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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>Next

 Exponents/100948: Do you know any other websites that can show me free worksheets on how to work on exponents? I need them tomorrow. Yours, Arialyn1 solutions Answer 73462 by stanbon(57224)   on 2007-09-27 21:03:20 (Show Source): You can put this solution on YOUR website!http://www.coolmath.com/algebra/algebra-practice-polynomials.html ------------- Try this or use Google with search phrase algebra exponents practise ================ Cheers, Stan H.
 Expressions-with-variables/100949: This question is from textbook Algebra structure and Method If I need to find the average of these numbers: 18+(-17)+(-22)+(16)+(0) do I count the 0 in my number of terms?? In other words, do I divide the total (5) by 4 or 5? thanks. Kim 1 solutions Answer 73459 by stanbon(57224)   on 2007-09-27 20:59:28 (Show Source): You can put this solution on YOUR website!Yes you need to count the 0. Yes you need to divide by 5. ============ Cheers, Stan H.
 Quadratic_Equations/100958: Solve the equation by completing the square 4x^2 + 16x + 7 = 01 solutions Answer 73456 by stanbon(57224)   on 2007-09-27 20:33:09 (Show Source): You can put this solution on YOUR website!Solve the equation by completing the square 4x^2 + 16x + 7 = 0 4(x^2+4x+? = -7 + 4*? 4(x^2+4x+4)= -7 + 4*4 4(x+2)^2 = 9 (x+2)^2 = 9/4 x+2 = 9/2 or x+2 = -9/2 x = -2+(9/2) or x = -2 -(9/2) x = 5/2 or x = -13/2 ======================== Cheers, Stan H.
 Finance/100918: Hello! I am reviewing future values for my Finance class and am completely befuddled on the logical progression of the time value of money formulas. It has been quite some time since I have taken Algebra, and that is essentially why I can't figure this transformation out. FV1 = PV + kPV must transform into: FV1 = PV(1+k) I understand the basics cross-multiplying, but cannot for the life of me figure out how the former was transformed into the latter. Your assistance would be greatly appreciated! Jonathan Pounds 1 solutions Answer 73455 by stanbon(57224)   on 2007-09-27 20:27:50 (Show Source): You can put this solution on YOUR website!FV1 = PV + kPV must transform into: FV1 = PV(1+k) I understand the basics cross-multiplying, but cannot for the life of me figure out how the former was transformed into the latter. Your assistance would be greatly appreciated! -------------------- Try it with numbers and you will see that it works. ------------- The property is called "distribution" A statement of the property says: Multiplication distributes over addition. Here it is in symbols: a(b+c) = ab+ac ---------------- Your Problem: FV1 = PV + kPV Fv1 = PV(1+k) ------------------- If PV = 4 and k=3 then FV! = 4+3*4 = 16 -------------------- similarly 4(1+3)= 16 --------- Therefore 4+3*4 = 4(1+3) ------------------- ================= Cheers, Stan H.
 Miscellaneous_Word_Problems/100879: I think i have the right answer, but the problem is that my book dosen't really explain well enough on how to write the equation. The band leader wants to line up the 92 members in 4 rows so that each row has two more than the row before. How many members whould be in the shortest row? I'm sure the answer is 17. But I can't figure out for the life of me how to write the equation. I've been working in it all day.1 solutions Answer 73443 by stanbon(57224)   on 2007-09-27 17:06:02 (Show Source): You can put this solution on YOUR website!The band leader wants to line up the 92 members in 4 rows so that each row has two more than the row before. How many members whould be in the shortest row? ------------- Let the shortest line have x members The next is x+2 members Then x+2+2=x+4 members And finally x+4+2 = x+6 members ------------------------ EQUATION; x + x+2 + x+4 + x+6 = 92 4x+12 = 92 4x = 80 x = 20 (number in the shortest line) ============== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/100874: the slope of the line perpendicular to x+3y=5 a)-1 b)3 c)-1/3 d)1/3 e)11 solutions Answer 73433 by stanbon(57224)   on 2007-09-27 15:54:12 (Show Source): You can put this solution on YOUR website!the slope of the line perpendicular to x+3y=5 The given line can be written as y = (-1/3)x+(5/3) which has slope -1/3 ----------------- Any line perpendicular to the given line must have slope = -(-1/3)^-1 = 3 ================= Cheers, Stan H.
 Radicals/100865: Simplify. Assume x represents a positive number. sqrt (75x^4)1 solutions Answer 73432 by stanbon(57224)   on 2007-09-27 15:36:21 (Show Source): You can put this solution on YOUR website!sqrt (75x^4) =sqrt(25x^4)*sqrt(3) =5x^2sqrt(3) ============== Cheers, Stan H.
 Equations/100872: The intercepts of the equation x-2y= 6 a)(0,-3) and (3,0) b)(0,6) and (2,0) c)(0,-3) and (6,0) d)(0,3) and (0,0) e)(0,0) and (0,0) Please help.. Im stuck on this!1 solutions Answer 73430 by stanbon(57224)   on 2007-09-27 15:21:01 (Show Source): You can put this solution on YOUR website!The intercepts of the equation x-2y= 6 x-intercept: Let y=0, then x=6; so (6,0) is the x-intercept ---------------- y-intercept: Let x=0, then y = -3: so (0,-3) is the y-intercept ===================== Cheers, Stan H.
 Radicals/100868: solve. sqrt(x-1)=x-31 solutions Answer 73429 by stanbon(57224)   on 2007-09-27 15:18:28 (Show Source): You can put this solution on YOUR website!solve. sqrt(x-1)=x-3 --------------- Square both sides to get: x-1 = x^2-6x+9 x^2-7x+10=0 (x-5)(x-2)=0 x = 5 or x=2 ----------------- Check the answers in the original equation: Does x=5? sqrt(4)=5-3 True -------------- Does x=2? sqrt(1) = 2-3 sqrt1 = -1 False -------------- Only solution: x=5 ====================== Cheers, Stan H.
 Radicals/100869: simplify. sqft75a^2 / sqrt 51 solutions Answer 73428 by stanbon(57224)   on 2007-09-27 15:14:17 (Show Source): You can put this solution on YOUR website!simplify. sqrt75a^2 / sqrt 5 = 5a(sqrt3)/sqrt5 Multiply numerator and denominator by sqrt5 to get: = a(sqrt15) ================= Cheers, Stan H.
 Radicals/100867: simplify. (10+sqft2)(10-sqrt2)1 solutions Answer 73426 by stanbon(57224)   on 2007-09-27 15:11:44 (Show Source): You can put this solution on YOUR website!(10+sqft2)(10-sqrt2) This is the form (a+b)(a-b) which equals (a^2-b^2) ================ Your Problem: = 10^2 - (sqrt2)^2 = 100-2 = 98 =================== Cheers, Stan H.
 Trigonometry-basics/100848: Use appropriate identities to find the exact values of the following. a. sec(75degrees) so far I have sec(45deg+30deg)? then stuck. b. sin(7pi/12) I think this converts down to sin(2pi/3)? then stuck.1 solutions Answer 73425 by stanbon(57224)   on 2007-09-27 15:09:21 (Show Source): You can put this solution on YOUR website!Use appropriate identities to find the exact values of the following. a. sec(75degrees) so far I have sec(45deg+30deg)? then stuck. = 1/[cos(45+30)] = 1/[cos45*cos30-sin45sin30] = 1/[1/sqrt2 * sqrt3/2 - 1/sqrt2 *1/2] = 1/[sqrt3/2sqrt2 - 1/2sqrt2] = 2sqrt2/[sqrt3 - 1] = [2sqrt2(sqrt3+1)]/[3-1] = [2sqrt6 +2sqrt2]/2 = sqrt6 + sqrt2 ========================= b. sin(7pi/12)= sin(pi/3 + pi/4) = sin(pi/3)cos(pi/4)+cos(pi/3)sin(pi/4) = (sqrt3)/2 * (sqrt2)/2 + (1/2)(sqrt2)/2 = (sqrt6)/4 + (sqrt2)/4 = [sqrt6 + sqrt2]/4 =========================== Cheers, Stan H.
 Trigonometry-basics/100849: Suppose that sec(2t)=(-13/12), and that pi/2 Find the exact value of cos(t)1 solutions Answer 73423 by stanbon(57224)   on 2007-09-27 14:28:01 (Show Source): You can put this solution on YOUR website!Suppose that sec(2t)=(-13/12), and that pi/2 Find the exact value of cos(t) ------------------------------ sec(2t)=(-13/12) cos(2t)=(-12/13) 2t = cos^-1(-12/13) = 157.38 degrees t = 78.69 degrees ---------------- Cheers, Stan H.
 Functions/100850: I do not understand how to work this problem: y=x^3-8x. I know that the y-intercept is (0,0), but I can not figure out how to find the x-intercepts.1 solutions Answer 73422 by stanbon(57224)   on 2007-09-27 14:22:16 (Show Source): You can put this solution on YOUR website!y=x^3-8x. I know that the y-intercept is (0,0), but I can not figure out how to find the x-intercepts. ---------------- To find the x-intercepts, let y=0. x^3-8x=0 x(x^2-8)=0 x=0 or x^2-8=0 x=0 or x=2sqrt2 or x=-2sqrt2 ================================== Cheers, Stan H.
 test/100854: Describe the graph of 3x+y<1 a) a dotted line with shading below the boundary line 3x+y=1 b) a solid line with shading abouve the boundary line 3x+y=1 c) a solild line wtih shading below the boundary line 3x+y=1 d) a dotted line with shading above the boundary line 3x+y=11 solutions Answer 73421 by stanbon(57224)   on 2007-09-27 14:19:38 (Show Source): You can put this solution on YOUR website!Describe the graph of 3x+y<1 --------------- Solve for y: y <-3x+1 ----------------------------- The boundary of the solution set is y=3x+1 --------------- Take a test point that is not on the boundary, like (0,0) Substitute the x and y values of the test point into the inequality: 0 < 0 +1 This is false, so the half-plane solution set for the inequality is on the side of the boundary that does not contain (0,0)-------------that would be the half-plane above the boundary line. --------------- Note the boundary line is NOT part of the solution set because equality is not stated in the original equation. ----------------------- The solution is "d". -------------------------- Cheers, Stan H.
 test/100855: Evaluate the expression x4 -9x2+4x+8 for x=0 (the 4 and 3 are up high to the left of the x and -9)1 solutions Answer 73419 by stanbon(57224)   on 2007-09-27 14:12:24 (Show Source): You can put this solution on YOUR website!x4 -9x2+4x+8 for x=0 Put 0 in place of x and you end up with = 8 ================== Cheers, Stan H.
 test/100858: let f(x)=2x+1 evaluate f as indicated f(5+h)1 solutions Answer 73418 by stanbon(57224)   on 2007-09-27 14:10:14 (Show Source): You can put this solution on YOUR website!let f(x)=2x+1 evaluate f as indicated f(5+h) ----------- f(5+h) = 2(5+h)+1 = 10+2h+1 =11 + 2h -------------- Cheers, Stan H.
 Quadratic_Equations/100859: Please can you help solve: 0.75x²-2.4x+75.Calculate the value of x when h = 73.081 solutions Answer 73417 by stanbon(57224)   on 2007-09-27 14:08:32 (Show Source): You can put this solution on YOUR website!h = 0.75x²-2.4x+75.Calculate the value of x when h = 73.08 ----------------------------- 0.75x²-2.4x+75= 73.08 0.75x^2-2.4x+1.92 Multiply thru by 100 to get rid of the decimals: 75x^2 - 240x +192 = 0 x = [240 +- sqrt(240^2-4*75*192)]/150 x = [240 +- 0]/150 x = 8/5 =0.16 ============== Cheers, Stan H.
 Expressions-with-variables/100837: Which of the following expressions represents the product of 3 less than twice x and 2 more than the quanity 3 times x? A. -6xsquared + 25x + 6 B. 6xsquared + 5x + 6 C. 6xsquared - 5x + 6 D. 6xsquared - 5x -6 E. 6xsquared - 13x - 61 solutions Answer 73412 by stanbon(57224)   on 2007-09-27 12:46:17 (Show Source): You can put this solution on YOUR website!Which of the following expressions represents the product of 3 less than twice x and 2 more than the quanity 3 times x? --------------- (2x-3)(3x+2) = 6x^2-5x-6 ----------------- Cheers, Stan H.
 Expressions-with-variables/100833: can someone show how to solve the system by elimination method. Show all steps and check the answer? Thanks! x - 2y = -1 3X + y = 41 solutions Answer 73411 by stanbon(57224)   on 2007-09-27 12:43:13 (Show Source): You can put this solution on YOUR website!1st: x - 2y = -1 2nd: 3x + y = 4 ---------------------- Multiply 2nd thru by 2 to get: 3rd: 6x + 2y = 8 ---------------- Add 1st and 3rd to get: 7x =7 x = 1 ------------- Substitute that into 1st to solve for Y: 1 -2y = -1 2y = 2 y = 1 ------------------ Check the answer in 2nd: 3*1 + 1= 4 3 + 1 = 4 4 = 4 =============== Cheers, Stan H.
 Equations/100824: I have the number 25. That was the total after taking 75% off. How do we find the original number? What is the mathematical equation?1 solutions Answer 73408 by stanbon(57224)   on 2007-09-27 11:53:32 (Show Source): You can put this solution on YOUR website!I have the number 25. That was the total after taking 75% off. How do we find the original number? What is the mathematical equation? --------------- Let the original number be "x". EQUATION: x-0.25x = 25 0.75x = 25 x = 25/0.75 x = 33.3333.... Cheers, Stan H.
 Polynomials-and-rational-expressions/100820: The cost in dollars of manufacturing w wing nuts is given by the expression 0.07w + 13.3. Find the cost when 375 wing nuts are made. What is the average cost to manufacture one wing nut?1 solutions Answer 73406 by stanbon(57224)   on 2007-09-27 11:51:15 (Show Source): You can put this solution on YOUR website!The cost in dollars of manufacturing w wing nuts is given by the expression 0.07w + 13.3. Find the cost when 375 wing nuts are made. What is the average cost to manufacture one wing nut? ---------------------------------- The price of each wing nut is (0.07w+13.3)/w. So the price of 375 nuts is 375[(0.07w+13.3)/w] = (26.25w + 4987.5)/w = (26.25 + (4987.5/w)) ===================== Cheers, Stan H.
 Angles/100821: The supplementary angle is 15 degrees less than 4 times the complementary angle. Find the angle. In the office, we have come up with two different solutions: 55 degrees and 39 degrees. Which one is right?1 solutions Answer 73404 by stanbon(57224)   on 2007-09-27 11:40:20 (Show Source): You can put this solution on YOUR website!The supplementary angle is 15 degrees less than 4 times the complementary angle. Find the angle. --------------- Let the angle be "x". The complement is "90-x" The supplement is "180-x" ------------------ Equation: 180-x = 4(90-x)-15 180-x = 360-4x-15 3x = 165 x = 55 degrees (this is "the angle") ===================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/100822: Find the center of an ellipse with the equation 7(x-2) raised to the 2 + 3(y-2) raised to the 2=21. I have math notes, but I'm having a hard time understanding where the numbers come from. Thanks for your help!1 solutions Answer 73403 by stanbon(57224)   on 2007-09-27 11:36:07 (Show Source): You can put this solution on YOUR website!Find the center of an ellipse with the equation 7(x-2)^2 + 3(y-2)^2 = 21 ------------------- General Form: (x-h)^2/a^2 + (y-k)^2/b^2 = 1 -------------------------------- Matching that with your problem you see that h=2 and k=2. So the center is at (2,2). =============== Cheers, Stan H.
 Polynomials-and-rational-expressions/100771: Use the ac test to determine if the trinomial can be factored. x^2+2y-151 solutions Answer 73387 by stanbon(57224)   on 2007-09-27 06:33:53 (Show Source): You can put this solution on YOUR website!Use the ac test to determine if the trinomial can be factored. x^2+2y-15 -------- Find two integers whose product is AC= -15 and whose sum is B=2 ------------------ The numbers are 5 and -3 ------------------------- So the trinomial can be factored using the AC Method. --------------------------- (x+5)(x-3) ------------ Cheers, Stan H.
 Linear-equations/100773: In direct variation, is it possible for one variable to get bigger as the other variable decreases?1 solutions Answer 73386 by stanbon(57224)   on 2007-09-27 06:29:54 (Show Source): You can put this solution on YOUR website!Not if the two variables are directly variable. That would be a contradiction. Cheers, Stan H.
 Square-cubic-other-roots/100595: 2T^-4 -5T^-2 +2=0 2T HAS A NEGATIVE EXPONENT OF -4 AND 5T HAS A NEGATIVE EXPONENT OF -2 solve thanks1 solutions Answer 73373 by stanbon(57224)   on 2007-09-26 23:20:12 (Show Source): You can put this solution on YOUR website!2T^-4 -5T^-2 +2=0 -------------- Let x = T^-2 You get: 2x^2 - 5x + 2 = 0 (2x-1)(x-2)=0 x = 1/2 or x = 2 ---------------- Therefore: T^-2 = 1/2 or T^-2 = 2 T = (1/2)^(-1/2) or T = 2^(-1/2) T = sqrt2 or T = (sqrt2)/2 ========================= Cheers, Stan H.
 Trigonometry-basics/100617: what quadrant identities would cos (theta)>0 and csc(theta)<0 fall into? what is the reciprocal identity of cos(theta) if sec(theta) equals -3? what quadrant would -113.5 fall into? what are all values of theta if the interval is at (0,360) when cot(theta) equals 1?1 solutions Answer 73372 by stanbon(57224)   on 2007-09-26 23:13:00 (Show Source): You can put this solution on YOUR website!what quadrant identities would cos (theta)>0 and csc(theta)<0 fall into? theta would be in the 4th Quadrant where cos is positive and csc is negative. -------------------------- what is the reciprocal identity of cos(theta) if sec(theta) equals -3? cos(theta) = 1/-3 = -1/3 ----------------------------- what quadrant would -113.5 fall into? If that is degrees the quadrant would be the 3rd -------------------------- what are all values of theta if the interval is at (0,360) when cot(theta) equals 1? theta = 45 degees or 235 degrees ================ Cheers, Stan H.
 Angles/100762: This question is from textbook My daughter and I had trouble with this: Five times the compliment of an angle less twice the angles supplement is 40 degrees. Find the measure of te supplement. Please Help!1 solutions Answer 73369 by stanbon(57224)   on 2007-09-26 23:06:11 (Show Source): You can put this solution on YOUR website!Five times the compliment of an angle less twice the angles supplement is 40 degrees. Find the measure of te supplement. ---------------- Let the angle be "x". The complement is "90-x" The supplement is "180-x" EQUATION:' 5(90-x)-2(180-x)=40 450-5x-360+2x = 40 90-3x = 40 3x = 50 x = 50/3 = 16 2/3 degrees ------------- The supplement = 180 - 16 2/3 = 153 1/3 degrees ===================== Cheers, Stan H.
 Quadratic_Equations/100700: describe the resulting graphs by identifying the vertex point, the graphs direction and any axis intercepts gleaned from the table or graphs y = -x + 11 solutions Answer 73363 by stanbon(57224)   on 2007-09-26 22:39:53 (Show Source): You can put this solution on YOUR website!describe the resulting graphs by identifying the vertex point, the graphs direction and any axis intercepts gleaned from the table or graphs y = -x + 1 ------------------- That equation graphs as a line; it has no vertex. y-intercept: Let x = 0, then y = 1 is the y-intercept -------------- x-intercept: Let y = 0, then x = 1 is the x-intercept --------------- Cheers, Stan H.
 Equations/100754: Solve for y: 3x+2y=12 Is it y=-3x+61 solutions Answer 73358 by stanbon(57224)   on 2007-09-26 22:28:31 (Show Source): You can put this solution on YOUR website!Solve for y: 3x+2y=12 ------------- 2y = -3x + 12 y = (-3/2)x + 6 ================== Cheers, Stan H.