Thursday
September 1, 2016

Posts by Reiny

Total # Posts: 35,615

Math
The third angle of triangle RST is 180-38-75 = 67 which is one of the given angle of the second triangle. So both triangles have the same angles and the sides are proportional. The two triangles are similar, therefore one is a dilation of the other.
March 28, 2016

Pre calc aesthetic quadratic stuff
let the two numbers be x and y so we have: x+y = 9 --->y = 9-x and xy = 20 x(9-x) = 20 9x - x^2 - 20 = 0 the equation you want is: x^2 - 9x + 20 = 0 easily solved, it even factors nicely.
March 28, 2016

math
card > 2 AND < 7 must be 3,4,5, or 6 there are 16 in that group prob(of your event) = 16/52 = 4/13
March 28, 2016

math
don't know how detailed your "unit circle" is , but you should easily read off that sin30° = 1/2 cosπ = -1 sin 11π/6 = sin 330° = - sin30° = -1/2 cos 135 = -cos 45 = -√2/2
March 28, 2016

EASY Math
14000 = -2000t + 20000 2000t = 60000 carry on
March 28, 2016

Math please help
let the angle be x then its supplement is 180-x 180-x = 2x + 30 150 = 3x x = 50 the angle is 50°, the supplement is 130° check: Its supplement would be 130 is that 30 more than twice 50 ? YES!
March 28, 2016

Math
Good job
March 28, 2016

maths
number of rows --- x number of students in a row --- y Then the number of students = xy case1: 4 students added to each row --- y+4 rows is reduced by 2 ----- x-2 (x-2)(y+4) = xy case2: 4 student taken off each row --- y-4 number of rows is now --- x+3 (x+3)(y-4) = n so (x-2)(...
March 28, 2016

Maths
simplest way is using vectors. resultant vector = (4cos38,4sin38) + (5cos67,5sin67) = (3.152.., 2.4626..) + (1.9536..., 4.6025..) = (5.1056.., 7.065...) distance = √(5.1056..^2 + 7.065.^2) = appr 8.717 correct to 3 decimals bearing: tanØ = 7.065../5.1056.. Ø...
March 28, 2016

Math
What kind of cup? A coffee cup, a cup o' tea? There is such a thing as the "metric cup" where 1 cup = 250 ml In that case 1 cup would cost 31 cents 1 U.S. customary cup = appr 236.588 ml In that case 1 cup would cost $1.25 ÷ (1000/236.588) = $.295 or 30 ...
March 28, 2016

Maths
ratio of correct to wrong = 6 : 2 = 3 : 1 = 3x : x total questions = 4x given: 3x = 54 x = 18 so there were 4(18) or 72 questions percentage correct = 54/72 = .75 or 75% we could have seen that from the top correct = 3x, total = 4x percentage correct = 3x/4x = 3/4 = .75
March 28, 2016

Math
let the width be x m let the length be y m So we need 2 widths and 1 length given: xy= 448 y = 448/x 2x + y = 60 2x + 448/x = 60 times x 2x^2 + 448 = 60x x^2 - 30x + 224 = 0 (x-16)(x-14) = 0 x = 16 or x = 14 then y = 448/16 or y = 448/14 y = 28 or y = 32 The field could be 16 ...
March 28, 2016

Algebra
so you have the points: (-2,1), (0,5), and (4,-59) let the function be y = ax^2 + bx + c for (0,5) 5 = 0 + 0 + c -----> c = 5 so we could reduce our equation to y = ax^2 + bx + 5 for (-2,1) 1 = 4a - 2b + 5 4a - 2b = -4 2a - b = -2 *** for (4, -59) -59 = 16a + 4b + 5 16a + ...
March 28, 2016

Math
Sal Khan does an excellent job of this topic in this video. https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/cc-6-mad/v/mean-absolute-deviation He goes through two different cases
March 28, 2016

math
8 red 3 white 9 blue total = 20 at least one is white ---- exclude case of all non-white prob(that 3 of 19 are all non-white) = C(17,3) x C(3,0)/C(20,3) = 680/1140 = 34/57 prob(at least one white) = 1 - 34/57 = 23/57 one of each colour = C(8,1) x C(3,1) x C(9,1)/c(20,3) = 216/...
March 28, 2016

math
look at the first of the Related Questions below
March 28, 2016

math
prob(fail) = .2 prob(not fail) = .8 prob(exactly 2 of 10 will fail) = C(10,2) .2^2 .8^8 = appr .302 2 or more defective ---> exclude 0 not fail and 1 not fail = 1 - C(10,0) .8^0 .2^10 - C(10,1) (.8)( .2^9) = .... more than 5 = prob(exactly 6) + prob(exactly 7) + ... + prob(...
March 28, 2016

Algebra
just plug in ... a(15) = -4(15) + 1 = ...
March 27, 2016

Calculus Urgent
I see what you mean, the two curves appear to coincide form -1 to 1 http://www.wolframalpha.com/input/?i=y%3Dcos(pi*x%2F2),+y%3D1-x%5E2 Because of the symmetry, I looked closer from 0 to 1 and it shows that the parabolo lies above the cosine curve for that domain, and of ...
March 27, 2016

College Algebra 1
Again first look for a common factor in the constants which is -4 -36a^2-96ab-64b^2 = -4(9a^2 + 24ab + 16b^2) the 9a^2 and 16b^2 are both perfect squares, could we perhaps have (3a + 4b)^2 ? A quick mental expansion shows this is indeed the case, so -36a^2-96ab-64b^2 = -4(9a^2...
March 27, 2016

College Algebra 1
HCF of -36, -96, and -54 is -6 I see no same variable in all 3 terms -36a^2-96ab-54b^2 = -6(6a^2 + 16ab + 9b^2) the trinomial does not factor further over the rationals. Mentally expand to check the answer.
March 27, 2016

Math
A picture is worth a thousand words, (groan) Draw a vertical line and mark it 120 inches the centre must be 76 inches from the floor or 44 inches from the ceiling. Since the picture is 34 inches high and you want its centre, just add half of 34 or 17 inches to 76. So the top ...
March 27, 2016

math
Cannot read your last two posts.
March 27, 2016

math
so you want y = a csc (2/3)x where a is whatever your (−‡,−2]¾[2,‡) means well, y = csc (2x/3) looks like this: http://www.wolframalpha.com/input/?i=plot+y+%3D+csc+(2x%2F3) the vertical lines are asymptotes at x = 0, ±3&#...
March 27, 2016

Calculus
the graph of f(x) = x/(x-4) looks like this: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%2F(x+-+4)+for+0+to+10 the vertical line x=4 is the asymptote
March 27, 2016

Calculus
For f^-1(10), 10 = x^3 + x by quick inspection, x = 2 so f^-1(10) = 2 similarly for f-1(2), 2 = x^3 + x --> x=1 so f^-1(2) = 1
March 27, 2016

Pre calc 11
term(20)=186 ---> a+19d = 186 a = 186-19d sum(12) = 6(2a + 11d) = 186 2a + 11d = 31 2(186-19d) + 11d = 31 -27d = -341 d = 341/27 a = 186-19(341/27) = -1457/27 sum(40) = 20(-1467/27+ 39(341/27) = -16041/27 better check my arithmetic, did not expect such weird numbers
March 27, 2016

math
prob = C(8,3)xC(5,0)xC(2,0)/C(15,3) = 56/455 = 8/65 prob(both homeowners plus one of the others) = C(2,2) x (13,1)/C(15,3) = 13/455 = 1/35 one of each: C(8,1) x C(5,1) x C(2,1)/C(15,3) = 80/455 = 19/91
March 27, 2016

math
4 NDC 3 NPP 3 others total = 10 i) one of each party: C(4,1) x C(3,1) x C(3,1)/C(10,3) = 36/120 = 3/10 ii) C(3,2) x (7,1)/C(10,3) = 21/120 = 7/40 iii) follow my steps of ii)
March 27, 2016

Algebra
speed of raft ---- x km/h speed of boat ----12 km/h when the boat caught up with the raft, they both had gone 20 km time for raft = 20/x time for boat = 20/12 20/x - 20/12 = 5 hrs, 20 min = 16/3 times 12x 240 - 20x = 64x 240 = 84x x = 240/84 km/h = 20/7 km/h check" time ...
March 27, 2016

Calculus
.638 = 1(1/2)^(t/5730) log .638 = (t/5730)log .5 t/5730 = log .638/log .5 = .64837... t = appr 3715 years
March 27, 2016

maths
If y = x/2 - 7/2 and it passes through C and E which are the x and y intercepts respectively, the for C, let y = 0 0 = x/2 - 7/2 x/2 = 7/2 x = 7, so C is (7,0) Why all that extra stuff about parabolas etc ?
March 27, 2016

math
Yesterday, I gave you this solution, but for some reason you didn't like it: See Related Question #1 below. "Let the amount of old stuff drained be x gallons so you have 4-x gallons left of 25% solution .25(4-x) + x = .5(4) 1 - .25x + x = 2 .75x = 1 (3/4)x = 1 x = 4/3...
March 27, 2016

math
so have a diamond, which means there are 51 cards left, of which 13 are still spades Prob(spade) = 13/51
March 26, 2016

precal
Always proofread your post before sending it, to make sure it makes sense.
March 26, 2016

Calculus
You probably expected this to come out as S = c/x^2 + k/(d-x)^2 = c x^-2 + k(d-x)^-2 dS/dx = -2cx^-3 - 2k(d-x)^-3 = 0 for a min c/x^3 = k/(d-x)^3 but k = 9c c/x^3 = 9c/(d-x)^3 1/x^3 = 9/(d-x)^3 (d-x)^3 = 9x^3 d-x = (9^(1/3))x d = x( 9^(1/3) - 1) x = d/(9^(1/3) - 1)
March 26, 2016

Algebra
400/s + 160/s + 240/(s-20) = 11 ok, hint: multiply each term by s(s-20) to get a quadratic. Hint: it comes out to be a nice whole number
March 26, 2016

Algebra
I did this for you here http://www.jiskha.com/display.cgi?id=1458920959 hoping you would be able to find the equation yourself then Steve finished it for you here: http://www.jiskha.com/display.cgi?id=1458939085
March 26, 2016

math
tan(t)=1/tan (t) tan^2 t = 1 tan t = ± 1 t = π/4, 3π/4, 5π/4, and 7π/4 2sin(t)cos(t) + sin(t) -2cos(t)-1= 0 by grouping: sint(2cost + 1) - (2cost + 1) = 0 (2cost+1)(sint-1) = 0 cost = -1/2 or sint = 1 I will let you finish that one 2cos3x = 1 cos3x...
March 26, 2016

calculus2
amount = a (1/2)^(t/74) where t is in years so when t = 10 amount = a(.5)^(10/74) = .91058.. a so appr 91% will be left
March 26, 2016

Algebra 1
corresponding function: y = x^2 - 9 which is a parabola opening upwards, centre at (0,-9) and x-intercepts of ±3 I assume you know how to graph a curve like this. solution : x = ±3
March 26, 2016

contempory math
I noticed the Fibonacci Number property, that is, adding the last two numbers produces the next number. note: 3+4=7 4+7=11 11+7=18 etc
March 26, 2016

math
Let the amount of old stuff drained by x gallons so you have 4-x gallons left of 25% solution .25(4-x) + x = .5(4) 1 - .25x + x = 2 .75x = 1 (3/4)x = 1 x = 4/3 so drain 4/3 gallon of the current solution, then top it up with pure antifreeze
March 26, 2016

math
easiest algorithm for area of any polygon: list the points in a column going counterclockwise, repeat the first point listed: area = (1/2)(downproducts - upproducts) 8 11 2 3 8 3 11 7 8 11 area = (1/2)(24+6+56+121 - (22+24+33+56)) = 36
March 26, 2016

math
could be AB or BA , but the order in which they are sold shouldn't matter, so prob(AB) = (1/9)(1/3) = 1/27
March 26, 2016

math
Prob(defect) = .2 prob(not defective = .8 prob(exactly 2 of 10 are defective_ = C(10,2) (.2)^2 (.8)^8 = .... 2. Use the "back-door" approach if 2 or more are defective, then we can't have: none defective or only 1 defective. = 1 - C(10,0) (.2)^0 (.8)^10 - C(10,1...
March 26, 2016

maths
what is 55-40 ? what is 15/40 ?
March 26, 2016

mathematics-cubic equation
They probably expect you to use factoring, so try factors of 8 so x = ±1, ± 2 , ± 4 would be values to start with, Sure enough on the third try, x = 2 works Thus x-2 is a factor and by synthetic division, 2x^3-11x^2+18x-8=0 (x-2)(2x^2 -7x + 4) = 0 so one ...
March 26, 2016

Finance
In order for the ordinary formulas to work, the interest period must match the payment period. In this question, the payment period is annually, but the interest period is semiannually. So we must first find what annual interest rate is equivalent to 4% per annum compounded ...
March 25, 2016

Pre-Calc
checking: from f(2) = 6 6 = a b^2 from f(0) = 54 54 = a b^0 so a = 54 ----> you had that back in 6 = 54 b^2 b^2 = 6/54 = 1/9 b = 1/3 ---> you had b = 33, which is close but not quite accurate enough then f(x) = 54(1/3)^x f(-3) = 54(1/3)^-3 = 54(3)^3 = 54(27) = 1458 ---&...
March 25, 2016

Polynomials
No idea what you are talking about.
March 25, 2016

Probability
prob(3 boys) = (1/2)^3 = 1/8 prob(at least 1 girl) = 1 - prob(all boys) = 1 - 1/8 = 7/8
March 25, 2016

Algebra
Steve did this yesterday http://www.jiskha.com/display.cgi?id=1458866531
March 25, 2016

math
done here http://www.jiskha.com/display.cgi?id=1458950977
March 25, 2016

math
What is C(43,9) ?
March 25, 2016

Algebra
amount at 6% --- x amount at 2% ---1900-x solve for x .06x + .02(1900-x) = 94
March 25, 2016

Calculus
Using common sense: for any value xy, where x + y is a constant, the largest value xy is obtained when xy is a perfect square, So the largest value of xy+xz+zy is obtained when all three are the same value but 10 cannot be split into 3 equal parts so the best we can do is ...
March 25, 2016

Algebra
First part of trip: distance = 400 km speed = x km/h time = d/r = 400/x hrs return trip 2/5 of 400 at x km/h, then 3/5 of 400 at x-20 km/h how far did the train go at x km/h ? how far did the train go at x-20 km/h ? What is the time for the first part of this return trip? What...
March 25, 2016

Algebra
Most of these distance-rate-time problems are basically the same. I did the last one for you, give this one fair try, and let me know at which point you get stuck. Hint: let the "certain" speed be x km/h then the slower speed is x-20 km/h
March 25, 2016

Algebra
I will assume that the speed of the raft is the speed of the current. Let the speed of the current be x km/h speed of boat against current = 12-x km/h time with boat = 25/(12-x) time on raft = 25/x 25/x - 25(12-x) = 10 divide by 5 5/x - 5/(12-x) = 2 multiply each term by x(12-...
March 25, 2016

Trigonometry
sin^2 Ø + cosØ -2 = 0 1-cos^2 Ø + cosØ - 2 = 0 cos^2 Ø - cosØ + 1 = 0 cosØ = (1 ± √-3)/2 which is not real you are correct, there is no solution.
March 25, 2016

Math
Would have been easier to type: 27.36 + 8.09 + 65.073 now just add them
March 25, 2016

Math
Not enough information. You will need an angle or the third side.
March 25, 2016

Probability
Since the order in which the numbers are chosen does not matter, it will be C(54,6) = 25,827,165
March 25, 2016

math
let the unit digit be x and the tens digit be y so x+y = 9 ---> y = 9-x the number is 10y+x the number reversed is 10x + y 3(10y+x) = 8(10x + y) 30y + 3x = 80x + 8y 22y = 77x 2y = 7x 2(9-x) = 7x 18 - 2x = 7x 18=9x x=2 y=7 the number is 72 check: number is 72 reverse is 27 ...
March 25, 2016

Probability
correct
March 25, 2016

Math
time walking = 4/8 hrs = 1/2 hr time jogging = 6/12 hrs = 1/2 hr total time = 1 hr avg speed = 10 km/1 hr = 10 km/h
March 24, 2016

Maths
suppose she had an original amount of x after giving to her brother she has 3x/4 left of that she spends (1/3)(3x/4) and (1/6)(3x/4) or (1/4)x + (1/8)x total amount spent = x/4 + x/4 + x/8 = (5/8)x so she has 3/8 of her money left, which she donated. check: suppose she has 24 ...
March 24, 2016

Math
You probably forgot to mention that those equal parts are sectors of the circle (like slices of pizza) each part would have a central angle of (360/9)° , so ...... carry on
March 24, 2016

geometry
area of one triangle = 37.2/5 = 7.44 cm area = (1/2)base x height 7.44 = (1/2)(base)(3.2) base = 2(7.44)/3.2) = ...
March 24, 2016

Precalculus
period = 2π/k k = 2π/44 = π/22 d = -88 sin ( (π/22)(t+11) ) must be a magic coiled spring, it never seems to lose its bounce.
March 24, 2016

calc. 1
let the width of the poster be x cm let the length of the poster be y cm then the width of the print area = x-10 and the length of the print area = y - 2 given: xy = 625 y = 625/x area of print = A = (x-10)(y-2) = xy - 2x - 10y + 20 = x(625/x) - 2x - 6250/x + 20 = 645 - 2x - ...
March 24, 2016

prealgebra or algebra1
Easiest way: since the lines are parallel, they would differ only in the constant so the equation is 4x + y = c plug in the given point to find c and you are done
March 24, 2016

Trigonometry
b) correct, the period would be 2π/60π = 1/30 c) when t = 3 d = (1/12)sin (180π) = 0 d) sin(60πt) = 0 when t = 0 , 1/30, 1/15 ... so the first positive value is 1/30
March 24, 2016

math
really ?
March 24, 2016

Geometry
The wording of this question is not clear It does not say if the sides of 15 and 18 are the parallel sides, or if they are adjacent sides. I must conclude that they are adjacent sides or else the height between them would be constant area of ||gram is base x height so 15(9) = ...
March 24, 2016

Check Mathh Answers!!
I agree with all you answers except #4 #4 , the outlier is 1.5
March 24, 2016

Math
I agree with what you have so far, other than skipping the integral sign and the dx from the last term. You seem to have the concept however. ∫e^(3x) sin(2x) dx = (-1/2)e^(3x)cos(2x) - ∫(-1/2)(3e^(3x))(cos(2x) dx = (-1/2)e^(3x)cos(2x) + (3/2)∫ e^(3x) cos(2x) ...
March 24, 2016

trigonometry
2sin^2 A + 5cosA = 4 2(1 - cos^2 A) + 5cosA - 4 = 0 2cos^2 A - 5cosA + 2 = 0 (2cosA -1)(cosA - 2) = 0 cosA = 1/2 or cosA = -2, the latter is not possible, so cosA = 1/2
March 23, 2016

Algebra, functions
to have one root, (actually two equal roots) b^2 - 4ac = 0 k^2 - 4(1)(5) = 0 k^2 = 20 k = ± √20 = ± 2√5 check: x^2 + 2√5x + 5 = (x + √5)^2 x^2 - 2√5x + 5) = (x - √5)^2
March 23, 2016

math
change in volume = 15x20x3 cm^2 which must have been caused by the volume of the rock.
March 23, 2016

algebra
your notation clearly did not show up as you intended. I will guess you meant: (b+7)/(b+4) = c/9 c = 9(b+7)/(b+4) I have this very old fashioned computer language called BASIC. I ran a stupid little program for b = -5000 to b = 5000 and it found the following pairs (b,c) >...
March 23, 2016

Geometry
Make a side-view of the pyramid, and drop a perpendicular. let the side of the base be 2x, (that way I don't have fractions in my variable) in the right-angled triangle tan 52° = 147/x x = 147/tan52 = ... then base side = 2x = ....
March 23, 2016

Calculus
You don't describe the diagram, but I am familiar with this type of question. Assuming there is a common width between the two fields let the width be x ft let the length of the combined field be y so 3x + 2y = 1200 y = 600 - (3/2)x area = xy = x(600 - (3/2)x) = 600x - (3/...
March 23, 2016

Math
Ruth's speed --- x km/h Tom's speed --- x+10 km/h in two hour: Ruth went 2x km Tom went 2(x+10) km solve for x 2x + 2(x+10) = 308
March 23, 2016

trig
No, it isn't the simplification of the expression is -1/sinx, as you can see from my steps however, if -1/f(x) = -1/sinx then f(x) = sinx
March 23, 2016

trig
I will "simplify and write the trigonometric expression in terms of sine and cosine" the part "=-1/f(x)=f(x)=____________ " makes little sense to me cot(-x)cos(-x)+sin(-x) = (cos(-x))/sin(-x))(cos(-x) + sin(-x) = (cosx/-sinx)(cosx) - sinx = - cos^2 x/sinx...
March 23, 2016

math
I certainly would not want to support laziness, so I will not answer you question. Why would you possible need papers to find 5/6 times 12 I did that in my head in about 3 seconds
March 23, 2016

Bus. Math
What is a rate of 9-15/18? Did you mean consecutive discounts of 9%, 15%, and 18% ? if so final percentage = .91(.85)(.82) = .63427 or 63.427% of the original price looks like b) is correct and you are right.
March 23, 2016

Math
A meaningless question. The value of c can be any real number to have a quadratic expression. "TheKnowItAll" found the value of c so that the expression becomes a perfect square, but that was not the question.
March 23, 2016

math !
surface area = 2lw + 2lh + 2wh = NOT 1134.375 , I get 731.5
March 23, 2016

mathematics-slope of tangent
differentiate implicitly, x^2 + xy + y^2 = 4 2x + x y' + y + 2y y' = 0 y' (x + 2y) = -2x - y y' = (-2x-y)/(x+2y) for (2,-2) y' = (-4 + 2)/(2 -4) = -2/-2 = 1
March 23, 2016

Algebra II
q = k(1/m^2)(rx) plug in the given values 2.5 = k(1/16)(8) solve for k
March 23, 2016

Algebra II
Did you find the equation for the flight path of the plane ? Did you find the equation of the parabola? Did you solve the two equations and got a real answer? If you have a solution, the the plane intersects the closed airspace. If you have no solution ...... etc
March 23, 2016

MATH
different shapes: 1 1 12 1 2 6 1 3 4 2 2 3 number of different bases for each one: 1 1 12 --->1 1 12, 1 12, 1 ----- 2 of them 1 2 6 ---> 1 2 6, 1 6, 2, 2 6 1 --- 3 of them 1 3 4 ---> 1 3 4, 1 4 3, 3 4 1 --- 3 of them 2 2 3 ---> 2 2 3, 2 3 2 ----- 2 of them 10 ...
March 23, 2016

Math
good job, they were all correct
March 23, 2016

division and remainder...error ws from my teacher not me
Sum(1) = 1 = 1mod5 sum(2) = 1 + 2^2 = 5 = 0 mod5 sum(3) = 5 + 3^3 = 32 = 2 mod5 sum(4) = 32 + 4^4 = 288 = 3 mod5 To divide by 5 all we need to do is look at the last digit. If the digit is form 0 to 4, then that digit is the remainder when dividing by 5 If the digit is from 5 ...
March 23, 2016

maths
for the additions, the common denominator is 60 grind out the sum of the inner bracket then multiply that by 5/8, simplify if needed finally multiply that by 8 let me know what you got, so I can check it for you btw, are you sure that -4/5 is not supposed to be +4/5 ?? It ...
March 23, 2016

geometry
None of the answers given are correct by the cosine law: f^2 = 8^2 + 13^2 - 2(8)(13)cos72° = 168.724... f = 12.989398... by sine law: sinG/8 = sin72/12.989... sinG = .58574... G = 35.86° correct to 2 decimals With modern calculators, there is no reason to round off ...
March 23, 2016

@ Steve - trigonometry
Steve, I worked on this for a while this morning, and I got that far as well. I also noticed that sinA = .618033989.. which is the decimal part of the golden ratio (1+√5)/2, ... interesting from xsinA= ycosA I had y/x = sinA/cosA = tanA from xsin^3A=y I had y/x = sin^3 A...
March 23, 2016

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