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 Equations/101212: The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item). A) If the fixed cost is \$40 and the variable cost is \$10, write the cost equation.1 solutions Answer 73678 by stanbon(57361)   on 2007-09-29 18:38:55 (Show Source): You can put this solution on YOUR website!The cost of producing a number of items x is given by C = mx + b, in which b is the fixed cost and m is the variable cost (the cost of producing one more item). A) If the fixed cost is \$40 and the variable cost is \$10, write the cost equation. Cost = 10m + 40 ============== Cheers, Stan H.
 Functions/101210: please help!..Find the domain and Range of the function f(x)= 2 / x-2 **the / = fraction bar not division..thanks! 1 solutions Answer 73676 by stanbon(57361)   on 2007-09-29 18:36:41 (Show Source): You can put this solution on YOUR website!Find the domain and Range of the function f(x)= 2 / x-2 Domain: all Real Numbers except x=2 Range: all Real numbers except f(x)=0 --------------------- Cheers, Stan H.
 Functions/101203: f(x) = 2x -1 g(x) = Square root (x-1) Find the domain of f, g, f+g, f-g, fg, ff, f/g, and g/f. I actually got the answers to the domain of f and g, but i'm confused on how to find the others based on just f and g. Like for the domain of f, I got (-infinity, positive infinity) then for the domain of g, (negative infinity, 1) U (1, positive infinity) 1 solutions Answer 73675 by stanbon(57361)   on 2007-09-29 18:33:57 (Show Source): You can put this solution on YOUR website!(x) = 2x -1 g(x) = Square root (x-1) Find the domain: f: all real numbers g: x>=1 f+g: x>=1 because sqrt(x-1) is one of the terms f-g: x>=1 becaue sqrt (x-1) is one of the terms fg= f(sqrt(x-1))= 2sqrt(x-1)-1: x>=1 same reason ff: all Real numbers f/g = (2x-1)/sqrt(x-1) Domain is x > 1 g/f = sqrt(x-1)/(2x-1) Domain is x>=1 ===================== Cheers, Stan H.
 Quadratic_Equations/101208: how do you find a and b and c of a quadratic equation? I have data that is: when x is 0, y is 1,. when x is 1, y is 2. when x is 2, y is 4. when x is 3, y is 7. when x is 4, y is 11. when x is 5, y is 16. and I have to write an equation for this data, which is quadratic I think. I don't know how to find a and b and c of the equation.1 solutions Answer 73673 by stanbon(57361)   on 2007-09-29 18:25:06 (Show Source): You can put this solution on YOUR website!how do you find a and b and c of a quadratic equation? I have data that is: when x is 0, y is 1,. when x is 1, y is 2. when x is 2, y is 4. when x is 3, y is 7. when x is 4, y is 11. when x is 5, y is 16. and I have to write an equation for this data, which is quadratic I think. I don't know how to find a and b and c of the equation. -------------- If it is quadratic, y = ax^2+bx+c and you need to find a,b, and c. So,substitute x,y values from above to form 3 equations in a,b,c. --------------------- (0,1) implies 1 = 0a+0b+c (1,2) implies 2 = a + b + c (2,4) implies 4 = 4a+2b+c ----------------------------- Solve that system of equations by any means you know how. I get a=(1/2), b=(1/2), c=1 ================= Cheers, Stan H.
 Mixture_Word_Problems/101204: A fuel distributor has 161,798 gallons of fuel with 1% sulfur content, which exceeds pollution control standards of 0.6% sulfur content. How many gallons of fuel oil with a 0.1% sulfur content must be added to the 161,798 gallons to obtain fuel oil that complies with the pollution control standards? Round up to the next higher gallon. 1 solutions Answer 73671 by stanbon(57361)   on 2007-09-29 17:14:34 (Show Source): You can put this solution on YOUR website!A fuel distributor has 161,798 gallons of fuel with 1% sulfur content, which exceeds pollution control standards of 0.6% sulfur content. How many gallons of fuel oil with a 0.1% sulfur content must be added to the 161,798 gallons to obtain fuel oil that complies with the pollution control standards? Round up to the next higher gallon. ----------------------------- 1% oil DATA: Amt = 161,798 gals ; Amt of sulfur = 0.01*161,798 = 1617.98 gallons --------------------- 0.1% oil DATA: Amt = x gals ; Amt of sulfur = 0.001x gallons ---------------------- 0.6% Mixture DATA: Amt = 161798+x ; Amt of sulfur = 0.006(161798-x) = 970.788 - 0.006x gals ----------------------- EQUATION: sulfur + sulfur = sulfur 1617.98 + 0.001x = 970.788 - 0.006x 647.192 = 0.005x x = 129,438.4 gallons of 0.1% oil must be added to bring the tank down to 0.6% sulfur content. ============== Cheers, Stan H.
 Trigonometry-basics/101196: a.(1-tan^2u)/(1+tan^2u)=cos(2u) I think this is a half angle identity?verify the identity. b. compare the graphs of y1=(1-tan^2u)/(1+tan^2u) and y2=cos(2u)1 solutions Answer 73659 by stanbon(57361)   on 2007-09-29 15:39:17 (Show Source): You can put this solution on YOUR website!verify the identity. a.(1-tan^2u)/(1+tan^2u)=cos(2u) (1-tan^2u)/sec^2u = cos^2u-sin^2u [1/sec^2u] - [tan^2u/sec^2u] = cos^2u-sin^2u cos^2u - sin^2u = cos^2u - sin^2u ================================= b. compare the graphs of y1=(1-tan^2u)/(1+tan^2u) and y2=cos(2u) --------- Can't do that on this site. -------------------------------------- Cheers, Stan H.
 Functions/101197: This question is from textbook Find the difference quutient : f(x + h) - f(x) _________________ (h does not equal 0) h f(x) = 2 + 4x1 solutions Answer 73657 by stanbon(57361)   on 2007-09-29 15:13:20 (Show Source): You can put this solution on YOUR website! f(x + h) - f(x) _________________ (h does not equal 0) h -------------------------- f(x) = 2 + 4x f(x+h) = 2 + 4(x+h) = 2 + 4x + 4h ------------------- [f(x+h)-f(x)]/h = 4h/h = 4 =================== Cheers, Stan H.
 Numbers_Word_Problems/101191: The lesser of two consecutive even integers is 10 more than one-half the greater. Find the integers.1 solutions Answer 73650 by stanbon(57361)   on 2007-09-29 14:20:42 (Show Source): You can put this solution on YOUR website!The lesser of two consecutive even integers is 10 more than one-half the greater. Find the integers. ---------------------- Let the consecutive even integers be 2x, and 2x+2 ------------------- EQuATION: 2x = (1/2)(2x+2)+10 2x = (x+1) + 10 x = 11 2x = 22 (smaller even integer) 2x+2 = 24 (larger even integer) =================== Cheers, Stan H.
 Rate-of-work-word-problems/101185: Ellen's motorboat can travel 30 mi/h in still water. If the boat can travel 7 miles downstream in the same amount of time it takes to travel 3 miles upstream, what is the rate of the river's current?1 solutions Answer 73646 by stanbon(57361)   on 2007-09-29 14:13:45 (Show Source): You can put this solution on YOUR website!Ellen's motorboat can travel 30 mi/h in still water. If the boat can travel 7 miles downstream in the same amount of time it takes to travel 3 miles upstream, what is the rate of the river's current? ----------------- Let the river rate be "c". ---------- Down stream DATA: Rate = 30+c ; distance = 7 mi ; time = d/r = 7/(30+c) --------------- Up stream DATA: Rate = 30-c ; distance = 3 mi : time = d/r = 3/(30-c) ---------------- EQUATION: 7/(30+c) = 3/(30-c) 210-7c = 90+3c 10c = 30 c = 3 mph (speed of the current) ==================== Cheers, Stan H.
 Square-cubic-other-roots/101187: What is the square root of y+12=5? (the square root sign is over y+12)1 solutions Answer 73639 by stanbon(57361)   on 2007-09-29 14:03:11 (Show Source): You can put this solution on YOUR website!What is the square root of y+12=5 -------------------- sqrt(y+12) = 5 Square both sides to get: y+12 = 25 y = 13 ---------- Check that answer in the original equaltion: sqrt(13+12)=5 5 = 5 =================== Cheers, Staln H.
 Graphs/101132: solve by addition method: 3/7x + 5/9y = 27 1/9 x + 2/7y = 7 1 solutions Answer 73633 by stanbon(57361)   on 2007-09-29 13:57:23 (Show Source): You can put this solution on YOUR website!1st: 3/7x + 5/9y = 27 2nd: 1/9 x + 2/7y = 7 ------------------- Multiply 1st by 63 and 2nd by 63 to get rid of the denominators: 3rd: 27x + 35y = 27*63 4th: 7x + 18y = 7*63 ------------- Multiply 3rd by 7 and 4th by 27 to get: 5th: 189x + 245y = 189*63 6th: 189x + 486y = 189*63 -------------- Subtract 5th from 6th to get: 241y = 0 y = 0 ------------ Substitute into (3/7)x+(5/9)y = 27 to solve for "x": (3/7)x = 27 x = (7/3)27 = 63 ======================================== Cheers, Stan H.
 Functions/101133: when trying to find a function you put in 2,5,4,3,and get out 4,13,10,7. What is the function is it that I am trying to find? and what is the answer in the form of x>>something.1 solutions Answer 73616 by stanbon(57361)   on 2007-09-29 08:25:51 (Show Source): You can put this solution on YOUR website!when trying to find a function you put in 2,5,4,3,and get out 4,13,10,7. What is the function is it that I am trying to find? and what is the answer in the form of x>>something. ------------------------------- That can be rearranged as follows: x:... 2,3,.4,.5 f(x): 4,7,10,13 --------------- Since there is a constant difference in the f(x) line you know the eqution you are looking for is linear, i.e. y = mx+b ------------ So substitute two of the x,f(x) points into that linear form to get: 4 = 2m + b 13= 5m + b -------------- Subtract the 1st from the 2nd to get: 9 = 3m m = 3 ---------- Substitute that into 4 = 2m + b to solve for "b": 4 = 2*3 + b b = -2 ------------- So the equation you want is y = 3x -2 ================== Cheers, Stan H.
 Square-cubic-other-roots/101134: the nth term sequence is T(n)=4n-3 what are the first 5 terms of the sequence and can you explain it.1 solutions Answer 73615 by stanbon(57361)   on 2007-09-29 08:16:22 (Show Source): You can put this solution on YOUR website!the nth term sequence is T(n)=4n-3 what are the first 5 terms of the sequence and can you explain it. ------------------------ 1st term = T(1) = 4*1-3 = 1 2nd term = T(2) = 4*2-3 = 4 3rd term = T(3) = 4*3-3 = 9 4th term = T(4) = 4*4-3 = 13 5th term = T(5) = 4*5-3 = 17 =========================== Cheers, Stan H.
 Average/101135: can you give me a formula for the cost in pence of? 1. n cakes at 18p each 2. m oranges at j pence each 3. ten stamps at t pence each1 solutions Answer 73614 by stanbon(57361)   on 2007-09-29 08:11:43 (Show Source): You can put this solution on YOUR website!can you give me a formula for the cost in pence of? 1. n cakes at 18p each............= 18n pence 2. m oranges at j pence each......= jm pence 3. ten stamps at t pence each.....= 10t pence ============== Cheers, Stan H.
 Trigonometry-basics/101115: 5(2x + y) - 4(2x + y) _>_ 4 Help with this problem and graph. PLEASE1 solutions Answer 73608 by stanbon(57361)   on 2007-09-28 22:57:09 (Show Source): You can put this solution on YOUR website!5(2x + y) - 4(2x + y) _>_ 4 10x+5y-8x-4y >=4 2x+y >= 4 y >= -2x+4 -------------------- Graph the boundary line: y = -2x+4 --------------------- To find the solution for the inequality pick a test point that is not on the boundary, like (0,0). Test the x, y values in the inequality: 0 > -2*0 + 4 0 > 0+4 False Therefore the solution half-plane is the one on the other side of the boundary line: darken that side. The solution is the boundary and the darkened half-plane. ----------------------- ==================== Cheers, Stan H.
 Linear-systems/101075: Your family likes to go to baseball games. At one game your family bought 5 soft drinks and 5 hot dogs for \$22.25. At the next game your family attended they bought 4 soft drinks and 3 hot dogs for \$14.50. What is the cost of one soft drink and one hot dog? Let s = the cost of one soft drink Let h = the cost of one hot dog a. Write a system of equations modeling the situation described above. b. Solve the system for the cost of one soft drink + one hot dog. (You will have to add your solutions together for this one.) 1 solutions Answer 73607 by stanbon(57361)   on 2007-09-28 22:20:03 (Show Source): You can put this solution on YOUR website!family bought 5 soft drinks and 5 hot dogs for \$22.25. At the next game your family attended they bought 4 soft drinks and 3 hot dogs for \$14.50. What is the cost of one soft drink and one hot dog? Let s = the cost of one soft drink Let h = the cost of one hot dog a. Write a system of equations modeling the situation described above. 1st: 5s + 5h = 22.25 2nd: 4s + 3h = 14.50 ----------------------------- b. Solve the system for the cost of one soft drink + one hot dog. Multiply 1st by 3 and 2nd by 5 to get: 3rd: 15s + 15h = 66.75 4th: 20s + 15h = 72.50 -------------- Subtract 3rd from 4th to get: 5s = 5.75 s = 1.15 (price of a solf drink) --------------------- Substitute into 1st to solve for "h". 5(1.15)+5h = 22.25 5.75 +5h = 22.25 5h = 16.50 h = 3.50 (price of a hot dog) ========================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/101111: crystal sells coffee. her special blend is a combination of french roast @ \$7.50 a lb. and kona deluxe @ \$11.50 a lb. how many pounds of kona should she mix with 12 lbs. of french roast to get a blend to be sold for \$10.00 a lb.?1 solutions Answer 73605 by stanbon(57361)   on 2007-09-28 22:04:31 (Show Source): You can put this solution on YOUR website!crystal sells coffee. her special blend is a combination of french roast @ \$7.50 a lb. and kona deluxe @ \$11.50 a lb. how many pounds of kona should she mix with 12 lbs. of french roast to get a blend to be sold for \$10.00 a lb.? -------------- Amt. of french is 12 lbs; value of this is 7.50*12 = 90 dollars ------------ Let amt of kona be x lbs; value of this is 11.50x dollars --------------- Amt of mixture is 12+x lbs; value is 10(12+x)=120+10x dollars ---------------------- EQUATION: 90 + 11.50x = 120+10x 1.5x = 30 x = 20 lbs. (Amount of kona that must be added to make the blend) ============ Cheers, Stan H.
 Linear-systems/101076: How do I work this problem? Suppose you just have just enough dimes and quarters to pay for a loaf of bread and quart of milk, which cost \$3.45. You have a total of 15 dimes and quarters. Let d = the number of dimes you have. Let q = the number of quarters you have. a. Write a system of equations that models the information given above. b. Solve the system for the number of dimes and quarters you have. You may want to solve this by graphing. 1 solutions Answer 73601 by stanbon(57361)   on 2007-09-28 21:51:26 (Show Source): You can put this solution on YOUR website!Suppose you just have just enough dimes and quarters to pay for a loaf of bread and quart of milk, which cost \$3.45. You have a total of 15 dimes and quarters. Let d = the number of dimes you have. Let q = the number of quarters you have. a. Write a system of equations that models the information given above. Quantity EQUATION: d+q = 15 Value EQUATION: 10d + 35q = 345 cents --------------------- b. Solve the system for the number of dimes and quarters you have. You may want to solve this by graphing. It's easier to solve by elimination: 10d + 10q = 150 10d + 35q = 345 ----------------- Substract to get:25q = 195 q = 7.8 ---------- Comment: q should be a whole number. Check your posting to see if you have it correct. -------------- Cheers, Stan H.
 Graphs/101109: Solve by graphing ,indicatewheter it is dependent,independent ,or inconsistent. y = 3x-4 y=-2 x + 1 1 solutions Answer 73599 by stanbon(57361)   on 2007-09-28 21:44:35 (Show Source): You can put this solution on YOUR website!1st: y = 3x - 4 2nd: y =-2x + 1 ----------------- Substitute to get: 3x-4 = -2x+1 5x = 5 x = 1 -------------- Substitute into 1st to solve for Y y = 3*1-4 y = -1 ---------------- The system is consistent. ----------------- Cheers, Stan H.
 Numeric_Fractions/101086: 3+y/4=-y/81 solutions Answer 73579 by stanbon(57361)   on 2007-09-28 20:52:17 (Show Source): You can put this solution on YOUR website!3+y/4=-y/8 Multiply thru by 8 to get: 24 + 2y = -y 3y = -24 y = -8 ---------------- cheers, Stan H>
 expressions/101106: (1*2*6)/(1-1)*a1 solutions Answer 73577 by stanbon(57361)   on 2007-09-28 20:48:31 (Show Source): You can put this solution on YOUR website!Answer is "undefined" because the denominator is zero. Cheers, Stan H.
 Linear-systems/101028: Could someone please help me solve this question: Solve the following system of two linear equations by substitution: x + 2 y – 8 =0 & 2 x + 4 y + 4 =0. Noting each equation represents a line, draw both lines and interpret the results. Thank you, for taking the time to help me.1 solutions Answer 73571 by stanbon(57361)   on 2007-09-28 20:17:29 (Show Source): You can put this solution on YOUR website!Solve the following system of two linear equations by substitution: x + 2 y – 8 =0 & 2 x + 4 y + 4 =0. Noting each equation represents a line, draw both lines and interpret the results. ----------------------- 1st: x + 2 y = 8 2nd: 2 x + 4 y = - 4 ------------------- Multiply the 1st be 2 to get: 3rd: 2x + 4y = 16 ----------- Subtract 2nd from 3rd to get: 0 = 20 That is a contradiction that happened because we assumed the "x" in one equation was the same as the "x" in the other, and the same for the "y". They are not the same; the system in called "inconsistent" ------------------ If you were to graph the two equations you would get two parallel lines. there is no solution for the system of equations. ================== Cheers, Stan H.
 Distributive-associative-commutative-properties/101023: -2ab2(-3a - 2b +7ab)1 solutions Answer 73567 by stanbon(57361)   on 2007-09-28 20:10:34 (Show Source): You can put this solution on YOUR website!-2ab2(-3a - 2b +7ab) = 6a^2b^2 + 4ab^3 - 14a^2b^3 ============ Cheers, Stan H.
 Miscellaneous_Word_Problems/101082: Sally buys a radio for \$120. She pays for it with \$2 and \$5 bills. If Sally used a total of 30 bills, how many of each did she use? The unit is in solving problems using one variable. What would the algebraic equation be for this problem? 1 solutions Answer 73566 by stanbon(57361)   on 2007-09-28 20:07:58 (Show Source): You can put this solution on YOUR website!Sally buys a radio for \$120. She pays for it with \$2 and \$5 bills. If Sally used a total of 30 bills, how many of each did she use? The unit is in solving problems using one variable. What would the algebraic equation be for this problem? -------------------- Let # of \$5 bills be "x"; Value of these is 5x dollars ---------------------- # of \$2 bills is "30-x"; value of these is 2(30-x)= 60-2x dollars ---------------------- EQUATION: value + value = \$120 5x + 60-2x = 120 3x = 60 x = 20 (# of \$5 bills) 30-x = 10 (# of \$2 bills) ================= Cheers, Stan H.
 Graphs/101091: Write the equation of the line that passes through point (0, –5) with a slope of 6.1 solutions Answer 73565 by stanbon(57361)   on 2007-09-28 20:02:10 (Show Source): You can put this solution on YOUR website!Write the equation of the line that passes through point (0, –5) with a slope of 6. ----------- You are told the slope is 6 and the y-intercept is -5. The equation is y = 6x -5 ============ Cheers, Stan H>
 Linear_Algebra/101084: Solve for the variable indicated W=4r-3R solve for "R"1 solutions Answer 73564 by stanbon(57361)   on 2007-09-28 20:00:25 (Show Source): You can put this solution on YOUR website!W=4r-3R solve for "R" ------------- 3R = 4r-W R = (4r-W)/3 ============= Cheers, Stan H.
 Graphs/101090: Write the equation of the line passing through (3, –1) and (3, 6).1 solutions Answer 73563 by stanbon(57361)   on 2007-09-28 19:58:25 (Show Source): You can put this solution on YOUR website!Write the equation of the line passing through (3, –1) and (3, 6). ------------- Find the slope: m = [6--1]/[3-3] = undefined because the denominator is zero So the slope is undefined; the line is a vertical line. ------------ Since the line passes thru two points with x=3 the equation of the line is x=3. =============== Cheers, Stan H.
 Linear_Algebra/101088: c=1/4(A-3c) solve for c1 solutions Answer 73562 by stanbon(57361)   on 2007-09-28 19:54:31 (Show Source): You can put this solution on YOUR website!c=1/4(A-3c) 4c = A-3c 7c = A c = A/7 ============ Cheers, Stan H.
 Graphs/101051: Two rainstorms occurred in one week in a certain area. In the first rainstormn 15ML of rain fell per hour, and in the second rainstorm 40ML of rain fell per hour. Rain fell that week for a total of 65 hours for a total rainfall of 1850ML. How long was each of the two rainstorms? 1 solutions Answer 73557 by stanbon(57361)   on 2007-09-28 17:59:47 (Show Source): You can put this solution on YOUR website!Two rainstorms occurred in one week in a certain area. In the first rainstormn 15ML of rain fell per hour, and in the second rainstorm 40ML of rain fell per hour. Rain fell that week for a total of 65 hours for a total rainfall of 1850ML. How long was each of the two rainstorms? ------------------------ Let the length of the 40ML/hr rain be "x" hr. Amt of rain is 40x ML --------------------- The length of the 15ML/hr rain is 65-x hrs; rain amt= 15(65-x)= 975-15x ML ---------------------- rain + rain = 1850 ML 40x + 975-15x = 1850 25x = 875 x= 35 hr (length of the 40ML/hr rain) 65-15=30 hr (length of the 15ML/hr rain) ==================== Cheers, Stan H.
 Sequences-and-series/100999: Find the 37th term of the sequence 2,5,8,11,14,... Then make a series of the sequence in above problem and identify it as geometric or arithmetic.1 solutions Answer 73556 by stanbon(57361)   on 2007-09-28 17:20:51 (Show Source): You can put this solution on YOUR website!Find the 37th term of the sequence 2,5,8,11,14,... Then make a series of the sequence in above problem and identify it as geometric or arithmetic. ---------------------- Aritmetic with a(1)=2 and d=3 a(37)=a(1)+(n-1)d a(37)=2 + 36*3 a(37) = 110 =============== Cheers, Stan H.
 Finance/101007: of the \$50,000 that Natasha pocketed on her last real estate deal, \$20,000 went to charity. She invested part of the remainder with an annuak yield of 16% and the rest with an annual yield of 25%. if she made \$6060.00 on these investments in one year, then how much did she invest in each fund?1 solutions Answer 73555 by stanbon(57361)   on 2007-09-28 17:14:34 (Show Source): You can put this solution on YOUR website!of the \$50,000 that Natasha pocketed on her last real estate deal, \$20,000 went to charity. She invested part of the remainder with an annuak yield of 16% and the rest with an annual yield of 25%. if she made \$6060.00 on these investments in one year, then how much did she invest in each fund? ----------------------- 16% DATA: Amt invested = x dollars; interest = 0.16x dollars --------------- 25% DATA: Amt invested = 30,000-x dollars; interest = 0.25(30,000-x)=7500-0.25x dollars -------------- EQUATION: interest + interest = 6060 dollars 0.16x + 7500 - 0.25x = 6060 -0.09x = -1440 x = 16000 (amt invesed at 16%) 30000-16000= 14000 (amt invested at 25%) ========================== Cheers, Stan H.