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# Recent problems solved by 'stanbon!'

stanbon! answered: 97 problems
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Rational-functions/22588: how do you solve (x^2\16)+ (y^2\16)=1 y=x+3
1 solutions

Answer 11625 by stanbon!(97)   on 2005-12-24 12:37:33 (Show Source):
You can put this solution on YOUR website!
Multiply thru by 16 to get x^2+y^2 = 16
Substitute y=x+3 to get:
x^2 +x^2+6x+9=16
2x^2 + 6x -7 =0
Use the quadratic formula to get
 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=92 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.89791576165636, -3.89791576165636. Here's your graph:

Cheers,
Stan H.

 Word_Problems_With_Coins/11267: John has 7 more pennies than nickels and 2 fewer quarters than pennies. His total amount of money is \$2.87. How many of each type of coin does he have?1 solutions Answer 11624 by stanbon!(97)   on 2005-12-24 12:27:22 (Show Source): You can put this solution on YOUR website!Let number of nickels be "x". Then number of pennies is "x+7" And number of quarters is "x+7-2" = "x+5" Value of nickels is (5)x cents Value of pennies is (1)(x+7)= x+7 cents Value of quarters is (25)(x+5)= 25x+125 cents EQUATION: Value of nickels + Value of pennies + Value of quarters = 287 cents 5x + x+7 + 25x+125 = 287 31x = 155 x = 5 (number of nickels) x+7 = 12 (number of pennies) x+5 = 10 (number of quarters)
 Equations/23140: I am having problems with solving equations. The following are equations and it's methods that I don't seem to understand. Thank you for your assistance! Solve using the addition (elimination) method. 2x + 3y = -16 5x-10y=30 -------------------------------------------------------------------------------- Solve using the addition (elimination) method 2y - 8 = -2x - 8x 8x - 3y = 31 + y -------------------------------------------------------------------------------- Solve using the substitution method x = 3y + 7 x = 2y - 1 -------------------------------------------------------------------------------- Solve using the substitution method 4x + 3y = 0 2x - y = 0 1 solutions Answer 11620 by stanbon!(97)   on 2005-12-24 08:59:08 (Show Source): You can put this solution on YOUR website!Elimination: 1st: 2x+3y=-16 2nd: 5x-10y=30 Multiply 1st by 5 and 2nd by 2 to get the following: 1st: 10x+15y=-80 2nd: 10x-20y=60 Now subtract the 2nd from the 1st to eliminate the x's: 35y = -140 y = -4 Substitute that value of "y" into the original 1st equation to solve for "x": 2x+3(-4)= -16 2x-12 = -16 x = -2 Check this answer of x=-2 and y=-4 in the 2nd original equation: 5(-2)-10(-4)= 30 -10+40 = 30 30 = 30 Cheers, Stan H.
 Word_Problems_With_Coins/12023: A collection of 30 coins worth \$5.50 consists of nickles, dimes, and quarters. There are twice as many dimes as nickles. How many quarters are there?1 solutions Answer 11619 by stanbon!(97)   on 2005-12-24 08:46:31 (Show Source): You can put this solution on YOUR website!Let number of nickels be "x". Then number of dimes is "2x". And number of quarters is "30-3x" Value of nickels is (5)x cents Value dimes is (10)2x = 20x cents Value of quarters is (25)(30-3x)= 750-75x cents EQUATION: Value of nickels + Value of dimes + Value of quarters = 550 cents 5x + 20x + 750-75x = 550 -50 x = -200 x = 4 (number of nickels) 2x = 8 (number of dimes) 30-3x = 30-12 = 18 (number of quarters) Cheers, Stan H.
 Graphs/22433: (2,1); m=1 Write an equation in standard form. Please help1 solutions Answer 11610 by stanbon!(97)   on 2005-12-23 20:54:03 (Show Source): You can put this solution on YOUR website!y=mx+b The point (2,1) gives you an "x" and a "y" value and you are also given the "m" value. Substitute to get 1 = (1)(2)=b 1 = 2b b = 1/2 The equation is y = x+1/2 Now, put that in standard form which is ax + by = c Multiply (y=x+1/2) thru by "2" to get: 2y= 2x + 1 Write this as 2x+(-2y)= -1 That is the equation in standard form. Cheers, Stan H.
 Expressions-with-variables/22550: how do u write an algebraic expression to represent the cost of a concert ticket,h, with a service of \$6.751 solutions Answer 11609 by stanbon!(97)   on 2005-12-23 20:43:48 (Show Source): You can put this solution on YOUR website!If you buy one ticket cost = \$6.75 + h If you buy two tickets cost = \$6.75 +2h If you buy three tickets cost= \$6.75 + 3h Let "x" be the number of tickets you are going to buy. Then Cost = \$6.75 + xh Cheers, Stan H.
 Equations/23138: I am completely lost in trying to solve the following equations. I respectfully ask for your help and assistance. Thank you. Robert 1. Use the addition method to solve the following system of equations: (1/3)X + Y = 3 AND (1/2)X - (1/4)Y = 1 2. Use the substitution method to solve the following system of equations: 2x+5y = 1 and -x+6y = 8 1 solutions Answer 11608 by stanbon!(97)   on 2005-12-23 20:37:37 (Show Source): You can put this solution on YOUR website!Prob. #1 First, get rid of the fractions: Multiply 1st equation thru by 3 to get: X + 3Y=9 Multiply 2nd equation thru by 4 to get: 2x- Y = 4 Now multiply this last equation thru by 3 so we can get rid of the Y's. 6X -3Y = 12 This is now the equations you are working with: 1st: X +3Y= 9 2nd: 6X-3Y= 12 Now add the two equations to get: 7x = 21 x = 3 Put this value into one of the early equations to solve for "Y". 3 + 3Y = 9 3Y = 6 Y = 2 Solution: X= 3 and Y= 2 Check that answer in the original equations. 2nd Problem: 2x+5y=1 x=6y-8 Substitute this value of "x" into the 1st equation to get: 2(6y-8)+5y = 1 12y-16+5y = 1 17y = 17 y = 1 Substitute that value into one of the original equations to get: x=(6(1))-8 x= 6-8=2 Solution: x = 2 and y = 1 Check that answer in the othe original equation. Cheers, Stan H.
 Travel_Word_Problems/23139: a boat takes 2 hours longer to go 45 miles up a river than to return. If the boat's speed in still water is 12 mph, what is the rate of the current. Can you please show you step this time.1 solutions Answer 11607 by stanbon!(97)   on 2005-12-23 20:10:47 (Show Source): You can put this solution on YOUR website!Downstream Data: distance= 45; rate=12+c; time=45/(12+c) Upstream Data: distance = 45: rate = 12-c; time= 45/(12-c) EQUATION: Time Upstream - Time Downstream = 2 hours 45/(12-c) - 45/(12+c) = 2 Divide thru by 45 to get: 1/(12-c) - 1/(12-c) =2/45 Simplify : 45[(12+c)-(12-c)]= 2[(12-c)(12+c)] 45[2c] =2[144-c^2] 90c = 288-2c^2 c^2+45c-144=0 (c-3)(c+48)=0 current speed = 3 mph Cheers, Stan H.
 Radicals/22465: (x- sqrt2)² 1 solutions Answer 11588 by stanbon!(97)   on 2005-12-23 10:56:56 (Show Source): You can put this solution on YOUR website!Use FOIL to get: (x-sqrt2)(x-sqrt2) = x^2 -xsqrt2-xsqrt2+2 = x^2-2sqrt2(x)+2 Cheers, Stan H.
 Quadratic_Equations/22831: how whoud you find the volume of a wine glass using the parabola1 solutions Answer 11587 by stanbon!(97)   on 2005-12-23 10:53:56 (Show Source): You can put this solution on YOUR website!You have to use Calculus to get that answer. Cheers, Stan H.
 Travel_Word_Problems/23133: The exam starts at school at 09:00. You want to get there 15min early. it takes 20 min to 30 min to get to school, depending on the buses. You plan to study for 1 hour at home. It will take you 1 hour to shower, dress, and eat breakfast. For what time should you set your alarm?1 solutions Answer 11586 by stanbon!(97)   on 2005-12-23 10:52:18 (Show Source): You can put this solution on YOUR website!15min + 30min + 1hr+ 1hr = 2hr 45 min Set your alarm for 9 - 2hr 45 min. Cheers, Stan H.
 Linear-systems/23134: Sir, pl. help to solve this simple interest question. A man borrowed Rs. 80,000 from a bank at rate 7% per annum. After 2 years, he returned Rs. 30,000. How much balance amount he has to pay at the end of 5th year. Ans is Rs. 71700.1 solutions Answer 11585 by stanbon!(97)   on 2005-12-23 10:48:58 (Show Source): You can put this solution on YOUR website!Is this what you mean? He accumulated simple (not compound) interest on the loan for two years at 7% annual rate, then he paid off 30000 of the combined pricipal and accumulated interest. Then he accumulated 7% simple (not compound) interest for three years on that remaining balance and finally paid off the entire accumulated balance? If your answer to this question is , yes, I do not see how the answer to the question is 71700. Cheers, Stan H.
 Linear-equations/23081: write an equation of the line that passes through the given two points. (-7,8)(-4,11) (7,0)(27,-60) (2,3)(8,0)1 solutions Answer 11576 by stanbon!(97)   on 2005-12-22 21:34:53 (Show Source): You can put this solution on YOUR website!Let's try the 1st pair of points. The others are worked in the same way. The two-point form is y-y1 = m (x-x1) where m= (change in y)/(change in x) So for your problem m = (11-8)/(-4-(-7)) = 3/3=1 Now the x1,y1 comes from one of your two points; it doesn't matter which point you pick out. We'll try (-4,11). Then y-(11) = (1)(x-(-4) And y-11 = (x+4) Then y = x+4+11 y = x+15 Cheers, Stan H.
 Equations/23116: What do we call a chart that helps compare facts and numbers or quantities?1 solutions Answer 11574 by stanbon!(97)   on 2005-12-22 21:17:31 (Show Source): You can put this solution on YOUR website!Maybe you are describing a "bar chart"
 Word_Problems_With_Coins/12187: A change purse contains 14 coins consisting of nickels and dimes and having a total value of \$1.10. How many nickels are there?1 solutions Answer 11573 by stanbon!(97)   on 2005-12-22 21:05:46 (Show Source): You can put this solution on YOUR website!Let number of nickels be "x". Then number of dimes is "14-x" Value of nickels is (5)x cents Value of dimes is (10)(14-x) = (140-10x) cents EQUATION: Value of nickels + Value of dimes is 110 cents. 5x +140-10x = 110 -5x = -30 x = 6 ( number of nickels) Cheers, stan H.
 Word_Problems_With_Coins/12236: coin collection worth \$2.90 contains nickels, dimes, and quaters. There are three times as many dimes as there are nickels, and the number of quarters is 2 more than the number of nickels1 solutions Answer 11572 by stanbon!(97)   on 2005-12-22 20:47:20 (Show Source): You can put this solution on YOUR website!Let number of nickels be "x". Then number of dimes is "3x". And number of quarters is "x+2". Value of nickels is (5)x cents. Value of dimes is (10)(3x)= 30x cents Value of quarters is (25)(x+2)=25x+50 cents EQUATION: Value of nickels + Value of dimes + Value of quarters is 290 cents. 5x + 30x + 25x+50 = 290 60x=240 x= 4 (number os nickels) 3x= 12 (number of dimes) x+2= 6 (number of quarters)
 Graphs/23129: x>7/8y +5 2x>=3/4y+7 Determine if the given points are solutions to the given systems of inequalities. a. The point is a solution to the system b. The point is not a solution to the system. 1 solutions Answer 11569 by stanbon!(97)   on 2005-12-22 15:43:48 (Show Source): You can put this solution on YOUR website!You need to post the points along with the set of inequalities. If you want to do the problem yourself. take one of the point values (the x value and the y value) and substitute them into both of your inequalities. If the numerical result is "true" the point is in the solution of the system. If the numerical result is "false" the point is not. Cheers, Stan H.