Wednesday
July 27, 2016

Posts by Reiny

Total # Posts: 35,358

Logarithm
I answered this further up the listing
April 9, 2016

Logarithm
Ln2+Lnx=1 ln(2x) = 1 by definition of ln e^1 = 2x x = e/2
April 9, 2016

Math: Parametric Equations
does this help? https://www.wolframalpha.com/input/?i=plot+x+%3D++cos(4t),+y+%3D+sin(6t)
April 9, 2016

MAth
let n be the number of half-years i = .072/2 = .036 73,000(1.036)^n = 100,000 1.036^n = 1.36986... log both sides and use log rules n log 1.036 = log 1.36986.. n = 8.898.. half-years = appr 4.45 years
April 9, 2016

algebra
number of whites --- x number of yellows --- 18-x 995x + 1250(18-x) = 22245 (I changed the $'s to cents) solve for x, has to come out as a whole number
April 9, 2016

Canadian finances
I have placed *** behind my choices. If you see no *** or no comment, I agree with your answer. which of the following services do banks not provide? a. lines of credit b. health insurance *** c. currency exchange d. none of above (THIS ONE) which institutions does not offer ...
April 9, 2016

Math
x(x+5) = 350 x^2 + 5x - 350 = 0 too bad it doesn't factor. By the formula x = (-5 + √1425)/2 = appr 16.37 ft take over remember perimeter = 2width + 2length
April 9, 2016

math
i = .038/365 n= 365(4) = 1460 principal = 3500 amount = 3500( 1 + .038/365)^1460 = 4074.53 So interest earned = 4074/53-3500 = 574.53 which is choice a)
April 9, 2016

Geometry
width ---- x length ---- 2x+5 x(2x+5) = 1375 2x^2 + 5x - 1375 = 0 solve the quadratic hint: it factors, but it may be just as fast to use the formula
April 9, 2016

Precalculus
How about this way: Since AC supports a 45 degree angle at the circle, AC must support a 90 degree angle at the centre. let the radius be r r^2 + r^2 = 8^2 2r^2 = 64 r^2 = 32 Area = pi r^2 = 32 pi or appr 100.53 Notice just as Damon pointed out, we don't even need to know ...
April 9, 2016

karki
let the AP be a, a+d, a+2d so 3a + 3d = 45 a+d = 15 ---> d = 15-a and a(a+d)(a+2d)=300 a(a^2 + 3ad + 2d^2) = 300 a(a^2 + 3a(15-a) + 2(15-a)^2) = 300 a(a^2 + 45a - 3a^2 + 450 - 60a + 2a^2) = 300 a(- 15a + 450) = 300 -15a^2 + 450a - 300 = 0 a^2 - 30a + 20 = 0 a = (30 ±...
April 9, 2016

Trigonometrt
sin ( 810- theta) I am sure you meant: sin(180 - θ) which is sinθ cot(θ - 360) .... recall that tan(-x) = -tanx and tan(360-x) = -tanx and of course the cot behaves just like the tan cot(θ-360) = -cot(360-θ) = -(-cotθ) = cotθ cos(-180 - θ...
April 9, 2016

Probability (Math)
You are correct
April 9, 2016

math
Since Mathematics is a precise language, it requires precise and correct English to express a problem to be solved. Please re-type your problem using correct and proper English so that it makes sense to me. "Texting" English doesn't cut it.
April 9, 2016

gemoetry
I don't see any diagram but by a simple trig ratio, we have cos 75.5 = 20/L L = 20/cos75.5 = appr 79.9 ft Wow, a ladder to go up about 8 stories high???
April 9, 2016

Math
If x = 2√2 and x = -2√2 then two of the factors are (x - 2√2) and (x + 2√2) or (x^2 - 8) must be a factor of your polynomial. Do a long algebraic division to get x^4+4x^3-4x^2-32x-32 = (x^2 - 8)(x^2 - 4x + 4) we can get more roots from x^2 - 4x + 4 = 0...
April 9, 2016

math
Just replace the units with their equivalents. 24 miles / 1 hour = 24*1760 yards / 60 minutes = (42240/60) yards/min = 704 yards/min I agree with your answer
April 9, 2016

MATH
I agree with your equation and I get $4011.25. Beyond that, I can't help you since I don't know what you mean by "syntax" error.
April 9, 2016

I NEED HELP!!!
arrange it in more standard form 2x^2 + 6x - 5 = 0 use the formula: x = (-6 ± √76)/4 = (-6 ± 2√19)/4 = (-3 ± √19)/2
April 9, 2016

Algebra
you are basically looking for the vertex of this downwards opening parabola the t of the vertex is -b/2a = -64/-32 = 2 seconds it will take 2 seconds to reach the maximum height when t = 2 h = -16(4) + 64(2) + 9 = 73 ft
April 8, 2016

Algebra
the real parts of the left side must match the real parts of the right side, and the imaginary parts .... your steps are correct, so x = -4, y = 1
April 8, 2016

Algebra
A(t) = 3- 2t^2 + 4^t A(2) - A(1) = 3 - 2(4) + 4(4) - (3 - 2(1) + 4(1)) = 3 - 8 + 16 - 3 + 2 - 4 = 6 you are correct
April 8, 2016

Math
let y = (3x - 7)/(x + 1) for the inverse , exchange the x and y's x = (3y-7)/(y+1) now solve this for y ... xy + x = 3y - 7 xy - 3y = -x - 7 y(x-3) = -x - 7 y = (-x - 7)/(x - 3) = (x+7)/(3-x) f^-1 (x) = (x+7)/(3-x) check: f(1) = (3-7)/(2 = -2 f^-1 (-2) = (-2+7)/(3-(-2)) = ...
April 8, 2016

MATH
Your formula is a creative variation of the real one amount = 60000( (1 + .07/2)^50 - 1)/(.07/2) = 60000( 1.035^50 - 1)/.035 =
April 8, 2016

Math
8% per annum compounded semi-annually ---> 4% every half year so i = .04 number of half-years in 18 years = 36 amount = 20,000( 1.04^36), as Bob had = $82,078.65
April 8, 2016

math
number of small trucks --- x number of vans ----- 2x number of large trucks = 280 - 3x 30,000x + 25,000(2x) + 40,000(280-3x) = 8,000,000 divide by 5000 6x + 10x + 8(280-x) = 1600 carry on
April 8, 2016

Algebra 1-HELP!
(6^3/8)^2/5 = 6^((3/8)(2/5)) = 6^(3/20)
April 8, 2016

math
original fraction : x/y new fraction = .9x/(.5y) = 9x/5y (9x/5y) / (x/y) = 9x/5y * y/x = 9/5 = 1.8 so it increased by 80% e.g suppose we had 100/200 or 1/2 new fraction = 90/100 or 9/10 new ratio = (9/10) / (1/2) = 9/5
April 8, 2016

math
increases expressed as a single increase = 1.2(1.15) = 1.38 it increased by 38%
April 8, 2016

math
correct
April 8, 2016

math
Distance walking --- x distance by cab ---- 31-x time walking = x/4 time by cab = (31-x)/50 Your "formula", we call it an equation x/4 + (31-x)/50 = 2 solve for x, plug x into 31-x
April 8, 2016

geometry
The radius of the whole circle = 2πr = 10π Now, what fraction of that circumference is a 45 degree sector?
April 8, 2016

Math w/business apps
solve for x x(1 + .06/12)^12 = 20000
April 8, 2016

Algebra 1-HELP!
Did you first look for the HCF ? I see: 8(4a^2 + 12a^2 + 9) hint#2: Did you notice the perfect squares at front and end of the trinomial?
April 8, 2016

Algebra 1
hint: if there are x cans and you have 800 cans and bottles, wouldn't the number of bottles be 800-x ?
April 8, 2016

algebra
As Bob noted you don't have an equation. you probably have the expression (x - 1/x)/(1 + 1/x) and are asked to simplify it. Hint: how about multiplying the fraction by x/x
April 8, 2016

math
Why would "guess" for math problems Surely you could have tried to work them out #6 is trivial #8-12 deal with the rules of multiplying and dividing powers When multiplying powers with the same base, keep the base and add the exponents e.g. x^4 * x^8 = x^12 When ...
April 8, 2016

math {sequences}please help
#3 is geometric with a common ratio of 1/3 your other answers are correct
April 8, 2016

GEOMETRIC SEQUENCES
No Think of how you would obtain the next term you could take .18 of the previous term and subtract or just take .82 of it so the sequence is: 20000 , 20000(.82), 20000(.82)^2 , .... so r = .82 I am sure you can now answer the question
April 8, 2016

math
No interest ? Give it to me and after 35 years, my estate will pay you back 1000(12)(35) or $ 420,000
April 8, 2016

math
let the tens digit be x then the unit digit is 3x so the number is 10x + 3x = 13x the number reversed is 10(3x) + x = 31x 31x + 13x = 88 44x = 88 x = 2 3x = 6 The original number was 26 check: is 26 + 62 = 88 ? YES my answer is correct
April 8, 2016

linear equation in one variables
let unit digit be x then tens digit is 9-x the number is : 10(9-x) + x = 90 - 9x the number reversed is 10x + 9-x = 9x + 9 9x+9 - (90-9x) = 27 18x - 81 = 27 18x = 108 x = 6 unit digit is 6 tens digit is 3 The number is 36
April 8, 2016

elementary quantitative methos
This is just finding the P of a PV. Same formula, same story.
April 8, 2016

elementary quantitative methos
beginning of 2nd year ---> end of first year. I will assume the 12th payment has been made outstanding balance = 230000(1.01625)^12 - 3817.23( 1.01625^12 - 1)/.01625 = ....
April 8, 2016

elementary quantitative methos
subtract 100,000 from 240,000, that is your PV i = .195/12 = n = 240 P = ? straight formula application ( I got 3817.23 )
April 8, 2016

elementary quantitative methos
Use the PV formula I showed you in your previous post
April 8, 2016

elementary quantitative methos
i = .085/4 = .02125 n = 20 amount = A = 30000 payment = P = ? You must memorize the formulas A = P( (1+i)^n - 1)/i and PV = P (1 - (1+i)^-n )/i, where PV is the present value just sub in all your data and solve for the missing variable. 30000 = P( 1.02125^20 - 1).02125 30000...
April 8, 2016

Math
number of stickers ---- x number of ballons --- 6x bubbles ----- (1/3)(6x) = 2x x + 6x + 2x = 135 solve for x
April 7, 2016

Math
I assume you mean by just guessing. he must get 8 right, or 9 right or 10 right = C(10,8)(1/2)^8 (1/2)^2 + C(10,9)(1/2)^9(1/2) + C(10,10) (1/2)^10 = (1/2)^10 ( 45 + 9 + 1) = 55(1/2)^10 = 55/1024 not good, better study
April 7, 2016

Math
let the side of square ABCD be x then area = x^2 area of square EFGH = 2x^2 side of square EFGH = √2 x EF = √2 x AC^2 = x^2 + x^2 = 2x^2 AC = √2 x AB/AC = x/√2x = 1/√2 AB/EF = x/√2x = 1/√2 thus AB/AC = AB/EF
April 7, 2016

Math
original price ----- x dollars .85(1.08)x = 688.50 solve for x
April 7, 2016

Math
In a refection over the x-axis, the x coordinate would stay the same, but the y would turn into its opposite that is, (x,y) ---> (x, -y) A(2,-5) ---> A'(2,5) find the choice that matches this
April 7, 2016

pre ap math
If it is lauched from a height of 48 ft, then the equation should be h = -16t^2+32t+48 I will assume a typo you want h = 0 (at ground level h=0) 0 = -16t^2+32t+48 t^2-2t-3 = 0 It factors, (t-3)(t+1) = 0 t = 3 or t = -1, rejecting the negative time it took 3 seconds
April 7, 2016

linear equations in one variable
Let the number of ₹5 coins be x then the number of ₹2 = 3x and the number of ₹1 = 160 - x - 3x = 160 - 4x Now for the value: 5x + 2(3x) + 1(160 - 4x) = 300 5x + 6x + 160 - 4x = 300 7x = 140 x = 20 You have 20 ₹5 coins 60 of the ₹2 coins and 80 of ...
April 7, 2016

math probability
The prob that you get a 7 when rolling two dice = 1/6 so when two friends roll , (the same result as you rolling twice) prob(2 7's ) = (1/6)(1/6) = 1/36
April 7, 2016

math
area of trap = (1/2)(sum of parallel sides)(distance between them) (1/2(a + 12)(6) , where a is the other parallel side. (1/2(a + 12)(6) = 48 3(a+12) = 48 3a + 36 = 48 3a = 12 a = 4
April 7, 2016

math
Am I looking at 3 equations? separate them with commas. what is 3y+x-×=10-x ? is x-× a power like x^-x ??
April 7, 2016

Precal
Don't you have a calculator? make sure you catch the double negative in the last term since cos 135 is negative
April 7, 2016

Math-soh cah toa
make a sketch. label the ends of the bridge A and B make angle A = 41° and angle B = 48°. label the point on the river P and Q on AB so that PQ is at right angles to AB. Let PQ = h let QB = x , the AQ = 140-x tan41 = h/(140-x) h = (140-x)tan41 tan48 = h/x h = xtan48 So...
April 7, 2016

Math
I will do one of the components, you do the other , then subtract them a(x) = 3x - 7 and b(x) = 2 - x^3 a(b(3)) = a(2-3^3) = a(-25) = 3(25) - 7 = 68
April 7, 2016

Math
just follow the definition: f(a,b) = 2a - 3b^2 + 7 f(b,3) = 2b - 3(3)^2 + 7 = 90 2b - 27 + 7 = 90 2b = 110 b = 55
April 7, 2016

Math
y = 5x-12 inverse: x = 5y-12 5y = 12-x y = (12-x)/5 f^-1 (x) = (12-x)/5 f(x+1) = 5(x+1) - 12 = 5x - 7 5x-7 = (12-x)/5 25x - 35 = 12 - x 26x = 47 x = 47/26 check my arithmetic
April 7, 2016

Math
We are told : a#b=ab-a-b+1 so x#7 = 7x - x - 7 +1 = 42 6x = 48 x = 8
April 7, 2016

Math
x^2 + 12x = 73 let's complete the square, the easiest way to solve this particular one x^2 + 12x + 36 = 73+36 (x + 6)^2 = 109 x + 6 = ± √109 x = -6 ± √109 the positive one looks like √109 - 6 so a = 1, b = -6 a+b = -5
April 7, 2016

Math
What part of my solution I gave you here did you not like ? http://www.jiskha.com/display.cgi?id=1459995714
April 7, 2016

Geometry
did you notice that you are given two angles in each of the triangles ? Did you notice that their sum is 180 degrees? So they are similar, thus the corresponding sides are proportional. What are we supposed to find ?
April 7, 2016

Algebra II
Show Thomas a simplified example of why his idea is wrong 3^2 + 4^2 = 5^2 ---- true then 3 + 4 = 5 ????? If you want to take the square root, you have to take it of the whole side, not the individual terms
April 7, 2016

Calculus
f'(-4) = 9 f'(0) = 6 f'(x) = 3ax^2 + 2cx f'(-4) = 48a - 8c = 9 f'(0) = 0 + 0 = 6 Oh, oh, something fishy here. Check your typing or check the question
April 7, 2016

Calculus
f(x) is increasing if f'(x) is positive so (x−8)^7(x−1)^4(x+19)^8 > 0 we know that (x−1)^4(x+19)^8 is always positive since we have even exponents. So all we have to do is look at (x-8)^7 > 0 if x > 8 then (x-8)^7 > 0 if x < 8 it is ...
April 7, 2016

Calculus
f(x) = √(36-x^2) = (36-x^2)^(1/2) f ' (x) = (1/2)(36-x^2)^(-1/2) (-2x) = 0 for a max/min thus x = 0 , f(0) = 6 but f(1) = √(36-1) = √35 which is < 6 f(6) = √0 = 0 So the absolute minimum is 0
April 7, 2016

math
in a), b), and d) the first points don't work leaving c) in c) the 2nd point does not work so none of triples have all 3 correct
April 7, 2016

math
the way you typed according to BEDMAS (1/15)(6+x)=(1/6)(x+3) multiply both sides by 30 2(6+x) = 5(x+3) now it is easy, carry on What Bob meant was: did you mean, 1/(15(6+x)) =1/(6(x+3)) ? then we have an entirely different ballgame
April 7, 2016

math
All of them are NOT a solution
April 7, 2016

check this - maths
I must have made some kind of error in this big mess. I can't reconcile the fact that k = 6 will produce the 45 degree angle, but both of our solutions somehow showed that k = 2 I will look at it again later on today
April 7, 2016

maths
x^2 + xy - Ky^2=0 To have this equation represented by two straight lines, we must have it in a factored form such as (x + ay)(x - by) = 0 so that a+b = 1 and ab=-k e.g. if we had x^2 + xy - 6y^2 = 0 (x+3y)(x-2y) = 0 our two lines would be x+3y = 0 or x-2y = 0 slope of first...
April 7, 2016

Algebra
Winner of the most nonsensical question of the day.
April 6, 2016

Math
amount = 1500 + 1500(1.05^4 - 1)/.05 = 7965.19
April 6, 2016

Math
x^2 - 5x - 4 < 10 x^2 - 5x - 14 < 0 (x-2)(x+7) < 0 if y = (x-2)(x+7) we have a parabola opening upwards with x-intercepts of 2 and -7 the parabola would be below the x-axis, that is y < 0 , for -7 < x < 2
April 6, 2016

Math
the maximum area is obtained when your rectangle is a square. so let the side be s 4s = 24 s = 6 area = 36
April 6, 2016

Math
again, just like in your last post, just do it m/n@p/q = (m)(p)(q/n) 7/69@23/24$ , other than the confusing $ = 7(23)(24/69) = 56
April 6, 2016

Math
What's wrong with just plugging in the numbers and adding the fractions?
April 6, 2016

math
the last one looks just like http://www.jiskha.com/display.cgi?id=1459986016 but you changed the first term so the answer is not 2779 like in your previous question for the bagel question, which I did for you here http://www.jiskha.com/display.cgi?id=1459985491 how did you get...
April 6, 2016

Math
A(2) = 3 - 2(2)^2 - 4^2 = 3 - 8 - 16 = -21 find A(1) the same way, then subtract them
April 6, 2016

Geometry
Follow my steps in your previous post http://www.jiskha.com/display.cgi?id=1459994336
April 6, 2016

Trig
let the length of the chord be 2x ft Drop a perpendicular from the central vertex to the chord then sin 12.5 = x/30 x = 30sin12.5 2x = 60sin12.5 = 12.9864 or by cosine law: let the length of the chord be c c^2 = 30^2 + 30^2 - 2(30)(30)cos25 = 168.64598.. c = 12.9864 , same as ...
April 6, 2016

Geometry
let the width of the uniform border be x ft new width = 10+2x new length = 15 + 2x area of whole thing = (10+2x)(15+2x) (10+2x)(15+2x) - 150 = 100 150 + 50x + 4x^2 - 15 - 100 = 0 4x^2 + 50x - 100 = 0 2x^2 + 25x - 50 = 0 doesn't factor, so use the formula x = (-25 ±...
April 6, 2016

Math
let number of boys be 5x let numbe of girls be 3x after change: boys --- 5x+1 girls --- 3x+3 (5x+1)/(3x+3) = 4/3 15x + 3 = 12x + 12 3x = 9 x = 3 new class : boys = 16 girls = 12 total = 28
April 6, 2016

math
-3/4-(3/-8) = -3/4 + 3/8 = -6/8 + 3/8 = -3/8
April 6, 2016

correction - Math
scrap the 7,5,1,1 combination, they don't add up to 12 also scrap the 7,1,1,1,1, there should only be 4 digits.
April 6, 2016

Math
add = odd ?? notice that 12 = 7+5+1+1 or 12= 3+5+3+1 12 = 7+3+1+1 12 = 9+1+1+1 see if you can find any others. now each of my choices can be arranged in different orders 7,5,1,1 ---> yields 4!/2! or 12 of them 3,5,3,1, yields 4!/2! = 12 of them 7,1,1,1,1 etc one of them is ...
April 6, 2016

Geometry
Algebraic way: original width = x original length = 2x+3 x(2x+3) = 434 2x^2 + 3x - 434 = 0 (x - 14)(2x + 31) = 0 x = 14 or x = -31/2 , which I will reject original width is 14 ft original length is 31 ft new width = 18 new length = 35
April 6, 2016

Algebra
notice for each increase of 2 units of tem, the level drops 10 rate of change = -10/2 ft/h = -5 ft/hr
April 6, 2016

Algebra
between which readings ?
April 6, 2016

Geometry
ok, ok I stand corrected, there is a way, we have an angle. The apothem is the distance from the centre to the midpoint of a side Let's look at one of the triangles of the hexagon. It has a central angle of 60 so in a right-angled triangle formed by the apothem and half ...
April 6, 2016

Geometry
So, I guess we can't find the area, since we need the side
April 6, 2016

Geometry
Area = 1/2 x perimeter x apothem = 1/2 (6s)(6√3) once you tell me what the side (s) of the hexagon is, we an finish the question
April 6, 2016

Algebra
confusing wording Anyway, for y = mx + b m is the slope, or the rate of change the greater the value of m, the greater the rate of change.
April 6, 2016

math
looks like an AS with a = 4.5 and d= .5 term(5550) = a + 5549d = 4.5 + 5549(.5) = ....
April 6, 2016

math
2c + 4b = 600 2c + 7b = 825 subtract them: 3b = 225 b = 75 sub b = 75 back into the firs equation and solve for c let me know what you get.
April 6, 2016

Precal
We don't "work this out" I believe this is an identity, so we have to prove LeftSide = RightSide If it is an identiy, if we attempt to "solve" it, we end up 0=0 LS = cot^3 x+ cotx = cotx(cot^2 x + 1) = (cosx/sinx)((cos^2 x/sin^2 x + 1) = (cosx/sinx)(cos...
April 6, 2016

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