Posts by Reiny

Total # Posts: 40,977

  1. algebra 1

    You did not state a question, but I assume you want to find the amount. you have P = 3000 i = .065 t = ???? (you did not give me that) so just replace the t in amount = 3000(1.065)^t , evaluate and you are done.
  2. math

    3 books and 2 pens worth RM135 while 2 books and 3 pens worth RM 140. Calculate the price for each item. 3b + 2p = 135 -- times 3 --> 9b + 6p = 405 2b + 3p = 140 -- times 2 --> 4b + 6p =280 subtract them: 5b = 125 b = 25 sub back into one of the first equations to get p
  3. Finance

    In the standard compound interest formulas, the payment is made at the end of the month. So I will consider today's payment to be a down payment. Balance owing = 38500-690 = 37810 let the monthly rate be i the number of payments = 68 690( 1 - (1+i)^-68)/i = 37810 There is ...
  4. Math

    yes
  5. Trig

    Look up how to find the area of a triangle using Heron's Formula. Once you have the area in square feet, multiply that by 3.
  6. Math 6th grade

    The first place can be filled by 4 different flags, leaving 3 flags that go go in the second spot, leaving 2 flags that can go in the third spot, leaving you with 1 flag for the last spot, so, the number of ways = 4*3*2*1 = 4! = 24
  7. math

    since ?961 = 31 , see https://www.jiskha.com/display.cgi?id=1531557433
  8. math

    Using the following dinky 1980's style program in GW-BASIC 10 for a = 1 to 30 20 for b = 1 to 30 30 for c = 1 to 30 40 if sqr(a*a+b*b+c*c) = 31 then print a,b,c 50 next c 60 next b 70 next a if got the following: 5,6,30 <------ Steve's answer 6,14,27 6,21,22 14,18,...
  9. math

    What was asked for? the only thing you can really do is give an approximation, the was it sits it is a real number in exact form
  10. MATH - circles, circles, circles

    A circle can cut another circle in at most 2 places. So any new circle cuts Think along the lines of the "handshake" problems 2 people can shake hands in 1 way , C(2,2) 2 circles can intersect in 2 ways ---->2x1 = 2 3 people can shake hands in 3 way , C(3,2) 3 ...
  11. Math

    certain speed ---- x mph slower speed ---- x-6 mph time at certain speed = 56/x time at slower speed = 56/(x-6) 56/x + 56/(x-6) = 16 multiply each of the 3 terms by x(x-6) you will get a quadratic, according to my definition, x > 6 , so reject any invalid answers after you ...
  12. SAT math

    r(n) = (n-7)[(n+1)-7][(n+2)-7] r(1) = .... wherever you see an n, replace it with 1 r(1) = (1-7)[(1+1) - 7][(1+2) - 7] just work it out. Watch the order of operation, let me know what you get.
  13. Math

    If you see two or more ordered pairs with the same x value but different y valued, then the relation is NOT a function, so what can x not be ?? e.g. suppose x = -1 , then we would have (-1,3) and (-1,-4). That would be a no-no so x ? -1 What other values of x have that ...
  14. 7 math

    I count 8 variations of this question that you have now posted. You have been given answers by Steve, Ms. Sue, and bobpursley. What are you looking for ?? 12xyz and -6xy are both terms there are 15 different factors of 12xyz , 12, x, y, z, 12x,..... there are 7 different ...
  15. Math

    number of screws ---- x number of pegs ---- 2x number of nails ---- x-3 x-3=15 ---> x=18 so he used 36 pegs
  16. Math-Sine wave function

    Our equation should have the form: h = a sin k(t - Ø) + d since the range of the up/down (ud) is 50 cm a = 25 It dows 5 ud's in 15 seconds, so we have a period of 1 ud/5 sec then 2?/k= 3 ---> k = 2?/3 so far we have h = 25 sin (2?/3 t) + 100 we also have to move ...
  17. Math

    1/3 - 2/3 = -1/3 2/9 - 1/3 = -1/9 , so it is NOT arithmetic 1/3 ÷ 2/3 = 1/2 2/9 ÷ 1/3 = 2/3 , so it is NOT geometric let's change them to ... 2/3, 1/3, 2/9, 1/6 , .... = 2/3, 2/6, 2/9, 2/12, .... = 2/(3*1) , 2/(3*2) , 2/(3*3), 2/(3*4), .... mmmmhhhh?
  18. Math

    Key concept: they will have travelled the same distance time taken by the slower train ---- t hours time taken by the faster train ----- t-2 hrs 125(t-2) = 75t solve for t , sub into either 75t or 125(t-2)
  19. Math

    total ---- x son gets x/3 leaves 2x/3 for the 4 daughters so 2x/3 ÷ 4 = 2x/12 = x/6 each daughter gets 1/6 of the total check: 1/6+1/6+1/1+1/6+1/3 = 1
  20. Math

    width ---- x m length = x+1 m area = x(x+1) x(x+1) = 6 expand, arrange in the usual quadratic form, and solve. I assume you know how to solve basic quadratics, or else you wouldn't have these types of problems.
  21. Quadratic Equations

    For two equal roots, the discriminant has to be zero, ... b^2 - 4ac = 0 16 - 4(3)(m) = 0 16 = 12m m = .... For no real roots, b^2 - 4ac < 0 , so ....
  22. Quadratic Equations Word Problem

    length including border = 12 + 2x width including border = 8 + 2x area including border = (12+2x)(8+2x) = ..... area of just the pool = 12(8) = .... the difference would be the area of the border. then (12+2x)(8+2x) - 12*8 =44 simplify and solve for x I assume you know how to ...
  23. geometry

    Carefully study this example then adapt it to your particular problems. They do a good job of outlining the steps. I suggest you print out these steps, then follow them https://patch.com/new-jersey/wyckoff/find-orthocenter-of-a-triangle-geometry_eb93cdab
  24. Calculus

    What part of the answer I gave you on Wednesday to the same question did you not like ? https://www.jiskha.com/display.cgi?id=1530696164
  25. negative numbers 6th grade

    Good grief, this is the same type as the one I just answered for you. Just follow the same steps.
  26. negative numbers 6th grade

    first change those silly fractions to useful fractions 9(-5/3)÷(-10/3) = 9(-5/3)(-3/10) = 9/2
  27. probability

    So there are a total of 20 games, of which they win 13 so prob(wind) = .....
  28. math, algebra

    Kenny, how about this given A > B , e.g. A = 10, B = 3 then what is B-A ?? would it not be -7 then, then for B(B-A) > 0 , B would have to be negative, so B ? 3, but B = -3 will work and for the above example AB < 0 , so I and III are both correct how about letting ...
  29. Math

    I have a feeling James meant to say: "Mabel bought some notepads for $56. If she had been given a discount of 30% , she would be able to buy 40 notepads more. Let the original price be x Number of notepads bought when paying $56 = 56/x discounted price = .7x Number of ...
  30. Math

    The way it stands: 4 times the length of 18 ft, 4 inches, then subtract 3 ft for the doorway. Multiply that by 1.69 more realistic: Will there be any cut-off waste ? What happens it you can only buy the trim in 8 ft lengths? This question is much too simplistic.
  31. algebra

    Did you notice that two of the points have the same y value of -20 so the vertex must lie on x = 1 midway between the two x's , (because (-2 + 4)/2) = 1 ) So, let the quadratic be y = a(x-1)^2 + c for the point (0,-4) -4 = a + c for the point (4,-20) -20 = 9a + c subtract ...
  32. algebra

    I will assume you are solving. 8y=7+14x ---> 14x - 8y = -7 18y-2=-7x --> 7x + 18y = 2 I suggest multiplying the 2nd by 2, then subtracting them. That will eliminate the x's , then solve for y. You know what to do next.
  33. Maths

    in one minute the minute hand has moved 360/60 or 6° in one minute the hour hand has moved (360/60) ÷ 12 = .5° so the angle between them has changed by 6-.5 = 5.5° = 5° 30'
  34. Calculus

    Did you make your sketch? then Area (or distance) = (1/2)(.3)(0 + 24.5) + (1/2)(.7)(24.5+27.8) + (1/2)(.6)(27.8+28.3) + (1/2)(.4)(28.3+29.0) = .... I will let you do the arithmetic.
  35. Math

    They are the same thing. e.g. suppose there are 2 possible outcomes to some experiment, A and B and prob of event A is 5/19 then the prob of B is 1 - 5/19 = 14/19 odds in favour of event A = (5/19) ÷ (14/19) = (5/19)(19/14) = 5/14 or 5 : 14 or odds in favour of event A...
  36. probability with casework

    Damon, if we follow your interpretation, the outcomes would be dddd dddc --- (2/3)(2/3)(1/3) ddcd ddcc --- (2/3)(1/3)(1/2) dcdd dcdc -- (1/3)(1/2)(1/3) dccd dccc -- (1/3)(1/2)(1/2) then there would be 4 outcomes that end with a coin, for a total of 4/27 + 1/9 + 1/18 + 1/12 = ...
  37. probability with casework

    Let D be the outcome of a die at the end of a turn C be the outcome of a coin at the end of a turn Make a tree diagram we start with D we have either a D or a C at the end of the first toss, two branches from the D, we have a D or C at the end of the 2nd toss (the beginning of...
  38. Math

    Read carefully, the wire is attached 40 ft from the top, so the wire is attached 110 ft above the ground. So now it becomes very simple, a right-angled triangle with base angle of 40°, and an opposite side of 110 ft. We want the hypotenuse h, so sin40° = 110/h solve ...
  39. Algebra

    for the zeros of 2x(x+5)^2-8x 2x(x+5)^2-8x = 0 2x( (x+5)^2 - 4) = 0 x = 0 or (x+5)^2 = 4 x = 0 or x+5 = ±2 x = 0, -3, -7 proof: http://www.wolframalpha.com/input/?i=solve+2x(x%2B5)%5E2-8x+%3D0 I have no idea where you got your answers from, but they are not the zeroes ...
  40. Pure maths

    Why did you post this? Could you not do .... https://www.google.ca/search?source=hp&ei=lAk5W-eqNJLJ5gK9qqWICg&q=199%2B8799%2B687997345-852&oq=199%2B8799%2B687997345-852&gs_l=psy-ab.3...1775.1775.0.3547.3.2.0.0.0.0.176.176.0j1.2.0....0...1c.2.64.psy-ab..1.1.350.6..35i39k1.351....
  41. Maths

    after giving .6x to his brother, he has .4x left he gives half of those to the cousin. So he has .2x left .2x = 36 x = 180
  42. math

    simplify (9/12)(8/11)
  43. Math

    I read that as 14 8/15 m and 4 2/3 m , 14/8/15 makes little sense. P = 2L + 2W 14 8/15 = 2(4 2/3) + 2W 218/15 - 28/3 = 2W 2W = 26/5 W = 13/5 m or 2.6 m btw, metric units of measurement usually aren't stated as fractions like that, it would defeat the beauty and purpose of ...
  44. MATH

    ?8 = ?(4*2) = ?4*?2 = 2?2
  45. Quadratics

    For the equation ax^2 + bx+ 9 = 0 to have only one solution, (the parabola touches the x-axis at one point only) , the discriminant has to be zero, that is b^2 - 4a(9) = 0 b^2 = 36a a = b^2/36 Also MsPi suggested subbing in the given point (1,25) 25 = a(1)^2 + b(1) + 9 a+b = ...
  46. Trig

    I made a sketch saw that I had a triangle with sides 36 and 27 and a contained angle of 116° So, using the cosine law: let the distance between them be x x^2 = 36^2 + 27^2 - 2(36)(27)cos116 = 2877.19... x = appr 53.64 miles, which agrees with Daniel's answer.
  47. Mathematics

    (4x+3y):(3x+5Y) = 6:7 (4x+3y) / (3x+5Y) = 6/7 28x + 21y = 18x + 30y 10x = 9y substitute y = 10 and solve for x
  48. geometry

    Ok with x = 8 BUT, it asked for the length of RT and NQ if x = 8, RT = 7x-5 = 56 - 5 = 51 notice that NQ = 5x+11 = 40+11 = 51, the same as required So your choice would be b)
  49. Math

    consider 12:00 am , the hands will coincide. In on hour the minute hand makes one rotation, or 2?r inches = 2?(12) or 24? inches in the same time the hour hand will make 1/12 of a rotation. distance of hour hand = (1/12)(2?)(9) = 3?/2 inches So the difference = 24? - 3?/2 = 45...
  50. math

    charge = 5 + .75(k - 4), where k is the number of kilometres. 43.25 = 5 + .75(k - 4) solve for k
  51. pemdas

    which I did
  52. pemdas

    I read that as: 2/6 + (1/2)^2 + 1 = 1/3 + 1/4 + 1 = 4/12 + 3/12 + 12/12 = 19/12
  53. Math

    xy^2 = 1 x(2y)dy/dx + y^2 (1) = 0 dy/dx = -y^2/(2xy) at (1,-1) , dy/dx = -(-1)^2/(2(1)(-1))= 1/-2 = - 1/2 Now you have the slope and the given point. Find the equation of the straight line, using your method of choice.
  54. math

    I will find the payment for the first case: let the payment be P i = .09/12 = .0075 n= 12(22) = 264 P(1 - 1..0075^-264)/.0075 = 175000 P = .0075(175000)/(1 - 1.0075^-264) = $1524.56 Now the new rate is said to be 10% repeat the above process, them compare the payments take the...
  55. Math

    Very good, I agree with all your answers
  56. Rotations

    I don't know at what level you are working at, but if you are into matrices, here is an excellent video that not only develops the rotation matrix but actually uses a 90° rotation as an example. https://www.youtube.com/watch?v=OYuoPTRVzxY If you don't know what a ...
  57. Math

    I agree with your answers, good job
  58. math

    original amount --- x spent on food = 3x/5, leaving her with 2x/5 she spends 1/2 of that on a book, leaving her with (1/2)(2x/5) or x/5 so x/5 = 32 x = ....
  59. maths

    The way you typed it, it is false. It needs brackets, but the number of variations to place those brackets is too great for me to start guessing what you meant. e.g. did you mean : tanx + (secx -1)/(tanx - secx)+1 = (1+sinx)/cosx or (tanx + secx -1)/(tanx - secx+1) = 1+sinx/...
  60. Geometry

    I have my doubts that your teacher would use a notation or a concept that was never taught to you. What does your text say? Did you not attend your classes ?
  61. Geometry

    I am not familiar with your notations. e.g. • T<3,-6> ?????
  62. calculus2

    Let a circle x^2 + y^2 = r^2 be rotated about the x-axis to create the sphere so we need volume = ?? y^2 dx from -r to r or volume = 2?? y^2 dx from 0 to r because of the symmetry = 2?? r^2 - x^2 dx from 0 to r = 2? [r^2 x - (1/3)x^3 ] from 0 to r = 2? (r^3 - r^3/3) = 2?(2/3) ...
  63. Algebra

    C(29,6) or ??? ways
  64. math

    27 miles/1 hour = 27(5280) ft / (60(60))sec = 142560/3600 ft/s = 198/5 ft/s or 39.6 ft/s So if the cyclist goes 39.6 ft in 1 second, in 2 seconds he/she goes ......
  65. Vectors

    direction vector of AB = (3, 6, -6) <------ Steve had (3,4,-6), a slight arithmetic error. x = 1 + 3t y = 2 + 6t z = 3 - 6t direction vector CD = (-3,-3,1) x = 3 - 3s y = 5 - 3s z = 3 + s setting the x's equal ---> 1+3t = 3-3s or 3t + 3s = 2 setting the y's equal...
  66. Calculus

    h(t) = 0.8cost + 0.5sin2t v(t) = -.8sint + .5cos(2t)(2) = -.8sint + cos(2t) = .8 -.8sint + cos(2t) = .8 time -10 8sint - 10cos(2t) = -8 4sint - 5cos(2t) = -4 , but cos(2t) = 2sin^2 t - 1 4sint - 5(2sin^2 t - 1) + 8 = 0 4sint - 10sin^2 t + 5 + 8 = 0 10sin^2 t - 4sint - 13 = 0 ...
  67. Math

    Amount = principal(1 + i)^n your principal is 1400 i = .06 n = 8 + 5/12 = 101/12 you will definitely need a calculator, what answer did you get ?
  68. MATH

    2?[((-6561/4)+2430-(729/2))-((-1/4)+(10/3)-(9/2))] = 2?[ 1701/4 - (-17/12) ] = 2? [ 1280/3 ] = 2560/3 ? I have a feeling you messed up in the subtraction of the terms in the second bracket.
  69. geometry

    Since you told me the two angles are equal .... 14b - 22 = 11b solve for b
  70. MATH

    If you meant (?4)(x) , then it is indeed 2x if you meant ?(4x) = 2x, then it is true only for x=0 and x=1, it is false for all other values of x let's solve ?(4x) = 2x square both sides: 4x = 4x^2 4x^2 - 4x = 0 4x(x - 1) = 0 so x = 0 or x = 1
  71. MATH

    I read that as: Find the intersection of y=?4x and y=x^2/4 the x^2/4 = ?(4x) x^2 = 4?(4x) square both sides: x^4 = 16(4x) = 64x x^4 - 64x = 0 x(x^3 - 64) = 0 x=0 or x = 4 if x = 0, y = 0 if x = 4 , y = ?16 = 4 the two curves intersect at (0,0) and (4,4) (notice the two points ...
  72. Math

    Interpretation: I will see 4 cm of framing all around. Add 4 cm to each end of the width ---> width of frame = 32+8 = 40 cm length of frame = ..... area = length x width = ....
  73. Data

    The prob of drawing any specific number is 4/36 = 1/9 expected return on one game = expectation(2) + expectation(3) + ... + expectation(10) = (1/9)(2) + (1/9)(3) + ... + (1/9)(10) = (1/9)(2+3+4+...+10) = (1/9)(45) = 5 so it will cost 20($5) or $100 to play the 20 games the ...
  74. Maths (money and finance)

    What is 2500(1.09)^3 ?
  75. math

    It would really help it you had put your answers with each of the questions. I am NOT going to keep scrolling up and down, trying to match your choices with the question, sorry.
  76. Math

    The question was , "How many more litres are needed to fill it? the tank holds 36 litres, we both have that it already holds (1/6)(36) or 6 L 21 more are added, so now we have 27 L, which is 3/4 of the tank, so 9 more litres are needed to fill it.
  77. Math

    Let the capacity of the tank be x litres (1/6)x + 21 = (3/4)x solve for x to find the capacity of the tank. I am sure you can take it from there, e.g. 1/6 of the tank is ... then 21 litres were added, how many more are needed to fill it ?
  78. Vectors

    I set the x and y equations equal to each other to get: 4t - s = -11 t + 3s = 7 solving these, I got t = -2 and s = 3 which verified in the z value of 0 for both lines. So sub s=3 and t = -2 and it the corresponding lines and you get (x,y,z) = (-5,5,5)
  79. Math-trig

    small typo: 2ndF cos (/13) should have been 2ndF cos (1/3)
  80. Math-trig

    by arcsec(-3) you are looking for an angle Ø so that secØ = -3 or cosØ = -1/3 we know that the cosine is negative in quads II and III so Ø = 180° - 70.53° OR Ø = 180° + 70.53° Ø = appr 109.5° or appr. 250.5° I ...
  81. Math

    I assume you are proving this identity to be true. What have you done so far?
  82. Math

    from 8x + 8y = 18 x + y = 9/4 x^2 - y^2 = (x+y)(x-y) , using the difference of squares -3/8 = (9/4)(x-y) x-y = (-3/8) / (9/4) = (-3/8)(4/9) = -1/6 so 2x - 2y = .......
  83. math

    let the total be x solve : (2/3)x + (3/4)(1/3)x + 3 = x 2x/3 + x/4 + 3 = x suggestion: times 12 take it from there
  84. math

    Assuming your equations are: 2a + 12b = -7 3a + 2b = 7 multiply the 2nd equation by 6 to get 18a + 12b = 42 then subtract the 1st, that will eliminate the b, and go from there
  85. Geometry

    What do you call a triangle that has 2 equal sides ??
  86. Vectors

    You are right, at closer look I now see -1/14, with my failing eyesight I saw -1 1/14, which I changed to -15/14 so picking it up from ( (6)(1) + (-2)(p) + (3)(-2) ) = 7?(5 + p^2)(-15/14) should have been ( (6)(1) + (-2)(p) + (3)(-2) ) = 7?(5 + p^2)(-1/14) and then -2p = (-1/2...
  87. Vectors

    error in finding |b| |b| = ?(5+p^2) you need the dot product a dot b = |a| |b| cosØ ( (6)(1) + (-2)(p) + (3)(-2) ) = 7?(5 + p^2)(-15/14) -2p = (-15/2)?(5+p^2) 4p = 15?(5+p^2) 16p^2 = 225(5+p^2) 16p^2 = 1125 + 225p^2 209p^2 = -1125 No real solution, so no value of p ...
  88. Calculus

    for your given example , dy/dx = 2x/(3y^2) so you set that equal to 4 2x/(3y^2) = 4 2x = 12y^2 x = 6y^2 now plug that back into the original y^3 = x^2 y^3 = 36y^4 36y^4 - y^3 = 0 y^3(36y - 1) = 0 y = 0 or y = 1/36 if y = 0, the x = 0 <------ **** if y = 1/36, then x = 6(1/...
  89. Pre-Calc

    well, x^2-7x-8 factors to (x-8)(x+1) = 0 So the sides are (x-8) and (x+1) So what are your thoughts on this?
  90. math

    Glad you told me. Did you have a question?
  91. Calculus

    Exact answer: volume = ? ? (sec^2 x) dx from 0 to ?/3 = ? [ tanx ] from 0 to ?/3 , since the derivative of tanx = sec^2 x = ?( tan ?/3 - tan 0) = ?3 ? In your question, we have a case where the solution to find an approximate answer is more difficult than the actual solution ...
  92. Vectors

    When s = 0 , we get the point (2,9) when t=3, we get the point (0,8) Using your intersection point that you already found, find the lengths of the 3 line segments using the "distance between two points" formula. To find the area, use Heron's Formula, which says ...
  93. Math

    https://www.google.ca/search?q=Find+the+probability+that+you+throw+a+dart+and+land+in+the+region+labeled+%22G%22&rlz=1C5CHFA_enCA690CA690&tbm=isch&source=iu&ictx=1&fir=-mEy256_2S-OKM%253A%252COTpziutDtOkUGM%252C_&usg=__hp1tFrIfMKrhg0itf5IMc5zxeBE%3D&sa=X&ved=...
  94. Math

    Did you make your sketch? It should show an angle of 108° between XY and YZ by the cosine law: XZ^2 = 115^2 + 75^2 - 2(115)(75)cos 108° XZ = ..... or vector XY = 115(cos42, sin42) = (85.46165... , 76.95...) vector YZ = 75(cos-30 , sin -30) = (64.9519.. , -37.5) XZ = (...
  95. math

    It is C(52,5), trust us another approach: suppose you had to pick them in a specific order, then the number of ways would be 52x51x50x49x48 which is the same as 52! / 47! or P(52,5) But the order does not matter, as you said, so we have to divide by 5! the number of ...
  96. Math

    Here is how I do these: sin^-1 (.65) I know from CAST that the sine is positive in quadrants I and II so 2ndF sin .65 gave me .70758... That is my quad I angle, so ? - .70758 or 2.434 would be the quadrant II angle of course adding/subtracting 2? will yield other answers: my ...
  97. algebra

    Prob(boy from 7th grade) = 7/10 Prob(boy from 8th grade) = 2/4 = 1/2 Prob(2 boys) = (7/10)(1/2) = 7/20
  98. calculus2

    Let me know what you get, they probably want an "exact" answer.
  99. calculus2

    Notice that at the intersection of the two curves, x = ?/3 and we have symmetry, so we can take the area from 0 to ?/3, then double area = 2? (8cosx - sec^2 x) dx from 0 to ?/3 = 2[8sinx - tanx] from 0 to ?/3 = 2(8sin ?/3 - tan ?/3 - (8sin 0 - tan 0 ) = ...... your turn
  100. Algebra

    The simplest ratio of sides of a right-angled triangle is the 3:4:5 ratio so we have 9:x:y, clearly x = 12, and y = 15 check: 9^2 + 12^2 = 15^2 , YES
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