Thursday
August 21, 2014

Posts by Reiny


Total # Posts: 26,966

algebra
Steve is right, go with x-8 ≥ 20
February 21, 2014

algebra
After trying to make sense of your garbled English, I would pick x-8 > 20
February 21, 2014

algebra
Visualize the candy cane made in the form of a paper cylinder. Cut the cylinder open, you will see that the "ribbon" around the candy cane or cylinder consists of 4 diagonals for 4 different rectangles. the height of each of those rectangles is 20/4 or 5 cm and the ...
February 21, 2014

math help
poorly written up you lost the ratio notation and lack the equal sign correct presentation: 18 : 0.6 = 180 : 6 = 30 : 1
February 20, 2014

Math
I suspect you mean (x+1)/(x-2) = 3/6 confirm before I proceed
February 20, 2014

Algebra
the first one is already factored, so how come you are stuck on it ? 2nd: get the equation = 0 then it factors quite easily 4a^2 - 11a + 6 = 0 and 9r^r - 30r + 21 = -4 have you not been taught some kind of a method to factor these kind of trinomials? A common method these days...
February 20, 2014

Probability
I will assume that you filled in the Venn diagrams correctly n(M upside down u W) ---> n(M and W) = 14 n(M' U S) ---> n(M' or S) Since S is the symbol used for the universal set, the count would be 49 P( both mice are short-tailed) --- where does the "both&...
February 20, 2014

Algebra
Yeahhh! you got it
February 20, 2014

Algebra
4x^2 - 8x - 12 + 6x , looks like grouping works nicely = 4x^2- 8x+ 6x - 12 = 4x(x-2) + 6(x-2) = (x-2)(4x+6) = 2(x-2)(2x+3) 144 - 9p^2 , should have recognized difference of squares = (12-3p)(12+3kp) 5c^2 - 24cd - 5d^2 if it factors it must start with (5c ...)(c...) and end ...
February 20, 2014

Algebra 1 (Reiny)
Perimeter = 2s^3+4 + 5s + 4s^2 + 1 = 2s^3 + 4s^2 + 5s + 5 Why was this question difficult for you? If you are given the three sides of a triangle, wouldn't you just add them up to find the perimeter ?
February 20, 2014

Math
6x-2 = 3x+1 OR 6x-2 = -3x - 1 3x= 3 OR 9x = 1 x = 1 OR x = 1/9
February 20, 2014

Math
Mandy ---- b jay ------- b-3 kareem --- 2b look at my definitions,
February 20, 2014

Algebra
#1 should be -3x^2 + 5x- 12 #2 3x^2+ 5x - 6x - 10 = 3x^2- x - 10 #3, good, yeahhh #4, -2p^2 + 27p #5, yeahhh #6 good grief!!! = 2m^3 + 4m^2 + 8m - 4m^2 - 8m - 16 = 2m^3 - 16 #7, correct
February 20, 2014

math
let f(x) = ax^4 + bx^2 + c f(-1) = 0 , since it is a factor but f(-1) = a+ b + c so a+b+c = 0
February 20, 2014

advanced functions
-2t^3+3t^2+149t+410 = 980 2t^3 - 3t^2 - 149t + 570 = 0 could try 1, 2, 3, 4, 5 ,6, 7, 8, 9 ,10 Well, what do you know, t=5 works and so does t = 6 so there has to be 3 factors, I know the first two are (t-5)(t-6)(? t + ?) = 0 by the "common sense" theorem, the third ...
February 20, 2014

Algebra
see http://www.jiskha.com/display.cgi?id=1392932194
February 20, 2014

Algebra
If you meant y = -7/(x-16), then the domain is any real number, x ≠ 16 and for every x you pick there is one and only one value of y , except x=16 so it is a function.
February 20, 2014

Algebra
5y = 2x + 9 y = (2/5)x + 9/5 or y = (2x + 9)/5 now write f(x) = ... either of the two versions, both are correct
February 20, 2014

Math Algebra
Nice, that's the way I would do it,
February 20, 2014

Algebra
1/A + 1/B + 1/C = 3400 , #1 1/A + 1/B = 1900 (A+B)/(AB) = 1900 1900AB = A+B 1900AB - B = A B(1900A - 1) = A B = A/(1900A - 1) , #2 1/A + 1/C = 2300 A+C = 2300AC ... C = A/(2300A - 1) , #3 SUB #2 and #3 into #1 1/A + 1/(A/(1900A - 1)) + 1/A/(2300A - 1)) = 3400 1/A + (1900A - 1...
February 20, 2014

Algebra
just plug in k where you see an x
February 20, 2014

Algebra
done here http://www.jiskha.com/display.cgi?id=1392928082
February 20, 2014

Algebra
large frames ---- x small frames ---- 20-x 16x + 7(20 - x) = 176 solve, should be very straightforward
February 20, 2014

math
Pop(t) = 865 (1.15)^t , where t is the number of years
February 20, 2014

Pre algebra
There is no "answer" to y = 5x + 5 Your equation is represented by the graph of a straight line. The y-intercept is 5 , or the point (0,5) The x-intercept is -1 or the point (-1,0) Join these two points with a straight line and extend them in both directions. see: ...
February 20, 2014

Math
umhhh, Kimberly's age : Halley's age = 3 : 1 or 3/1
February 20, 2014

MATH 12
ahhh, just tried it again without the "solve" http://www.wolframalpha.com/input/?i=8500%281%2B12x%29%5E34+%2B+200%28+%281%2Bx%29%5E408+-+1%29%2Fx+%3D+193215.33 and got x = .0031041 or i = .0031041 12i = .0372492 So the equivalent annual rate of return for his ...
February 20, 2014

MATH 12
So I will assume a total time of 34 years or 408 months amount 30 years from now = 8500(1.0545)^34 + 200( 1.0025^408 - 1)/.0025 = 51641.968 + 141573.33655 = $ 193215.33 b) is quite complicated. Let the monthly return be i then 8500(1+12i)^34 + 200( (1+i)^408 - 1)/i = 193215.33...
February 20, 2014

math
a) amount = 8000 e^(12(.02)) = 8500 e^.24 = $ 10805.62 repeat procedure for the others
February 20, 2014

math
a) amount = 3500 e^(3(.0625)) = ..... same for the others.
February 20, 2014

Math
I suspect you mean: n(t)=5600/(0.5+27.5e^-0.044t) confirm my assumption before I proceed.
February 20, 2014

College Algebra
PV = 100000( 1 + .08/12)^-60 = 100000( 1.0066666..)^-60 = ...
February 20, 2014

math
2300 ----> 4600 after 1 decade so, once more gives you ??? I think your question is the incomplete version of this one, which was answered by Steve http://www.jiskha.com/display.cgi?id=1358452964
February 20, 2014

Finance
Assume an investment of $1.00 First Simple Bank: amount after 6 years = 1 + PRT = 1 + 1(.06)(10) = 1.60 Complex Bank: 1(1+i)^10 = 1.6 take 10th root of both sides ( (1+i)^10)((1/10) = 1.6^(1/10) 1+i = 1.048122.. i = .048122.. or appr 4.81%
February 19, 2014

Finance
32000 = 620 + 620( 1 - (1+i)^-59)/i My favourite webpage, Wolfram, says http://www.wolframalpha.com/input/?i=32000+%3D+620+%2B+620%28+1+-+%281%2Bx%29%5E-59%29%2Fx i = .0052576 or 12i = .06309 which is 6.309% per annum , compounded monthly (look past all that messy output to ...
February 19, 2014

Algebra
volume of 15% OJ --- x L volume of 10% OH --- 5-x L .15x + .1(5-x) = .11(5) times 100 , don't like them decimals! 15x + 10(5-x) = 55 15x + 50 - 10x = 55 5x = 5 x = 1 So 1 L of the 15% stuff and 4 L of the 10% stuff
February 19, 2014

math(algebra)
if f(x) varies directly with x, then f(x) = kx, where k is a constant given: if x=9 , f(x) = 49 so 49 = 9k k = 45/9 = 5 f(x) = 5x f(3) = 5(3) = 15 or just use a ratio 9/3 = 45/f(x) 9f(x) = 135 f(x) = 135/9 = 15
February 19, 2014

phisecs
Are you telling me you could not follow my solution to the same problem ? All you did was change one number. http://www.jiskha.com/display.cgi?id=1392776318
February 18, 2014

phisecs
What is phisecs, some small unit of time? rowing rate --- x km/h current rate --- y km/h A girl rows 11 km downstream in 2 h ---> 2(x+y) = 11 2x + 2y = 11 "Her return trip takes 4 h" ---> 4(x-y) = 11 4x - 4y = 11 first times 2 4x + 4y = 22 add to the 2nd 8x = ...
February 18, 2014

Math ~ Check Answers ~
Are you just guessing? Your second one happens to be correct, do you know why it is 2 ?
February 18, 2014

math
Poor wording of the problem. dy/dx = 8x^3 + 9x^2- 2x+ 5 y = 2x^4 + 3x^3 - x^2 + 5x + c but (2,3) lies on it 3 = 32 + 24 - 4 + 10 + c c = .... evaluate, plug c back into y = ....
February 18, 2014

math
slope of line is -1 dy/dx for y = 2/x+ k is -2/x^2 so -2/x^2 = -1 x^2= 2 x= ±2 if x = 2, 2+y = 1 ---> y = -1 so one point of contact is (2,-1) it must lie on y = 2/x + k -1 = 2/2 + k k = -2 you try the case where x = -2
February 18, 2014

algebra
x -28 + 7= 43 solve for x
February 18, 2014

math
nope consider a rectangle, with sides of width 4 cm and length 10 cm. I can also draw a parallelogram with opposite pair of sides of 4 and 10 cm. they are not congruent. I would go with "sometimes"
February 18, 2014

algebra
9|9-8 x|=2x+3 , x ≥ -3/2 |9-8 x|=(2x+3)/9 9-8x = (2x+3)/9 81 - 72x = 2x+3 -74x = -78 x = -78/-74 x = 39/37 or 9-8x = -(2x+3)/9 81 - 72x = -2x - 3 -70x = -84 x = 87/70 = 6/5 check: if x = 6/5 LS = 9|9-8(6/5)| = 27/5 RS = 2(6/5)+3 = 27/5 , so x = 6/5 if x = 39/37 LS = 9|9-...
February 18, 2014

Math
here is a nice youtube showing how it works http://www.youtube.com/watch?v=hJCHhWlyIws
February 18, 2014

Math
let f(x) = 2x^4 + 4x^3 + 3x^2 + 18 f(1) = 2+4+3+18 ≠ 0 f(-1) = 2 - 4 + 3 + 18≠0 f(2) ≠0 f(-2) ≠0 ... f(±9) ≠ 0 tried ±1, ±2, ±3, ±6, ±9, ±1/2, ± 3/2, ±9/2 none worked could not find ...
February 18, 2014

math
let the time taken be t minutes velocity = 265 ft/sec = 15900 ft/min distance traveled along the hypotenuse = 15900t ft Did you make a sketch of the right-angled triangle? I see it as ... sin 15° = 11000/15900t 15900t = 11000/sin15 t = 110/(159sin15) = 2.69 minutes
February 18, 2014

MATH
2(x-5) - 7 =2 2x - 10 = 9 2x = 19 x = 19/2
February 18, 2014

PRE-Algebra
tank A : tank B = 11:15 550/tankB = 11/15 11tankB = 8250 tankB = 750
February 18, 2014

back up - Geometry HELP HELP
oops, I misread the question, and got the wrong triangle (I used the y-axis, instead of the x-axis) so thepoints are (0,0), (2,2) and (5,0) same equation for the right-bisector of AB which is x + y = 2 the right bisector of line from A to (5,0) is x = 5/2 for centre: 5/2 + y...
February 18, 2014

Geometry HELP HELP
Make a sketch, and by some simple preliminary algebra you can see that the triangle is A(0,0) , B(2,2) and C(0, 10/3) the centre of the circle lies on the right bisectors of any of these sides midpoint of AC = (0, 5/3) so right-bisector equation is y = 5/3 midpoint of B(2,2) ...
February 18, 2014

math
first vector = (530cos0, 530sin0 = (530,0) 2nd vector = (80cos220 , 80sin 220 = (-61.28355, -51.423 resultant = ((468.71644 , -51.423) maginitude = √((468.71644^2 + (-51.423)^2 ) = 471.529 direction: tan ฿ = -51.423/468.71644 = -.839.. ฿ = E 40° S
February 17, 2014

math
I have a strong feeling you meant: (1-tan^2 Ø)/(1 + tan^2Ø) + 2tan^2 Ø = (1 - sin^2 Ø/cos^2 Ø)/sec^2 Ø + 2sin^2 Ø/cos^2 Ø = (1 - sin^2 Ø/cos^2 Ø)(cos^2 Ø) + 2sin^2 Ø/cos^2 Ø = cos^2 &...
February 17, 2014

pre-calc
Your given function will be the part of the parabola which lies to the right of the vertex (3, -9) so y = x^2 - 6x inverse is x = y^2- 6y y^2 - 6y = x complete the square: y^2 - 6y+ 9 = x+9 (y-3)^2= x+9 y - 3= ± √(x+9) y = 3 ± √(x+9) but we only used ...
February 17, 2014

Calculus
You are doing fine so far. For these kind of max/min questions, look for "something" which will be either maximized or minimized. What ever that "something" is , you will need an equation that says "something" = ...... In this case I see, "...
February 17, 2014

Geometry
original dimensions: l, w, h volume = lwh new length --- 2l/3 new width ---- w/10 new height = h/4 new volume + (2l/3)(h/4)(w/10) = 2 lwh/120 = lwh/60 or (1/60)lwh so , yes, it is B
February 17, 2014

math
4 2/3-1 1/6 = 14/3 - 7/6 = 28/6 - 7/6 = 21/6 = 7/2 or 3 1/2 Your second has the correct answer, but is nonsense in between 10 1/2-6 2/5 = 21/2 - 32/5 , ( LCD = 10 ) = 105/10 - 64/10 = 41/10 or 4 1/10 PS, I always consider an "improper" fraction in lowest terms a ...
February 17, 2014

Algebra
I will assume you mean u/(1-u) + 1 = 1.5 u/(1-u) = 1/2 2u = 1-u 3u = 1 u =1/3
February 17, 2014

Math
so let the width be x , we know the length is 30 30x = 600 x = 20 so he needs 20+20+30 = 70 ft
February 17, 2014

Math help
(2x^2)( y^4)( 2x^2 y) + 2xy - 3x^5 y^3 = 4x^4 y^5 + 2xy - 3x^5 y^3 now what? are we factoring ?
February 17, 2014

math fractions and decimals
ummhh, give me a whole number greater than 4 and less than 8. Am I missing something here?
February 17, 2014

Math - Check My Answers
remember , the method I used only works if the exponents are the same, that is, a^m * b^m = (ab)^m
February 17, 2014

Math - Check My Answers
#1. 2^(1/3)*4^(1/3) = 8^(1/3) = 2 #2,3 , ok #4 same reasoning as #1 3((1/3) * 9^(1/3) = 27(1/3) = 3 #5, 6, 7, 8, 9 are all ok
February 17, 2014

Gowith Steve - Geometry
messed up my typing don't know why my 1/3 suddenly became 2/3
February 17, 2014

Geometry
let the base of the pyramid and the cube be x by x let the height of the pyramid be h then the height of the cube is 2h volume of pyramid = (1/3)x^2 h = (2/3)h x^2 volume of cube = x^2 (2h) = 2h x^2 ratio of cube : pyramid = 2hx^2 : (2/3hx^2 = 2: 2/3 = 6:2 = 3:1 so it is 3 ...
February 17, 2014

Math
I don't understand your notation ^-^4 I will assume you meant: (5.7 x 10^3)^-4 = 5.7^-4 x 10^-12 = .000947.. x 10^-12 = 9.47 x 10^-16
February 16, 2014

Geometry
Did you mean positive whole numbers ? let the base be y and each of the equal sides be x To be a triangle, x > 2y or y < x/2 2x + y = 99 y = 99-2x y-intercept is 99, x-intercept is 49.5 so the x, or the base, can only be a number from 1 to 49 but to even have a triangle...
February 16, 2014

Foundations Math 12
option A: semiannual rate --- i 15000(1+i)^10 = 20000 (1+i)^10 = 4/3 1+i = 1.029186 semi-annual rate is 2.9186 % annual rate is 5.8372 % option B, monthly rate is .004864.. 15000(1 + .004864..)^60 = 20069.53 so option B Since the annual rate is the same, clearly the more ...
February 16, 2014

Math
I am going to assume you meant to type f(x) = 2/(x+3) (g ° f)(x) = g(f(x)) = g( 2/(x+3)) = 1/( 2/(x+3)) = 1(x+3)/2 = (x+3)/2 If you meant it the way you typed it, follow the same steps and make the appropriate changes.
February 16, 2014

algebra
width ---- x length --- 2x - 3 x(2x-3) = 44 2x^2 - 3x - 44 = 0 (x + 4)(2x - 11) = 0 x = -4, which would make no sense or x = 11/2 or 5.5 yds the width is 5.5 yrds and the length is 8 yards check: 8(5.5) = 44
February 16, 2014

Foundations Math 12
PV( 1.00075)^48 ) = 225.50 PV = $217.53
February 16, 2014

Math
3 ln 2 – ln 4 + 5 ln x = ln 3 + 2 ln 5 ln 2^3 - ln4 + ln x^5 = ln 3 + ln 5^2 ln ((8x^5)/4) = ln (75) none of those match this left in log form, I had ln (8x^5/4) = ln 75 none of your choices match this.
February 16, 2014

Math
So the midpoint is (5, -1) and the equation would be (x-5)^2 + *y+1)^2 = r^2 plug in one of the end points of the diameter to get r^2 check your answer by plugging in the other point, you should get the same r^2 value
February 16, 2014

Calculus
let the width of the rectangle be 2x let the height of the rectangle by y then sides of triangle are 2x each and its height is √3 x area = (1/2((2x)(√3x) + 2xy = √3 x^2 + 2xy 200 = √3 x^2 + 2xy u = (200 - √3x^2)/(2x) Perimeter = P = 6x + 2y = 6x...
February 16, 2014

Math
what is 2000( 1.06^40 - 1)/.07 ?
February 14, 2014

Math
You want the ratio of fantasies : total books = 50 : 85 = 10 : 17 you had that. end of problem
February 14, 2014

Arithemetic progression
term(18) = a+ 17d but d = 3 and term(18) = 549 a + 17(3) = 549 a = 498 term(56) = a + 55d = ..... sum(32) = (32/2)(2(498) + 31(2) ) = ...
February 14, 2014

Math
We know that (√x)^2 = x , by the very definition of √x suppose we take x(1/2) and square it (x^(1/2)^2 by the exponents rules this would be x( (1/2)(2) ) = x so (√x)^2 = (x^(1/2) )^2 then √x = x^(1/2) so x^(1/2) behaves the same way as √x by the ...
February 14, 2014

Math (I'm really confused). Please help.
So the sides must be the same .... 9x - 14 = 7x 2x =14 x = 7 ( I am confused that this confused you)
February 14, 2014

Math PLZ help
sides of a 30-60-90 triangle are in the ratio of 1 : √3 : 2 so x : ? : 18 = 1 : √3 : 2 x/1 = 18/2 x = 9
February 14, 2014

ijhs
let original number be 10x + y then the number reversed is 10y + x difference= 10x+y - (10y+x) = 9x - 9y but 9x - 9y= 36 x - y = 4 since x and y must both be integers between 1 and 9 that little equation tells me that the difference between the digits is 4 possible (x,y) are (...
February 14, 2014

math
Huhh?
February 14, 2014

Math.G.P
arithmetic mean of 1st and 3d = (x-2 + x+6)/2 = (2x + 4)/2 = x+2 let the 2nd be y then y/(x-2) = (x+6)/y y^2 = (x-2)(x-6) y = ± √((x-2)(x+6)) mean:2nd = 5:3 (x+2)/√((x-2)(x+6)) = 5/3 square both sides and expand (x^2 + 4x + 4)/(x^2 + 4x - 12) = 25/9 25x^2 + ...
February 14, 2014

Math 2
number of feet = 8(2.5) = 20 number of yds = 20/3 or 6 yards and 8 inches
February 14, 2014

Math
-48x(7x^2 - 6) ...|336 288 4 |84 72 4 | 21 18 3 | 7 6 The GCF of 336 and 288 = 4x4x3 = 48
February 13, 2014

Maths
present value of remaining balance = 600( 1 - 1.00583333^-36)/.00583333 = $19,431.88 you are paying an extra $1000 leaving a present value balance of $18,431.88 so ... 600( 1 - 1.00583333^-n)/.005833333 = 18431.88 1 - 1.005833333^-n = .179198811 1.00583333^-n = .820801188 log ...
February 13, 2014

algebra
Looking at all the "Related Questions" below, you must have a typo. Most say "Alex spent twice as much as Terry" let Terry's amount be x let Nick's amount be y let Alex' amount be 865-x-y after the spending: Terry has (3/5)x = 3x/5 Nick has y-40...
February 13, 2014

Algebra
you will find that the question contained in http://www.jiskha.com/display.cgi?id=1305681090 has the same setup as yours, just change the numbers and follow my method.
February 13, 2014

math
number of paperclips ---- x reds ---- (1/6)x blue ---- (5/12)x sofar: x/6 + 5x/12 = (7/12)x remainders ---- x - 7x/12 = 5x/12 so (2/5)(5x/12) = 10 10x/60 = 10 x/6 = 10 x = 60 reds = 60/6 = 10 blues= 5(60)/12 = 25 So there are 15 more blues than reds check: reds and blues = 35 ...
February 13, 2014

Algebra
using y = mx + b -4 = (4/5)(7) + b -4 - 28/5 = b b = -48/5 y = (4/5)x - 48/5
February 13, 2014

German help - Reiny
correct
February 13, 2014

Maths
last term is a + (n-1)d = 37a 36a = 49(n-1) 36a = 49n - 49 n = (36a+49)/49 or (36/49)a + 1 but n must be an integer, so a must be a multiple of 49 if a=49 , n = 37 if a = 98 , n = 73 if a = 147 , n = 109 etc (n increases by 36) check my second example, a = 98 , n = 73 terms ...
February 13, 2014

geometry
V = πr^2 h h = 335/(π r^2) SA = 2π r^2 + 2πrh = 2πr^2 + 2πr(335/(πr^2) = 2πr^2 + 670/r d(SA)/dr = 4πr - 670/r^2 = 0 for a min of SA 4πr = 670/r^2 4πr^3 = 670 r = (670/(4π))^(1/3) = 3.763757606.. subbing back into h h...
February 13, 2014

maths
Did you mean: a grocery man bought 300 apples ... ? We need the cost price to establish the profit.
February 12, 2014

German Help please
Just noticed that your opening phrase in #5 is a mix of English and German. It should have been something like this: Die Schwester meines Vetters ist (if the cousin was male) or Die Schwester meiner Kusine ist (if the cousin was female)
February 12, 2014

German Help please
All correct except #3 I think you have a typo, since #3 is the same as #4 According to you choses answer of "meine Geschwister" , I will guess that it was: mein Bruder und meine Schwester.
February 12, 2014

Algebra - Rational Exponents
Depends what you mean by raising a power to a power e.g. (3^2)^3 = (3^2)(3^2)(3^2) = (9)(9)(9) = 729 or = 3^6 = 729 if the two exponents are at the same "horizontal level" then you multiply the two or more exponents (a^x)^y = a^(xy) do not confuse that with (a^x)(a^y...
February 12, 2014

pre cal
I agree. What about it?
February 12, 2014

Math
What is 1/3 of 1/5 ? isn't that just 1/15 ??
February 12, 2014

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