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 expressions/104478: 7 a raised to 3 b raised to 2,when a=1/2 and b=1/31 solutions Answer 76163 by ankor@dixie-net.com(15656)   on 2007-10-17 05:07:52 (Show Source): You can put this solution on YOUR website!7 a raised to 3 b raised to 2, : Assuming this is what you mean here: = : when a=1/2 and b=1/3: : = = = = 12.25 : : If you mean: = : when a=1/2 and b=1/3: : = = = = 1.75
 Age_Word_Problems/104495: Three years ago, Milcah is 3 times older than Joshua. 4 years from now, Milcah is 8 years older than Joshua. Find Joshua's and Milcah's age.1 solutions Answer 76162 by ankor@dixie-net.com(15656)   on 2007-10-17 04:46:49 (Show Source): You can put this solution on YOUR website!Three years ago, Milcah is 3 times older than Joshua. 4 years from now, Milcah is 8 years older than Joshua. Find Joshua's and Milcah's age. : M = M's age now J = J's age now : Write what it says: "Three years ago, Milcah is 3 times older than Joshua." (M-3) = 3(J-3) M - 3 = 3J - 9; multiplied what's inside the brackets M = 3J - 9 + 3 M = (3J-6) : "4 years from now, Milcah is 8 years older than Joshua." M+4 = (J+4) + 8 M + 4 = J + 12 M = J + 12 - 4 M = J + 8 : Find Joshua's and Milcah's age. Substitute (3J-6) for M in the above equation: 3J - 6 = J + 8 3J - J = 8 + 6 2J = 14 J = 14/2 J = 7 yrs; J's age now : Find M: M = J + 8 M = 7 + 8 M = 15 yrs; M's age now : : Check solution using the statement: "Three years ago, Milcah is 3 times older than Joshua." (15-3) = 3(7-3) 12 = 3(4); confirms our solution
 Expressions-with-variables/104519: This question is from textbook Introductory & Intermediate Alegbra The question is to solve each system. If there is no solution or if there are infintely many solutions and a system's equations are dependent so state. You have to solve the system in Three Variables but I have no clue how. The question is x+y+2z=11 x+y+3z=14 x+2y+3z=5 1 solutions Answer 76140 by ankor@dixie-net.com(15656)   on 2007-10-16 21:39:47 (Show Source): You can put this solution on YOUR website!x + y + 2z = 11 x + y + 3z = 14 x +2y + 3z = 5 : Look at it; you can see that subtracting the 1st eq from the 2nd, you eliminate x & y making it easy to solve for y: x + y + 3z = 14 x + y + 2z = 11 ------------------ Subtracting eliminates x & y 0 + 0 + 1z = 3 z = 3 : Substitute 3 for z in the 2nd and 3rd equations: 2nd equation: x + y + 3(3) = 14 x + y + 9 = 14 x + y = 14 - 9 x + y = 5 : 3rd equation x + 2y + 3(3) = 5 x + 2y + 9 = 5 x + 2y = 5 - 9 x + 2y = -4 : Using these two unknown equations: x + 2y = -4 x + y = 5 ------------subtracting eliminates x 0 + 1y = -9 y = -9 : Find x using the equation x + y = 5 x - 9 = 5 x = 5 + 9 x = 14 : We have x = 14; y = -9; z = 3 : Check solution in the 1st equation: x + y + 2z = 11 14 - 9 + 2(3) = 14 - 9 + 6 = 11 : Did this give you a clue, at least?
 Linear-equations/104405: Nikki and tatianna rollerblade in opposite direction. Tatianna averages 2 mph faster than nikki. If they began at the same place and ended up 20 mi apart after 2 hrs, how fast did each of them travel?1 solutions Answer 76136 by ankor@dixie-net.com(15656)   on 2007-10-16 21:15:32 (Show Source): You can put this solution on YOUR website!Nikki and tatianna rollerblade in opposite direction. Tatianna averages 2 mph faster than nikki. If they began at the same place and ended up 20 mi apart after 2 hrs, how fast did each of them travel? : Let s = N's speed Then (s+2) = T's speed : the total distance they will travel is 20 mi, write a distance equation. Distance = time * speed : N's dist + T's dist = 20 mi 2s + 2(s+2) = 20 : 2s + 2s + 4 = 20 : 4s = 20 - 4 : s = 16/4 : s = 4 mph is N's speed The 4 + 2 = 6 mph is T's speed : : Check solutions by finding the distance of each: 2*4 = 8 mi 2*6 = 12mi ------------ total 20 mi
 Surface-area/104357: The diameter of a small pizza is 16 centimeters. This is 2 centimeters more than two fiths of the diameter of a large pizza. Find the diameter of the larger.1 solutions Answer 76119 by ankor@dixie-net.com(15656)   on 2007-10-16 19:45:12 (Show Source): You can put this solution on YOUR website!The diameter of a small pizza is 16 centimeters. This is 2 centimeters more than two fifths of the diameter of a large pizza. Find the diameter of the larger. : Let x = diameter of the large pizza: = .4 : .4x + 2 = 16 .4x = 16 - 2 .4x = 14 x = 14/.4 x = 35 cm is the diameter of the large pizza
 Percentage-and-ratio-word-problems/104348: here is the question you invested \$8000 in two funds paying 2% and 5% annual interest respectively. At the end of the year, the interest from the 5% investment exceeded the the interest from the 2% investment by \$85. How much money was invested at each rate?1 solutions Answer 76117 by ankor@dixie-net.com(15656)   on 2007-10-16 19:34:59 (Show Source): You can put this solution on YOUR website!you invested \$8000 in two funds paying 2% and 5% annual interest respectively. At the end of the year, the interest from the 5% investment exceeded the the interest from the 2% investment by \$85. How much money was invested at each rate? : Let x = amt invested at 5% Then (8000-x) = amt invested at 2% : A simple equation Interest at 5% - interest at 2% = \$85 .05x + .02(8000-x) = 85 : .05x - 160 + .02x = 85 : .05x + .02x = 85 + 160 : .07x = 245 : x = 245/.07 : x = \$3500 invested at 5% Then 8000 - 3500 = \$4500 invested at 2% : Check solution by find the interest on both amts .05(3500) = 175 .02(4500) = 95 ---------------- Difference = 85 as given
 Graphs/104344: This is the question - If (x,y) is a point on the line l of slop -2 and y intercept 2, y=-2x+2. (So, for example, if (23,y) is a point on l, y= -2(23)+2= -44.) k is the line that is perpendicular to l and contains the point (18,13). If (x,y) is a point on k, express y in terms of x. Thank you for any help that you can give me to understand this type of question.1 solutions Answer 76062 by ankor@dixie-net.com(15656)   on 2007-10-16 15:17:39 (Show Source): You can put this solution on YOUR website!If (x,y) is a point on the line l of slope -2 and y intercept 2, y = -2x + 2. (So, for example, if (23,y) is a point on l, y= -2(23)+2 = -44.) : Assume you understand what they are saying here: : : k is the line that is perpendicular to l and contains the point (18,13). If (x,y) is a point on k, express y in terms of x. : Perpendicular lines have slope relationship that can be expressed: m1 * m2 = -1 Assume m1 = -2 (line l slope), and find m2 (k line slope which is perpendicular) -2*m2 = -1 : m2 = :m2 = + is the slope of k line : We know the slope of k so find the y intercept (b), by using x,y of 18,13 Using the slope intercept form y = mx + b 13 = 18 + b 13 = 9 + b 13 - 9 = b b = +4 Our k equation is: y = x + 4 : Confirm this, substitute 18 for x and see that y = 13 y = (18) = 4 y = 9 + 4 y = 13 : If you graphed these two lines, it would look like this: purple line is l, y intercept at +2 green line is k, y intercept at +4 : Did this help you understand this stuff somewhat?
 Miscellaneous_Word_Problems/104359: A plane took 1 hour longer to travel 560 miles on the first portion of a flight than it took to fly 480 miles on the second portion. If the speed was the same for each portion, what was the flying time for the second part of the trip?1 solutions Answer 76053 by ankor@dixie-net.com(15656)   on 2007-10-16 14:42:00 (Show Source): You can put this solution on YOUR website!A plane took 1 hour longer to travel 560 miles on the first portion of a flight than it took to fly 480 miles on the second portion. If the speed was the same for each portion, what was the flying time for the second part of the trip? : Let t = time required for the 2nd part of the trip Then (t+1) = time required for the 1st part : It said the speed was the same, write a simple speed equation: Speed = Dist/time : 1st part speed = 2nd part speed = Cross multiply and you have 560t = 480(t+1) 560t = 480t + 480 560t - 480t = 480 80t = 480 t = 480/80 t = 6 hrs for the 2nd part of the trip : Check solution by finding the speed of each portion of the trip; 1st part required 7 hrs = 80 = 80 : Kind of slow for a plane, but it checks out.
 Travel_Word_Problems/104324: This question is from textbook Algebra I Two friends live 60 miles apart. They ride their bikes to meet each other. Sally heads east at 21 mph. Therese heads west riding at a rate of 15 mph. How far does each cyclist ride in t hours. Write and solve an equation to find when they meet.1 solutions Answer 76051 by ankor@dixie-net.com(15656)   on 2007-10-16 14:20:53 (Show Source): You can put this solution on YOUR website!Two friends live 60 miles apart. They ride their bikes to meet each other. Sally heads east at 21 mph. Therese heads west riding at a rate of 15 mph. How far does each cyclist ride in t hours. Write and solve an equation to find when they meet. : Let t = time in hrs when they will meet : We know that when they meet they will have traveled a total of 60 mi. From this fact we can make a simple distance equation: Distance = Speed * time : S's dist + T's dist = 60 miles 21t + 15t = 60 36t = 60 t = 60/36 t = = 1 hrs or 1 hr 40 min : : Find how far each will travel and check solution for t: S's dist + T's distance = 60 miles 21* + 15* = 35 miles + 25 miles = 60 miles
 Linear-equations/104318: Graph the linear equation 3x-2y=6 1 solutions Answer 76050 by ankor@dixie-net.com(15656)   on 2007-10-16 13:44:38 (Show Source): You can put this solution on YOUR website!Graph the linear equation 3x-2y=6 Put the equation in the general "y= "form: 3x - 2y = 6 -2y = 6 - 3x : We always want a positive y here, mult equation by -1 2y = 3x - 6 : We want y to have a coefficient of 1, divide eq by 2 y = x - 3 : Plot at least two points. Here's three points: Substitute for: x = -2, x = -2 and x = +4, you should have: X | Y -------- -2 | -6 +2 | 0 +4 | +3 : The graph will look like this: : Can you do this now?
 Mixture_Word_Problems/104283: Cashews sell for \$4.00 per pound, Peanuts for \$1.50 per pound. If you mix 60 lbs of peanuts in a cashew/peanut mix, how many pounds of cashews do you need to add to make a mix that costs \$2.50 per pound.1 solutions Answer 76049 by ankor@dixie-net.com(15656)   on 2007-10-16 13:26:02 (Show Source): You can put this solution on YOUR website!: Cashews sell for \$4.00 per pound, Peanuts for \$1.50 per pound. If you mix 60 lbs of peanuts in a cashew/peanut mix, how many pounds of cashews do you need to add to make a mix that costs \$2.50 per : Let x = lb of cashews required Then The final amt = (x+60) : A nutty equation: 4x + 1.5(60) = 2.5(x+60) : 4x + 90 = 2.5x + 150 : 4x - 2.5x = 150 - 90 : 1.5x = 60 : x = 60/1.5 : x = 40 lb of cashews required : : Check solution in original equation: 4(40) + 1.5(60) = 2.5(40+60) 160 + 90 = 2.5(100) proves our solution : : Not that hard, right?
 Evaluation_Word_Problems/104406: The age of Nando is 8 years more 3 times his brother's age.find the age of each if 10 years from now ando will be 5 years more than twice his brother's age.1 solutions Answer 76040 by ankor@dixie-net.com(15656)   on 2007-10-16 09:55:13 (Show Source): You can put this solution on YOUR website!Impossible, N will always be older than A
 Rectangles/104383: I need help with this problem I am using 2l+2w but the answer I am getting isn't correct. Can someone please help me to understand what I am doing wrong. The question or problem I am trying to solve is: The length of a rectangle is 9 centimeters more than it's width. The perimeter is 82 centimeters. Find the demensions of the rectangle. Please help me with this problem. I am sleepy and getting very upset at this time.1 solutions Answer 75937 by ankor@dixie-net.com(15656)   on 2007-10-15 20:02:47 (Show Source): You can put this solution on YOUR website!The length of a rectangle is 9 centimeters more than it's width. This says: L = (W+9) : The perimeter is 82 centimeters. you know: 2L + 2W = 82 ; Substitute (W+9) for L, and find W: 2(W+9) + 2W = 82 : Simplify, divide equation by 2 and you have: W + 9 + W = 41 2W = 41 - 9 2W = 32 W = 32/2 W = 16 is the width : It said the length was 9 cm more: L = 25 cm : : Check the perimeter now 2(25) + 2(16) = 82
 Polynomials-and-rational-expressions/104027: PreAP/GT Algebra II, teacher supplements the textbook with worksheets from College Algebra books. Worksheet titled SAT/ACT Test Prep #4. 3 parts to this problem: x^ + y^ = 16 xy = 8 (x + y)^ = ?1 solutions Answer 75893 by ankor@dixie-net.com(15656)   on 2007-10-15 15:42:09 (Show Source): You can put this solution on YOUR website!x^2 + y^2 = 16 y^2 = 16 - x^2 y = : xy = 8 substitute for y, find x: x* = 8 Square both sides x^2(16-x^2) = 64 : -x^4 + 16x^2 - 64 = 0; a quadratic equation +x^4 - 16x^2 + 64 = 0; multiplied by -1 Factor: (x^2 - 8)(x^2 - 8) = 0 x^2 = +8 x = x = : Find y: *y = 8 y = y = (x + y)^2 = ? FOIL (+)*(+) = ? 4(2) + + + = 8 + 8 + 8 + 8 = 32
 Linear_Equations_And_Systems_Word_Problems/104231: A fence is to be built around a track so that there is a uniform gap between the outside edge of the track and the fence. The Length of the straight portion of the track is 100 meters and the diameter of the curve is 81 meters. What is the Maximum width of the gap between the track and the fence if no more than 777 meters of fencing is used?1 solutions Answer 75891 by ankor@dixie-net.com(15656)   on 2007-10-15 14:05:59 (Show Source): You can put this solution on YOUR website!A fence is to be built around a track so that there is a uniform gap between the outside edge of the track and the fence. The Length of the straight portion of the track is 100 meters and the diameter of the curve is 81 meters. What is the Maximum width of the gap between the track and the fence if no more than 777 meters of fencing is used? : Let x = width of the gap : If you draw this out, it is apparent that 200 m of fencing will run parallel to the straight portions of the track. Therefore, 777 - 200 = 577 ft is available for the two half circles. The radius of the two half circles will be (x+81). : Use the circumference formula: 2 * pi * (x+81) = 577 6.2832x + 508.938 = 577 6.2832x = 577 - 508.938 6.2832x = 68.062 x = 68.062/6.2832 x = 10.83 ft is the width between the fence and the track : Did this make sense? Any questions?
 Linear_Equations_And_Systems_Word_Problems/104086: My average electricity bill for the months of November, December, January, and February was \$200. The highest month was January which was twice February. December was \$10 less than January and November was \$24 less than February. How much was my bill in each of the months November, December, January, and February?1 solutions Answer 75882 by ankor@dixie-net.com(15656)   on 2007-10-15 10:53:50 (Show Source): You can put this solution on YOUR website!My average electricity bill for the months of November, December, January, and February was \$200. The highest month was January which was twice February. December was \$10 less than January and November was \$24 less than February. How much was my bill in each of the months November, December, January, and February? : = 200 : Write equations for each statement: : "January which was twice February." J = 2F or F = .5J : "December was \$10 less than January" D = J - 10 : "November was \$24 less than February." N = F - 24 We want to get everything in terms of J, substitute .5J for F: N = .5J - 24 : Substitute and you have; = 200 : Mult by 4 to get rid of the denominators, remove the brackets: .5J - 24 + J - 10 + J + .5J = 800 : .5J + J + J + .5J - 24 - 10 = 800; group like terms and do the math 3J - 34 = 800 3J = 800 + 34 J = 834/3 J = \$278 Then F = 278/2 = \$139 and N = 139 - 24 = \$115 and D = 278 - 10 = \$268 : : Check on a calc: = 200
 Quadratic_Equations/104052: Solve for (x + 5)^2 = 31 solutions Answer 75880 by ankor@dixie-net.com(15656)   on 2007-10-15 10:33:32 (Show Source): You can put this solution on YOUR website!Solve: : (x + 5)^2 = 3 Take the square root of both sides: x + 5 = +- : Subtract 5 from both sides x = -5 + sqrt(3) and x = -5 - sqrt(3)
 Miscellaneous_Word_Problems/104060: The demand and supply equations for a certain item are given by D = –5p + 40 S = –p^2 + 30p – 8 Find the equilibrium price. 1 solutions Answer 75879 by ankor@dixie-net.com(15656)   on 2007-10-15 10:24:22 (Show Source): You can put this solution on YOUR website!he demand and supply equations for a certain item are given by D = –5p + 40 S = –p^2 + 30p – 8 Find the equilibrium price. : The equilibrium price (p) occurs when D = S, therefore: : -5p + 40 = -p^2 + 30p - 8 : Arrange as a quadratic equation on the left: +p^2 - 5p - 30p + 40 + 8 = 0 : p^2 - 35p + 48 = 0 : This equation requires the quadratic formula to solve: a = 1; b =-35; c= 48 : : : : Two solutions p = 33.57 and p = \$1.43 : Only the lower price make sense, the higher value will give negative values in the original expressions. : You can check this by substituting 1.43 for p -5(1.43) + 40 = -(1.43^2) + 30p - 8 -7.15 + 40 = -2.0449 + 30(1.43) - 8 32.85 = -2.0449 + 42.9 - 8 32.85 = 32.85 equality reigns : Did this make sense to you? Did it help? Any question?
 Inequalities/104211: A small company produces both standard and deluxe playhouses. The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. The labor available is limited to 800 hours per week, and the total production capacity is 50 items per week. Existing orders require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week. Write a system of inequalities representing this situation, where x is the number of standard playhouses and y is the number of deluxe playhouses. Then graph the system of inequalities.1 solutions Answer 75876 by ankor@dixie-net.com(15656)   on 2007-10-15 09:58:48 (Show Source): You can put this solution on YOUR website!A small company produces both standard and deluxe playhouses. The standard playhouses take 12 hours of labor to produce, and the deluxe playhouses take 20 hours. The labor available is limited to 800 hours per week, and the total production capacity is 50 items per week. Existing orders require the company to produce at least 10 standard playhouses and 15 deluxe playhouses per week. Write a system of inequalities representing this situation, where x is the number of standard playhouses and y is the number of deluxe playhouses. Then graph the system of inequalities. : Let x = standard p.h; y = deluxe p.h : The labor equation: 12x + 20y =< 800 : put equation in the general (y=) form to plot the graph: 20y =< 800 - 12x y =< 800/20 - (12/20)x y =< 40 - .6x : : The production capacity equation: x + y =< 50 Put this in the "y=" form also y <= 50 -x : Existing order constraints x => 10 and y => 15 : Plot these using the equation givens. y = 40 - .6x; (purple line) y = 50 - x; (green line) y = 15; Note that y = 15 is a horizontal line going thru y = 15; black line x = 10 is a vertical line going thru x = 10, I am unable to put this in : I assume you know how to make up an x/y table and plot a graph, if you can't, let me known and we will go thru the graphing routine : Here is the graph: : When you draw your graph (or print this one) draw a vertical line thru x = 10 This will complete the area of feasibility which is: : 1.At or below, the purple line or the green line whichever is lower. 2.At or above the black horizontal line 3.At or to the right of the vertical line which you will add to the graph : Does this all make sense to you?
 Miscellaneous_Word_Problems/104187: A rectangular plot, bounded on one side by a river, is to be enclosed on the other 3 sides by a fence, and then divided into two equal sized pens by another fence. If you have 900 feet of fence available, what is the largest are that can be enclosed?1 solutions Answer 75809 by ankor@dixie-net.com(15656)   on 2007-10-14 21:54:15 (Show Source): You can put this solution on YOUR website!A rectangular plot, bounded on one side by a river, is to be enclosed on the other 3 sides by a fence, and then divided into two equal sized pens by another fence. If you have 900 feet of fence available, what is the largest are that can be enclosed? : Perimeter would be: L + 3W = 900 or L = (900-3W) : Area would be: A = W * L Substitute for L A = W(900-3W) A = -3W^2 + 900W : A quadratic, find the axis of symmetry using: x = -b/(2a); a = -3; b= 900 W = -900/(2*-3) W = -900/-6 W = 150 ft is the width for max area : Find Max area, substitute 150 for W A = -3(150^2) + 900(150) A = -3(22500) + 135000 A = -67500 + 135000 A = +67500 sq ft is max area : If you graph it: x = width, y = area : : Check it: L = 900 - 3(150) L = 900 - 450 L = 450 ft So it would be 450 by 150: 450*150 = 67500 sq ft : Did this help you?
 Mixture_Word_Problems/104172: keep getting a strange number for answer. Premium coffee sells for \$6.00 per pound and regular coffee sells for \$4.00 per pound. how many pounds of each type of coffee should be blended to obtain 100 pounds of a blend that sells for \$4.64 per pound. Thanks for any help1 solutions Answer 75787 by ankor@dixie-net.com(15656)   on 2007-10-14 19:26:57 (Show Source): You can put this solution on YOUR website! Premium coffee sells for \$6.00 per pound and regular coffee sells for \$4.00 per pound. how many pounds of each type of coffee should be blended to obtain 100 pounds of a blend that sells for \$4.64 per pound. : Let x = lb of premium coffee It says the total will be 100, therefore: (100-x) lb of regular coffee: : A simple equation: 6x + 4(100-x) = 4.64(100) : 6x + 400 - 4x = 464 : 6x - 4x = 464 - 400 : 2x = 64 : x = 64/2 : x = 32 lb of premium coffee : You can figure out how much regular coffee, I'm sure
 Finance/104145: solve for g 40= (2)(1+g)/ 13.8-g I am confused because we are solving for a varible that shows up in the equation more than once.1 solutions Answer 75769 by ankor@dixie-net.com(15656)   on 2007-10-14 16:47:36 (Show Source): You can put this solution on YOUR website!40 = (2)(1+g)/ 13.8-g : I am assuming you mean: = 40 : = 40; multiplied what's inside the brackets : 2 + 2g - 13.8g = 13.8(40); multiplied eq by 13.8, gets rid of the denominator : 2g - 13.8g = 552 - 2; Subtracted 2 from both sides : -11.8g = 550; do the math : g = 550/-11.8; divide both sides by -11.8 : g = -46.61 is the solution : : Check in original equation: = 40 = 40; minus a minus is a plus = 40; = 40; -6.61 + 46.61 = 40; confirms our solution : : If this is NOT the way you meant the problem to be, let us know, we can edit this solution
 test/104042: two cars pas each other traveling in opposite directions on a highway, one is goig 1.5 times as fast as the other. at the end of 3.5 hours they are 192.5 miles apart. find each cars rate. 1 solutions Answer 75768 by ankor@dixie-net.com(15656)   on 2007-10-14 16:25:06 (Show Source): You can put this solution on YOUR website!Two cars pass each other traveling in opposite directions on a highway, one is going 1.5 times as fast as the other. At the end of 3.5 hours, they are 192.5 miles apart. Find each cars rate. : Let s = speed of the slower car Then (1.5s) = speed of the faster car : Write a distance equation: Distance = time * speed. : They both will be traveling for 3.5 hr ; Fast car dist + slow car dist = 192.5 3.5(1.5s) + 3.5s = 192.5 5.25s + 3.5s = 192.5 8.75s = 192.5 s = 192.5/8.75 s = 22 mph is the slow car Then 1.5(22)) = 33 mph is the fast car : : Check solution: 3.5(33) + 3.5(22) = 115.5 + 77 = 192.5: confirms out solution