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 expressions/111065: How would you evaluate this expression? 4 with an exponent of -2 minus 4 with an exponent of -11 solutions Answer 81040 by stanbon(57967)   on 2007-11-18 21:37:11 (Show Source): You can put this solution on YOUR website!evaluate this expression? 4 with an exponent of -2 minus 4 with an exponent of -1 --------------- 4^(-2) - 4^(-1) = 1/16 - 1/4 = 1/16 - 4/16 = -3/16 =========== cheers, Stan H.
 logarithm/111060: Solve lnx= 3+ln(x-3)1 solutions Answer 81039 by stanbon(57967)   on 2007-11-18 21:35:08 (Show Source): You can put this solution on YOUR website!Solve lnx= 3+ln(x-3) lnx-ln(x-3) = 3 ln[x/(x-3)] = 3 x/(x-3) =e^3 x/(x-3) = 20.0855... x = (20.0855..)x - 60.2566.. 19.0855x = 60.2566... x = 3.15718... Cheers, Stan H.
 logarithm/111058: Solve 2ln(-x) = 71 solutions Answer 81034 by stanbon(57967)   on 2007-11-18 21:30:25 (Show Source): You can put this solution on YOUR website!Solve 2ln(-x) = 7 ln(-x) = 7/2 -x = e^(7/2) -x = 33.1155 x = -33.1155 =========== Cheers, stan H.
 Functions/111027: Let f(x)= -x^2+2x-3 and g(x)=-x^2+4x Find each of the following. a. f(-2) b. g(3) c. g(-k) d. g(3m) e. g(k-5) f. f(3-p) I was able to get the following..... a. 5(-2)-3 -10-3 =-13 b. -3^2+4(3) -3^2+12 -9+12 =3 c. -k^2+4(-k) =-k2+4k d. -3m^2+4(3m) -3^2+12m =-9m2+12m THe following is all that I could get for letter E but I dont think it is right can you please help? The answer is supposed to be -k^2+14k-45 but I cant get there e. (-k-5)^2=4(k-5) (k+5)^2+4(k-5) (k+5)^2=4k+20 The following is all I could get for letter F. The answer is supposed to be 12-5p. f. 5(3-p)-3 15-5p-3 10p-3 thank you for your assistance :) 1 solutions Answer 81032 by stanbon(57967)   on 2007-11-18 21:28:19 (Show Source): You can put this solution on YOUR website!Let f(x)= -x^2+2x-3 and g(x)=-x^2+4x Find each of the following. a. f(-2) = -(-2)^2+2(-2)-3 = -4-4-3=-11 b. g(3) = -(3)^2+4*3 = -9+12 = 3 c. g(-k) = -(-k)^2+4*(-k) = -k^2-4k d. g(3m) = -(3m)^2+4(3m) = -9m^2+12m e. g(k-5)= -(k-5)^2+4(k-5) = -k^2+10k-25+4k-20 = -k^2+14k=45 f. f(3-p)= -(3-p)^2+2(3-p)-3 = -9+6p-p^2+6-2p-3= -p^2+4p-12 ============== Cheers, Stan H.
 Expressions-with-variables/111043: This question is from textbook Intermediate Algebra Factor completely: x2-6wy+3xy-2wx1 solutions Answer 81029 by stanbon(57967)   on 2007-11-18 21:20:50 (Show Source): You can put this solution on YOUR website!Factor completely: x2-6wy+3xy-2wx Rearrange to get: x^2+3xy -2wx-6wy Factor the 1st two and the last two terms separately to get: = x(x+3y) -2w(x+3y) Factor again to get: =(x+3y)(x-2w) ================= Cheers, Stan H.
 Quadratic_Equations/111028: Calculate the value of the discriminant of x^2 + x + 3 = 0 By examining the sign of the discriminant in the previous equation, how many x-intercepts would the graph of y = x^2 +x + 3 have? why?1 solutions Answer 81026 by stanbon(57967)   on 2007-11-18 21:17:44 (Show Source): You can put this solution on YOUR website!Calculate the value of the discriminant of x^2 + x + 3 = 0 b^2 - 4ac = 1^2-4*1*3 = 1-12 = -11 ---------------------------------------- By examining the sign of the discriminant in the previous equation, how many x-intercepts would the graph of y = x^2 +x + 3 have? None ---------------------------------------- why? The x-intercepts are not Real Numbers; they are Complex numbers and they do not appear on the Real Number x-axis. ======================= Cheers, Stan H.
 Number-Line/111050: what is 3.75 rounded to the nearest tenth1 solutions Answer 81021 by stanbon(57967)   on 2007-11-18 21:13:36 (Show Source): You can put this solution on YOUR website!what is 3.75 rounded to the nearest tenth --------- It is 3.8 ======== Cheers, Stan H.
 Linear-systems/111051: This question is from textbook algebra 1 -2(4-x)-7=51 solutions Answer 81020 by stanbon(57967)   on 2007-11-18 21:12:24 (Show Source): You can put this solution on YOUR website!-2(4-x)-7=5 -8+2x-7=5 2x-15 = 5 2x = 20 x = 10 ============ Cheers, Stan H.
 Equations/111048: Steve hit four more home runs than twice the number of home runs Larry hit. Together they hit 10 home runs. How many home runs did Steve hit?1 solutions Answer 81018 by stanbon(57967)   on 2007-11-18 21:10:36 (Show Source): You can put this solution on YOUR website!Steve hit four more home runs than twice the number of home runs Larry hit. Together they hit 10 home runs. How many home runs did Steve hit? ----------------- Always let the smaller quantity be "x"; that way you avoid fractions. -------------- Let # of Larry home runs be "x". Then Steve his 2x+4 home runs. ------------- EQUATION: x + 2x+4 = 10 3x = 6 x = 2 (Larry hit two home runs) 2x+4 = 8 (Steve hit eight home runs) ========== Cheers, Stan H.
 Equations/111037: Will somrone please help me solve this problem? perform the indicated operation and simplify:5x/x-1-x/x+2+6/x^2+x-21 solutions Answer 81012 by stanbon(57967)   on 2007-11-18 20:38:15 (Show Source): You can put this solution on YOUR website!5x/(x-1)-x/(x+2)+6/(x^2+x-2) LCD = (x-1)(x+2) Rewrite each fraction with the LCD as its denominator: = [5x(x+2)/LCD] -[x(x-1)/LCD] + [6/LCD] All the denominators are the same so combine the numerators over the LCD: = [5x^2+10x-x^2+x+6]/LCD = [4x^2+11x+6]/LCD = [4x^2+8x+3x+6]/LCD = [4x(x+2)+3(x+2)]/LCD = [(x+2)(4x+3)]/[(x-1)(x+2)] = (4x+3)/(x-1) ================== Cheers, Stan H.
 Equations/111039: Will someone please help me solve this problem? The problem says to divide using long division:(x^4+2x^3-16x^2+x+6)/(x-3)1 solutions Answer 81010 by stanbon(57967)   on 2007-11-18 20:29:25 (Show Source): You can put this solution on YOUR website!divide using long division:(x^4+2x^3-16x^2+x+6)/(x-3) ------------ Use synthetic division: 3)....1....2....-26....1....6 ........1...5.....-11...-32..|..-90 ============== Quotient: x^3 + 5x^2 -11x -32 Remainder: -90 ===================== Cheers, Stan H.
 testmodule/111032: Add the following lengths. Give the answer in feet and inches in its simplest form. (I am having trouble converting the mixed numbers) 6ft.7in. 47in. 9ft.11in. 13 3/4ft. 18ft. 9 2/3ft. 17in. Example: 6' 7'' 0' 47'' 9' 11'' 1 solutions Answer 81007 by stanbon(57967)   on 2007-11-18 20:23:18 (Show Source): You can put this solution on YOUR website!Give the answer in feet and inches in its simplest form. (I am having trouble converting the mixed numbers) 6ft.7in. 47in. 9ft.11in. 13 3/4ft. 18ft. 9 2/3ft. 17in. --------------- Convert each one to inches; Add the inches: Divide by 12 to get the number of feet plus some number of inches. ========================================= 6'7" = 79 inches 47" = 47 inches 9'11" =119 inches [13(3/4)]' =165 inches 18' =216 inches [9 2/3]' =116 inches 17' = 17 inches ===================== Add to get: 759" = 63 ft 3 inches ================== Cheers, Stan H.
 Signed-numbers/111030: I would like to check my answer to this problem. Here is the number problem: The sum of two consecutive integers is 145. Find the two integers. What I have come up with is this: x+x+1=145; 72,73 Am I right on this solution? Thank You for your help, Barb Neely 1 solutions Answer 81004 by stanbon(57967)   on 2007-11-18 20:09:25 (Show Source): You can put this solution on YOUR website!You are right. Cheers, Stan H.
 Travel_Word_Problems/110994: In a race, Car A starts 1 mile behind Car B. Car A is traveling at 55 mph, while Car B is traveling at 40 mph. How long will it take for Car A to overtake Car B?1 solutions Answer 81002 by stanbon(57967)   on 2007-11-18 20:07:48 (Show Source): You can put this solution on YOUR website!In a race, Car A starts 1 mile behind Car B. Car A is traveling at 55 mph, while Car B is traveling at 40 mph. How long will it take for Car A to overtake Car B? ----------- Car A DATA: Rate = 55 mph ; Distance : x+1 mile ; Time = d/r = (x+1)/55 hrs. ------------- Car B DATA: Rate = 40 mph ; Distance : x miles ; Time = d/r = x/40 ---------------------------------------- A time = B time (x+1)/55 = x/40 40(x+1) = 55x 15x = 40 x = 8/3 miles ------------- Time = x/40 = (8/3)/40 Time = 1/15 hr. = 15 minutes ======================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/111002: 4. Determine if the following system of equations is independent, dependent, or inconsistent: –7x – 5y = –4 –35x – 25y = 13 A) Independent B) Dependent C) Inconsistent 1 solutions Answer 81001 by stanbon(57967)   on 2007-11-18 19:57:35 (Show Source): You can put this solution on YOUR website!Determine if the following system of equations is independent, dependent, or inconsistent: –7x – 5y = –4 –35x – 25y = 13 If you multiply thru the 1st equation by 5 you get: -35x -25y = -20 ---------------- Do you see how "inconsistent" that is with the 2nd equation?? How could the same expression equal 13 and also equal -20 ?? The system is inconsistent. A) Independent B) Dependent C) Inconsistent ----------------- Cheers, Stan H.
 Exponential-and-logarithmic-functions/110978: A radioactive element sodium-24 has a half-life of 14 hours and is used to help locate obstructions in blood flow. A procedure requires 1.5 grams and is scheduled to take place in 37 hours. At what rate is the sodium-24 decaying? What is the minimum amount of sodium-24 that must be on hand now? 1 solutions Answer 80999 by stanbon(57967)   on 2007-11-18 19:51:15 (Show Source): You can put this solution on YOUR website!A radioactive element sodium-24 has a half-life of 14 hours and is used to help locate obstructions in blood flow. A procedure requires 1.5 grams and is scheduled to take place in 37 hours. --------- EQUATION: A(t) = Ao(1/2)^(t/14) 1.5 = Ao(1/2)^(37/14) Ao = 1.5 / [(1/2)^(37/14)] Ao = 1.5 / 0.16011... Ao = 9.369 grams -------------------- At what rate is the sodium-24 decaying? [9.369-1.5]/37 = 0.21266 grams per hour ----------------------------- What is the minimum amount of sodium-24 that must be on hand now? 9.369 grams ============== Cheers, Stan H.
 Proportions/111010: on some days, a bakery packages cupcakes 4 to a box. On other days, they package cupcakes 6 or 8 to a box. On a given day, all of the cupcakes baked were packaged and there was one cupcake left over. Which of the following could not be the number of cupcakes baked on that day?1 solutions Answer 80998 by stanbon(57967)   on 2007-11-18 19:41:11 (Show Source): You can put this solution on YOUR website!You forgot to list the answer options. Cheers, Stan H.
 Quadratic-relations-and-conic-sections/111009: ok. i have gotten to x=3(-9 +/-(square root of 71) /all over 10) +3 i need to figure out what x can be. thank you1 solutions Answer 80982 by stanbon(57967)   on 2007-11-18 18:54:26 (Show Source): You can put this solution on YOUR website!i have gotten to x=3(-9 +/-(square root of 71) /all over 10) +3 i need to figure out what x can be ---------- I can't imagine how you came up with this but....... x = 3[-9 +- sqrt(71)/10] + 3 x = 3[-9+(1/10)sqrt(71)] +3 Or x = 3[-9-(1/10)sqrt(71)] +3 ================================================== Cheers, Stan H.
 Equations/110998: Will someone please help me solve this problem? simplify:x^2-14x+49/6x^2-37x-351 solutions Answer 80978 by stanbon(57967)   on 2007-11-18 18:47:16 (Show Source): You can put this solution on YOUR website!simplify:x^2-14x+49/6x^2-37x-35 = (x-7)^2 / [6x+5)(x-7)] = (x-7)/(6x+5) =============== Cheers, Stan H.
 Equations/110992: 1.) 3x/(x+1) + 6/2x = 7/x 2.) 6x/(x+4) + 4 = 2x+2/(x-1) 3.) 7x+1/2x+5 + 1 =10x-3/3x 4.) 10/x^2-2x + 4/x = 5/x-2 1 solutions Answer 80976 by stanbon(57967)   on 2007-11-18 18:34:45 (Show Source): You can put this solution on YOUR website!1.) 3x/(x+1) + 6/2x = 7/x x(x+1) is the LCM Multiply thru by the LCM: 3x^2 + 3(x+1) = 7(x+1) 3x^2 + 3x+3 = 7x+7 3x^2-4x-3=0 x = [4 +- sqrt(16-4*3*-3)]/6 x = [4 +- sqrt(52)]/6 x = [4 +- 2sqrt(13)]/6 x = [2 +- sqrt(13)]/3 x = (2 + sqrt(13))/3 or x = (2 - sqrt(13))/3 ========================== 2.) 6x/(x+4) + 4 = (2x+2)/(x-1) Multiply thru by (x+4)(x-1) to get: 6x(x-1) + 4(x+4)(x-1) = 2(x+1)(x+4) 6x^2-6x + 4x^2+12x-16 = 2x^2+10x+8 8x^2 -4x -24 = 0 4(2x^2 -x -12) = 0 2x^2 - x -12 = 0 x = [1 +- sqrt(1 -4*2*-12)]/4 x = [1 +- sqrt(97)]/4 x = (1+ sqrt(97))/4 or x = (1-sqrt(97))/4 =============== Cheers, Stan H. 3.) 7x+1/2x+5 + 1 =10x-3/3x 4.) 10/x^2-2x + 4/x = 5/x-2
 Expressions-with-variables/110991: Will someone please help me? The problem says multiply or divide and simplify:5x/x+6*x^2-36/x^2-6x1 solutions Answer 80970 by stanbon(57967)   on 2007-11-18 18:05:47 (Show Source): You can put this solution on YOUR website!simplify:[5x/(x+6) * [(x^2-36) /(x^2-6x)] Factor where you can; Cancel where you can. = [5x/(x+6)] * [(x-6)(x+6)/x(x-6)] = [5/1] * [1/1] = 5 ========================= Cheers, stan H.
 Miscellaneous_Word_Problems/110988: Biologists collected a sample of 600 fish form Lake Marie on May 1st and tagged each of them. When they returned on June 1st, a new sample of 800 fish was collected and 10 of these had been previosuly tagged. Use this experiment to approximate fish popultion of Lake Linda. 1 solutions Answer 80969 by stanbon(57967)   on 2007-11-18 18:00:31 (Show Source): You can put this solution on YOUR website!Biologists collected a sample of 600 fish form Lake Marie on May 1st and tagged each of them. When they returned on June 1st, a new sample of 800 fish was collected and 10 of these had been previosuly tagged. Use this experiment to approximate fish population of Lake Linda. -------------- Let Real population be "x" fish. ------- Proportion: Real pop/sample = tagged pop/tagged sample x/600 = 800/10 x = 600*800/10 x = 48,000 fish ==================== Cheers, Stan H.
 Polynomials-and-rational-expressions/110985: Factor out the GCF: 4x^2+36y^21 solutions Answer 80967 by stanbon(57967)   on 2007-11-18 17:55:32 (Show Source): You can put this solution on YOUR website!Factor out the GCF: 4x^2+36y^2 =4(x^2+9y^2 =============== Cheers, Stan H.
 Travel_Word_Problems/110986: This question is from textbook algebra stucture and method An ultralight plane had been flying for 40 min when a change in wind direction doubled its ground speed. The entire trip of 160 mi took 2 h. How far did the plane travel during the first 40 min?1 solutions Answer 80966 by stanbon(57967)   on 2007-11-18 17:51:06 (Show Source): You can put this solution on YOUR website!An ultralight plane had been flying for 40 min when a change in wind direction doubled its ground speed. The entire trip of 160 mi took 2 h. How far did the plane travel during the first 40 min? -------------- Against the wind DATA: Time = 2/3 hr. ; distance = x miles ; rate = x/(2/3) = 3x/2 mph ---------------------------- With the wind DATA: Time = (4/3) hr ; distance = 160-x ; rate = d/t = (160-x)/(4/3) mph ------------------------------ rate with the wind = 2*rate against the wind (160-x)/(4/3) = 2(3x/2) 3(160-x)/4 = 3x 480-3x = 12x 480 = 15x x = 32 miles -------------------- Cheers, Stan H.
 Radicals/110981: I am working a problem and need to know tif either x-3x-16 or x^2-x-12 can be factored?? Thank you for your help!1 solutions Answer 80965 by stanbon(57967)   on 2007-11-18 17:38:05 (Show Source): You can put this solution on YOUR website!need to know if either x-3x-16 or x^2-x-12 can be factored?? ------------ x-3x-16 = -2x-16 = -2(x++8) ============== x^2-x-12 = (x-4)(x+3) ============= Cheers, Stan H.
 Graphs/110984: This question is from textbook algebra structure and method x-y=9 x+y=-51 solutions Answer 80964 by stanbon(57967)   on 2007-11-18 17:34:31 (Show Source): You can put this solution on YOUR website!x-y=9 x+y=-5 ---------- Add the equtions to get: 2x = 4 x = 2 --------- Substitute into x-y=9 2-y=9 y = -7 ============ Cheers, Stan H.
 Linear-equations/110982: these are suppose to be fractions but i did not know how to put them in. 1/3x + 3/4x = 13 the one third and the three fourths are fractions. thanks for the help.1 solutions Answer 80962 by stanbon(57967)   on 2007-11-18 17:31:19 (Show Source): You can put this solution on YOUR website!(1/3)x + (3/4)x = 13 Multiply thru by 12 to get: 4x + 9x = 12*13 13x = 12*13 x = 12 ============ Cheers, Stan H.
 Linear-equations/110983: A. 5x + 6y =18 for y When graphed this equation would be a line. By examining your answer to part a, what is the slope and y-intercept of this line?1 solutions Answer 80961 by stanbon(57967)   on 2007-11-18 17:28:45 (Show Source): You can put this solution on YOUR website!5x + 6y =18 for y When graphed this equation would be a line. By examining your answer to part a, what is the slope and y-intercept of this line? --------------- slope-Intercept form: y (-5/6)x+3 ------------------- Graph: --------------------- slope = -5/6 ================== Cheers, Stan H.
 Exponential-and-logarithmic-functions/110973: This question is from textbook i need help solving this problem (answer in back says 64) log4 X=31 solutions Answer 80955 by stanbon(57967)   on 2007-11-18 16:23:46 (Show Source): You can put this solution on YOUR website!log4 X=3 ---------- Your problem says the log, or exponent, is 3. It says the base is 4 It says the result of applying that exponent to that base is "x". x = 4^3 x = 64 =========== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/110933: HOW MANY YEARS WILL IT TAKE \$3000 TO GROW TO \$4667 IF IT IS INVESTED AT AN ANNUAL RATE OF 13%, COMPOUNDED CONTINUOUSLY? ROUND YOUR ANSWER TO ONE DECIMAL PLACE.1 solutions Answer 80954 by stanbon(57967)   on 2007-11-18 16:21:08 (Show Source): You can put this solution on YOUR website!HOW MANY YEARS WILL IT TAKE \$3000 TO GROW TO \$4667 IF IT IS INVESTED AT AN ANNUAL RATE OF 13%, COMPOUNDED CONTINUOUSLY? ROUND YOUR ANSWER TO ONE DECIMAL PLACE. ------------- A(t) = Ao*e^rt 4667 = 3000*e^(0.13t) e^(0.13t) = 1.555666666 Take the natural log to get: 0.13t = 0.441904... t = 3.4 years =============== Cheers, Stan H.
 Proportions/110969: A building is casting a 100 ft. shadow at the same time that a 5 ft. post is casting a 1 ft. shadow. Write a proportion that involves the height of the building, the height of the post, and legnths of the shadows. How high is the building? 1 solutions Answer 80948 by stanbon(57967)   on 2007-11-18 16:11:59 (Show Source): You can put this solution on YOUR website!A building is casting a 100 ft. shadow at the same time that a 5 ft. post is casting a 1 ft. shadow. Write a proportion that involves the height of the building, the height of the post, and length of the shadows. --------- Let height of the building be "x": Proportion: x/100 = 5/1 x = 500 ft ------------------------ How high is the building? The building is 500 ft. high ====================== Cheers, Stan H.