x-7=5x+2 Add 7 to both sides: 8x-7+7=5x+2+7 8x=5x+9 . Subtract 5x from both sides: 8x=5x+9 8x-5x=5x+9-5x 3x=9 . Divide both sides by 3: (3x)/3=9/3 x=3
 Pythagorean-theorem/187647: Woody Woodpecker picked at a 17m wooden pole until it cracked and the upper part fell, reaching a point on the ground 10m from the foot of the pole. Since the pole had not completely broken off, Woody pecked away where it had cracked. How far was Woody above the ground?1 solutions Answer 140700 by nerdybill(6951)   on 2009-03-21 19:29:57 (Show Source): You can put this solution on YOUR website!Let x = distance Woody above ground then hypotenuse = 17-x . From Pythagorean: x^2 + 10^2 = (17-x)^2 x^2 + 100 = 289 - 34x + x^2 100 = 289 - 34x -189 = -34x -189/-34 = x 5.559m = x
 Linear-systems/187648: Draw a graph of the line passing through the points(-6,-7) and(-3,-5).Does the point (3,-1)also lie on this line? 1 solutions Answer 140681 by nerdybill(6951)   on 2009-03-21 14:57:56 (Show Source): You can put this solution on YOUR website!Draw a graph of the line passing through the points(-6,-7) and(-3,-5).Does the point (3,-1)also lie on this line? . Algebraically: slope m = (-5+7)/(-3+6) = 2/3 . y - y1 = m(x - x1) y - (-5) = (2/3)(x - (-3)) y + 5 = (2/3)x + 2 y = (2/3)x - 3 (this is the equation of the line) . Testing the point:(3,-1) y = (2/3)x - 3 -1 = (2/3)3 - 3 -1 = 2 - 3 -1 = -1 . So, YES, the point does lie on the line. .
 Equations/187638: This question is from textbook mathematial analysis If p represents price per unit in dollars and q represents the number of units per unit of time, find the equilibrium point. Supply: p= (q+10)^2 , Demand: p=388-16q-q^2 With details Thank you,1 solutions Answer 140668 by nerdybill(6951)   on 2009-03-21 11:32:52 (Show Source): You can put this solution on YOUR website!The equilibrium point is when supply and demand are equal. . Supply: p= (q+10)^2 , Demand: p=388-16q-q^2 . Notice BOTH equation defines 'p'. Set them equal to each other then solve for 'q': (q+10)^2 = 388-16q-q^2 Expanding the left side with FOIL: (q+10)^2 = 388-16q-q^2 (q+10)(q+10) = 388-16q-q^2 q^2 + 20q + 100 = 388-16q-q^2 Move all terms to the left: 2q^2 + 20q + 100 = 388-16q 2q^2 + 36q + 100 = 388 2q^2 + 36q - 288 = 0 Divide both sides by 2: q^2 + 18q - 144 = 0 Factoring the left: (q+24)(q-6) = 0 . q = {-24, 6} A negative solution does not make sense so: q = 6
 test/187479: how do you write this in vertex form?? y= x{squared}+ 18x-4 it is algebra 21 solutions Answer 140516 by nerdybill(6951)   on 2009-03-19 20:57:53 (Show Source): You can put this solution on YOUR website!The vertex form is: y= a(x-h)^2+k where (h,k) is the vertex . For more info, see: http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php . For your problem: y= x^2 + 18x - 4 . You must "complete the square": y= (x^2 + 18x) - 4 Take half of 18 and square it: y= (x^2 + 18x + 81) - 4 - 81 y= (x^2 + 18x + 81) - 85 y = (x+9)^2 - 85 (this is what they're looking for)
 Systems-of-equations/187419: 2x + 2y=8 and 4x-6y=36 solution (6,2) how did my text book come up with thesesolutions1 solutions Answer 140483 by nerdybill(6951)   on 2009-03-19 17:11:20 (Show Source): You can put this solution on YOUR website!Assuming you are expected to solve a system linear equations using the "elimination method": . 2x + 2y = 8 4x - 6y = 36 . multiply both sides of the top equation and add it to the second: 6x + 6y = 24 4x - 6y = 36 ------------ 10x = 60 Dividing both sides by 10: x = 6 . Now, we plug the value above into either equation to find y. Let's pick the top one: 2x + 2y = 8 2(6) + 2y = 8 12 + 2y = 8 2y = -4 y = -2 . therefore: (x,y) = (6, -2)
 Percentage-and-ratio-word-problems/187415: Mary went to a new shopping mall with a new \$50.00 dollar bill. She bought two b-day cards for a total of \$9.55 and a small OJ soda for .95 cents. She was required to pay an 8% state sales tax on the total purchase. What PERCENT of her hard earned money does she have left? Thanks!1 solutions Answer 140482 by nerdybill(6951)   on 2009-03-19 17:06:10 (Show Source): You can put this solution on YOUR website!cost of items = 9.55 + .95 = 10.5 tax on items = 10.5(.08) = 0.84 . Total amount spent = 0.84 + 10.5 = 11.34 . Amount left = 50 - 11.34 = 38.66 . Percent left = 38.66/50 * 100 = 0.7732 * 100 = 77.32%
 Exponential-and-logarithmic-functions/187155: 9^X = 1/2431 solutions Answer 140284 by nerdybill(6951)   on 2009-03-17 21:57:04 (Show Source): You can put this solution on YOUR website!9^X = 1/243 Take log9 (log base 9) of both sides: X = log9(1/243) X = log9(1) - log9(243) X = log(1)/log(9) - log(243)/log(9) X = 0/log(9) - log(243)/log(9) X = -log(243)/log(9) X = -2.5
 Equations/187094: Can you please help me solve this system of equations for x? 5x-2y=22 x+2y=2 thank you1 solutions Answer 140244 by nerdybill(6951)   on 2009-03-17 18:08:54 (Show Source): You can put this solution on YOUR website!You can use the "addition method". Starting with: 5x-2y = 22 x+2y = 2 . Add the two equation together to get: 5x-2y = 22 x+2y = 2 ---------- 6x = 24 Dividing both sides by 6 x = 4
 Quadratic_Equations/187102: This question is from textbook Algebra 2 Hello I was doing my homework on quadratic functions and I have a question on a problem that my teacher never went over before. 1. Find a quadratic function that includes each set of values. (1,-2),(2,-2),(3,-4) Please show me work because I would like to know how to do it. Thank You 1 solutions Answer 140242 by nerdybill(6951)   on 2009-03-17 18:06:26 (Show Source): You can put this solution on YOUR website!A quadratic looks like: y = ax^2 + bx + c . The problem gives you three points: (1,-2),(2,-2),(3,-4) Which relates to: (1,-2) -2 = a(1)^2 + b(1) + c -2 = a + b + c . (2,-2) -2 = a(2)^2 + b(2) + c -2 = 4a + 2b + c . (3,-4) -4 = a(3)^2 + b(3) + c -4 = 9a + 3b + c . Now, you have basically a "system of equations": -2 = a + b + c -2 = 4a + 2b + c -4 = 9a + 3b + c . Can you finish the problem from here?
 Polynomials-and-rational-expressions/186974: 2x^4+15x^2-8 How do I find the answer by using the grouping method? What are the steps?1 solutions Answer 140142 by nerdybill(6951)   on 2009-03-16 22:00:29 (Show Source): You can put this solution on YOUR website!For: 2x^4+15x^2-8 you do not need to use grouping. . Factoring would give you: (2x^2+1)(x^2-8)
 Expressions-with-variables/186736: The HP Laser Jet 9000 works twice as fast as the Laser Jet 2300. If the machines work together, a university can produce all its staff manuals in 15hr. Find the time it would take each machine, working alone, to complete the same job?1 solutions Answer 139972 by nerdybill(6951)   on 2009-03-15 10:50:53 (Show Source): You can put this solution on YOUR website! The HP Laser Jet 9000 works twice as fast as the Laser Jet 2300. If the machines work together, a university can produce all its staff manuals in 15hr. Find the time it would take each machine, working alone, to complete the same job? . Let x = speed of Laser Jet 2300 then 2x = speed of Laser Jet 9000 . 15(x + 2x) = 1 15x + 30x = 1 45x = 1 x = 1/45 the above says, completes a job in 45 hours (speed of Laser Jet 2300) . Laser Jet 9000: 2x = 2(1/45) = 2/45 = 1/22.5 the above says, completes a job in 22.5 hours (speed of Laser Jet 9000) .
 Graphs/186715: can you please help me with the math problem i got stuck on. my teacher says we need the bottom equation to solve the top equation then to find the answer to the bottom equation after. 0.3x-0.2y=0.5 x-2y=-51 solutions Answer 139971 by nerdybill(6951)   on 2009-03-15 10:44:55 (Show Source): You can put this solution on YOUR website!my teacher says we need the bottom equation to solve the top equation then to find the answer to the bottom equation after. 0.3x-0.2y = 0.5 (top equation) x- 2y = -5 (bottom equation) . Taking the "bottom equation", let's solve for 'x': x- 2y = -5 adding 2y to both sides we get: x = 2y -5 . Now, we take the above, and substitute it into the "top equation": 0.3x-0.2y = 0.5 0.3(2y -5)-0.2y = 0.5 distributing the 0.3 to terms inside the parenthesis: 0.6y-1.5 -0.2y = 0.5 combining y's: 0.4y-1.5 = 0.5 adding 1.5 to both sides: 0.4y = 2 y = 2/0.4 y = 5 (solution for y) . Finally, we take the above solution of y and plug it back into the bottom equation and solve for x: x- 2y = -5 x- 2(5) = -5 x- 10 = -5 adding 10 to both sides: x = 5 (solution for x) . Solution: y=5 x=5 . The above method is called the "substitution method".
 Quadratic_Equations/186696: Please Help me with this problem. I am very confused. Determine whether the following equation have a solution or not? √2 x² - 4x – 7 √2 = 01 solutions Answer 139953 by nerdybill(6951)   on 2009-03-14 22:22:28 (Show Source): You can put this solution on YOUR website!√2 x² - 4x – 7 √2 = 0 . The coefficients are: a = √2 b = -4 c = 7√2 . The determinant (stuff under the radical in the quadratic equation): b^2 - 4ac = (-4)^2 - 4(√2)(7√2) = 16 - 4(2)(7) = 16 - (8)(7) = 16 - 56 = -40 . Since the determinant is negative, you will have two complex solutions. . See: http://www.purplemath.com/modules/quadform3.htm for additional information
 Finance/186674: Tony put some money into a savings account and deposited no more into this account for one year. At the end of the year, there was \$5885 in the account, including 7% of the original amount for interest. How much did he deposit originally? and (seperated) After a 15% discount, an item was sold for \$61.20. What was the original price of the item? thank you for helping1 solutions Answer 139942 by nerdybill(6951)   on 2009-03-14 20:55:11 (Show Source): You can put this solution on YOUR website!Tony put some money into a savings account and deposited no more into this account for one year. At the end of the year, there was \$5885 in the account, including 7% of the original amount for interest. How much did he deposit originally? . Let x = original amount deposited then x + .07x = 5885 x(1+.07) = 5885 x(1.07) = 5885 x = 5885/1.07 x = \$5500.00 . . . After a 15% discount, an item was sold for \$61.20. What was the original price of the item? Let x = original price then x - .15x = 61.20 x(1 - .15) = 61.20 x(.85) = 61.20 x = 61.20/(.85) x = \$72.00
 Miscellaneous_Word_Problems/186660: if sally can paint a house in 4 hours, and john can paint the same house in 6 hours, how long will it take for both of them to paint the house together?1 solutions Answer 139919 by nerdybill(6951)   on 2009-03-14 16:07:53 (Show Source): You can put this solution on YOUR website!Let x = hours it takes for both: then x(1/4 + 1/6) = 1 x/4 + x/6 = 1 6x + 4x = 24 10x = 24 x = 2.4 hours or 2 hours and 24 minutes
 Angles/186648: The supplement of an angle measures 37 degrees more than twice its complement. Find the measure of the angle.1 solutions Answer 139917 by nerdybill(6951)   on 2009-03-14 15:04:23 (Show Source): You can put this solution on YOUR website!. If two angles are supplementary, their angles add up to 180. If two angles are complementary, their angles add up to 90. . Let x = measure of the angle . Supplement = 180-x Complement = 90-x . Finally, from: "The supplement of an angle measures 37 degrees more than twice its complement." we get: 180-x = 2(90-x) + 37 180-x = 180-2x + 37 -x = -2x + 37 x = 37 degrees
 Geometry_Word_Problems/186619: Suppose y varies directly as x, and y=-65 when x=-26. Write a direct variation equation that relates x and y.1 solutions Answer 139900 by nerdybill(6951)   on 2009-03-14 09:41:46 (Show Source): You can put this solution on YOUR website! Suppose y varies directly as x, and y=-65 when x=-26. Write a direct variation equation that relates x and y. . If "y varies directly as x" it is in the form of: y = kx where k is a constant . Using the values provided, you can find k. y = kx -65 = k(-26) -65/(-26) = k 2.5 = k . So, our equation is: y = 2.5x
 Geometry_Word_Problems/186620: Wite the slope-intercept form of an equation for a line that passes through (-1,0) and is perpendicular to the graph of 3x-5y=201 solutions Answer 139899 by nerdybill(6951)   on 2009-03-14 09:31:50 (Show Source): You can put this solution on YOUR website! Wite the slope-intercept form of an equation for a line that passes through (-1,0) and is perpendicular to the graph of 3x-5y=20 . First, determine the slope of 3x-5y=20 . Do this by putting it into the "slope-intercept" form: y = mx + b where m is slope b is y-intercept . 3x-5y=20 -5y = 3x + 20 y = (-3/5)x + (-3/5)20 y = (-3/5)x - 12 . So, if we want to be "perpendicular" to the line above, the NEW slope must be the "negative reciprocal" of -3/5. Let M = our new slope M(-3/5) = -1 M = 5/3 . The NEW line now has slope of 5/3 passing through (-1,0) . Plug the above into the "point-slope" form: y - y1 = m(x - x1) y - 0 = (5/3)(x - (-1)) y = (5/3)(x + 1) y = (5/3)x + 5/3 (this is what they're asking for)
 Geometry_Word_Problems/186616: An 18-foot ladder is placed 6 feet from the wall. Approximately how high does the ladder reach?1 solutions Answer 139897 by nerdybill(6951)   on 2009-03-14 09:24:51 (Show Source): You can put this solution on YOUR website!An 18-foot ladder is placed 6 feet from the wall. Approximately how high does the ladder reach? . Draw a diagram of the problem, it'll help you "see" the solution easier. . Basically, you have a right-triangle so you can apply Pythagorean theorem: . Let h = height the ladder reaches then h^2 + 6^2 = 18^2 h^2 = 18^2 - 6^2 h^2 = 324 - 36 h^2 = 288 h = sqrt(288) h = 16.97 feet
 Linear-systems/186643: in elmination how would i solve this:x+2y=-9 4x+2y=61 solutions Answer 139895 by nerdybill(6951)   on 2009-03-14 09:20:13 (Show Source): You can put this solution on YOUR website! x+2y=-9 4x+2y=6 . Multiply both sides of top equation by -1: -x-2y=9 4x+2y=6 . Now, add the two equation together: -x-2y=9 4x+2y=6 ------- 3x =18 x = 6 (solution for x) . Substitute the above back into the original top equation and solve for y: x+2y=-9 6+2y=-9 2y=-15 y=-15/2 (solution for y)
 Geometry_Word_Problems/186618: Find the slope of the line that passes through(-2,9.5) and (4,5).1 solutions Answer 139894 by nerdybill(6951)   on 2009-03-14 08:34:09 (Show Source): You can put this solution on YOUR website! Find the slope of the line that passes through(-2,9.5) and (4,5). . m (slope) = (y2 - y1)/(x2 - x1) . Plugging in our values into: m = (y2 - y1)/(x2 - x1) m = (9.5 - 5)/(-2.9 - 4) m = (9.5 - 5)/(-2 - 4) m = (4.5)/(-6) m = - 4.5/6 m = - 1.5/2 m = - (3/2)/2 m = - 3/4
 Linear-equations/186637: I have 28 coins in my pocket, they are all either nickels and dimes. There are eight more nickels than dimes. The value of these coins is 1.90. How many nickels? How many answers should I have?Define my variable, define in terms? Translate this information into an equation? Thank You guys you all are life savers in my class.1 solutions Answer 139893 by nerdybill(6951)   on 2009-03-14 08:29:33 (Show Source): You can put this solution on YOUR website! I have 28 coins in my pocket, they are all either nickels and dimes. There are eight more nickels than dimes. The value of these coins is 1.90. How many nickels? How many answers should I have?Define my variable, define in terms? Translate this information into an equation? Thank You guys you all are life savers in my class. . Let d = number of dimes and n = number of nickels . Since we have two unknowns, we'll need two equations. . from "I have 28 coins in my pocket" n+d = 28 (equation 1) from "There are eight more nickels than dimes." we get: n = d+8 (equation 2) . Solve equation 1 for 'd': n+d = 28 d = 28-n . Substitute the above into equation 2 and solve for n: n = d+8 n = 28-n+8 2n = 28+8 2n = 36 n = 18 (number of nickels) .
 Expressions-with-variables/186600: 2x^2+19x+351 solutions Answer 139874 by nerdybill(6951)   on 2009-03-13 22:51:24 (Show Source): You can put this solution on YOUR website!2x^2+19x+35 (2x + 5)(x + 7)
 logarithm/186596: log3 + 2 = log x solve for x logs are to base 101 solutions Answer 139859 by nerdybill(6951)   on 2009-03-13 20:09:47 (Show Source): You can put this solution on YOUR website!You will need to apply "log rules". Review them at: http://www.purplemath.com/modules/logrules.htm . log3 + 2 = log x log3 - log x = -2 log(3/x) = -2 3/x = 10^(-2) 3/x = 0.01 3 = 0.01x 3/0.01 = x 300 = x