Thursday
December 18, 2014

Posts by Reiny


Total # Posts: 28,251

maths
let the roots of the first be s and 4r let the roots of the second be s and 3r 1st: x^2 - 6x + a = 0 sum of roots = 6 product of roots = a s+4r = 6 and 4rs = a 2nd: x^2 - cx + 6 = 0 sum of roots = c product of roots = 6 s+3r =c and 3rs = 6 ---> rs = 2 so in 4rs = a , we ...
July 5, 2014

maths
Sachins would have been (x-4)(x-3) = 0 x^2 - 7x + 12 = 0 Rahul's would have been (x-3)(x-2) = 0 x^2 - 5x + 6 = 0 Sachin was wrong with the 12, should have been 6 Rahul was wrong with the -5x , should have been -7x Equation should have been x^2 - 7x + 6 = 0 (x-6)(x-1) = 0 x...
July 5, 2014

algebra
amount of the 30% solution needed ---- x L amount of the 16% solution needed --- 5-x L .3x + .16(5-x) = .272(5) times 100 30x + 16(5-x) = 136 30x +80 - 16x = 136 14x = 56 x = 4 L 4 L of the 30%, and 1 L of the 16% solution would be needed.
July 5, 2014

math
For any linear equation in the form Ax + By + C = 0 , the slope is -A/B So for both of your equations, the slope is -1/3 thus they are parallel
July 5, 2014

Algebra
For a complicated equation such as yours, the most powerful method is probably Newton's Method. let y = 3x^2+4lnx+4 dy/dx = 6x + 4/x newx = x - y/(dy/dx) = x - (3x^2+4lnx+4)/(6x + 4/x) which simplifies to newx = (3x^2 - 4lnx)/(6x + 4/x) now use an iteration process, I ...
July 3, 2014

algebra
Vikky, what Steve is telling you that complex roots, as well as irrational roots, always come in conjugate pairs. e.g. if one root is 5 - 7i, then there has to be a matching 5 + 7i e.g. if one root is (4 + 3√5)/2 , then there has to be a (4 - 3√5)/2 So, if you know...
July 2, 2014

math
Using a ruler and compass, draw the base line of 9 inches. Set your compass to 6 inches, from the left end of the base draw an arc above the base line. Set your compass to 4 inches, from the right end of the base, draw an arc above the base line The intersection of the two ...
July 2, 2014

Math
To be an arithmetic progression, (2t-1) - t = (2t+4) - (2t-1) solve for t
July 2, 2014

math
what is 60 + (2/5)(60) ?
July 2, 2014

algebra math
I don't see any obvious relationship, nor does Wolfram http://www.wolframalpha.com/input/?i=plot+%7B%282%2C3%29%284%2C5%29%286%2C4%29%288%2C6%29%2810%2C5%29%2812%2C12%29%2814%2C16%29%2816%2C22%29%2818%2C26%29%2820%2C32%29%7D
July 2, 2014

mat/simultaneous equation
I would use elimination here 1st times 3 ---> 6x - 15y = 39 2nd times 5 --> 25x - 15y = -75 subtract them: -19x = 114 x = -6 back into 1st -12 - 5y = 13 -5y = 25 y = -5 x = -6 , y = -5
June 29, 2014

calculus
Assuming we take the growth to be exponential , ... 5 e^(28r) = 7.5 e^(28r) = 1.5 ln both sides ln (e^(28r)) = ln1.5 28r = ln 1.5 r = .0145 the rate is 1.45% check: 5 e^(28*.0145) = 7.5
June 27, 2014

maths probability
Answered by MathMate a few days ago under a Physics heading http://www.jiskha.com/display.cgi?id=1403632512
June 27, 2014

math
In a 32:3 ratio, there are 35 parts 7 m or 700 cm divided by 35 = 20 cm by part So what do you think?
June 27, 2014

Math
I get 3t-9-20t+15 = 5-42t-7 25t = -8 t = -8/25
June 26, 2014

Math
I will assume you mean 120a^4b^2/(-24a^9b^-15) if so, then it would be -5 a^-13 b^17 or -5b^17/a^13
June 26, 2014

Algebra 1
Use this notation to indicate exponents: x^3 - x^2 - 4x + 4 = 0 grouping will work x^2(x - 1) - 4(x - 1) = 0 (x-1)(x^2 - 4) = 0 (x-1)(x+2)(x-2) = 0 so x = 1 , -2 , +2
June 26, 2014

Algebra
yes
June 26, 2014

calcus
Isn't that just a straight-forward Pythagorean calculation? Surely somebody who studies Calculus MUST know how to do that. Let me know where your problem lies.
June 26, 2014

maths
Again, having a hard time trying to establish the order of operation. e.g. #3 I put it into Wolfram the way you typed it , and the webpage interpreted it the same way I did http://www.wolframalpha.com/input/?i=+X%5Elogx%2B5%2F3%3D+10%5E5%2Blog+x What a messy equation that ...
June 26, 2014

maths
1. by definition of logs x^2 - 12x + 36 = 10^2 (x-6)^2 = 100 x-6 = ±√100 = ±10 x = 6 ± 10 = 16 or -4 2. you have the product of 3 numbers = 0 so one of them is zero but log4 and log2 are non-zero real numbers, so log2x must be 0 that is, x = 1 3.not ...
June 26, 2014

maths
11^(1/2) = √11 since 11 is not a perfect square, 11^(1/2) is irrational
June 26, 2014

maths
1st number --- x 2nd number -- 8-x sum of squares = x^2 + (8-x)^2 = x^2 + 64 - 16x + x^2 = 2x^2 - 16x + 64 d(sum of squares)/dx = 4x - 16 = 0 for max/min 4x=16 x = 4 the two numbers are both 4 check: for the answer, sum of squares = 16+16 = 32 let 1st be 3.99, the other 4.01 ...
June 26, 2014

math
first you need the monthly payment. i = .11/12= .00916666.. n = 12 Paym (1 - 1.0091666..^-12)/.009166.. = 15000 paym = 1325.72 Here are my titles to the amortization table ( they will not line up niceley) Time - payment - interest - repayment - balance now -- 0.00 -- 0.00 -- 0...
June 26, 2014

math
prob = C(4,3)*C(4,3)/C(52,6) = 16/20,358,520 4/5089630
June 25, 2014

math-Ms Sue please help
I am pretty sure that for loans lasting 25 years, compound interest would be used. i = .10/12 = .008333... n = 25(12) = 300 payment( 1 - 1.008333^-300)/.0083333) = 73700 I get payment = $ 669.71
June 24, 2014

math
All your questions deal with the use of our 4 basic compound interest formulas. What exactly do you not understand about these questions ? They all are very straight forward.
June 24, 2014

math
i = .08/12 = .006666.. n = 18(12) = 216 amount = 225( 1.00666..^216 - 1)/.00666.. = ... you do the button pushing
June 24, 2014

math
amount(1.02)^12 = 15000 amount = 11827.40
June 24, 2014

math
amount after 3 years at 5% pa compounded semiannually = 4494(1.025)^6 = 5211.66 so interest = 5211.66-4494 = 717.66
June 24, 2014

math
how about y = x^3/(x-1) confirmed: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E3%2F%28x-1%29
June 23, 2014

algebra
√50 = √25√2 = 5√2, which is choice A
June 23, 2014

MAT 221
-10 < -2 + 8x < 22 add 2 -8 < 8x < 24 divide by +8 , (no change in inequality sign) -1 < x < 3 Can't make out your symbols in the 2nd e.g. use <= for ≤ and >= for ≥
June 23, 2014

Frequency
assuming that they either supported it or not supported it, P(E) = 80/400 = 1/5
June 22, 2014

Algebra
yes, I would put your answer in set form, using { } brackets, eg. range = {2,-5}
June 21, 2014

Trigonometry help
Depends on the interpretation of "makes a 15° angle with the boat". If the rope makes a 15° angle with the water line, (parallel to the bottom of the boat) you would have: depth/24 = cos 75° or depth/24 = sin 15° , both giving you depth = 6.21 If the ...
June 21, 2014

Math
1 term(n) = ar^(n-1) term(10) = 16(-1/2)^9 = 16(-1/512) = - 1/32 2. ar^9 = 3/512 ar^14 = 3/16384 divide the 2nd by the first r^5 = 1/32 r = 1/2 back into the first a(1/2)^9 = 3/512 a(1/512) = 3/512 a = 3(512)/512 = 3
June 18, 2014

Math
looks like an arithmetic sequence with d = 17 and term2 = -243 a+d = -243 a = - 260 term(67) = a+66d = -260 + 66(17) = ... you should have at your finger-tips the formulas for the sum of n terms you have the a and the d, so plug in
June 18, 2014

oops - finite math
that should be .25 + .47 for OR the way I had it would have been for AND
June 17, 2014

finite math
what is .25(.47) ?
June 17, 2014

finite math
How many of the 59 homeruns went to left field ?
June 17, 2014

geometry
Did you carefully read the question ?
June 17, 2014

geometry
let me rephrase the question ... what is the greatest common factor of 720, 1008, and 672 ? 720 = 8*9*10 = 16*3*3*5 1008 = 8*9*14 = 16*3*3*7 672 = 16*3*2*7 so who is common? looks like 16*3 or 48 check: 720/48 = 15 1008/48 = 21 672/48 = 14 , nothing common in any of those 3 ...
June 17, 2014

Math
well, let's put z=2 into the 2nd z=y + 2 = 5 y = 3 So now we know that z=2 and y = 3 now into the 1st: x - 6 + 2 = 8 z = 12 So, where was your problem with this ? Looks very very easy.
June 17, 2014

Math
use term(n) = a + (n-1)d here a = -847 , d = 11 , n = ?? , and term(n) = -11 solve : -11 = -847 + (n-1)(11) which should be pretty straightforward to do.
June 17, 2014

probability and statistics
Ummmh, if everybody got an 85, wouldn't the average be 85 ??? , so mean = 85 and since nobody "deviated" from that score, wouldn't the standard deviation be zero ????
June 17, 2014

Math
It must be true that (2x-1) - (3x-2) = (4x-3) - (2x-1) -x + 1 = 2x - 2 -3x = -3 x = 1 check: terms would be 1 , 1, 1 strange sequence but it is arithmetic
June 17, 2014

Math
so you are adding 64 + 81 + 98 + ... for 17 terms a = 64 d = 17 n = 17 use the formula Sum(17) = (17/2)[128 + 16(17)] = 3400
June 17, 2014

algebra
so -2x^2 + 8x + 5 = 0 x^2 - 4x = 5/2 complete the square ... x^2 - 4x + 4 = 5/2 + 4 (x-2)^2 = 13/2 = 26/4 x-2 = √26/4 ........ since √26 is close to 5 x = appr 2 ± 5/2 = appr 4.5 or .5
June 17, 2014

Math
I saw this question and have not been able to get a handle on it we know that ln(x) has an expansion formula http://upload.wikimedia.org/math/6/d/b/6dbf56b2e5f34d298c1e71ddd93b3448.png but it only good for |x-1| < 1 so we could create a series of terms = 1/(x+1) ( (x-1) - (...
June 17, 2014

geometry
let the mean be x (1/8) / x = x / (8/32) x^2 = (1/8)(8/32) x^2 = 1/32 x = ± 1/√32 or ± 1/(4√2) or ± √2/8
June 17, 2014

Math
a=2 ,d=4 term(12) = a+11d = 2 + 44 = 46
June 17, 2014

Math
a = x-y d = 2x+y-3 just use your formula term(101) = a + 100d = x-y + 100(2x+y-3) = x-y + 200x + 100y - 300 = 201x + 99y - 300
June 17, 2014

Maths
You will need brackets to properly identify the order of operations. you probably mean : 5/(1/2) + 14( 5/(1/2) + 14)(1/4) which is 10 + 14(10+14)/4 = 10 + 60 = 70 As to the relationship between the two number ??? yes, you are right, they are both whole numbers or they are both...
June 17, 2014

Math
surface area = 2π(2.5)^2 + 2π(2.5)(9) = ---
June 17, 2014

MATH
Your solution is illustrated by http://www.google.com/search?q=intersection+of+3+planes&tbm=isch&imgil=VKeuvId73BKgcM%253A%253Bhttp%253A%252F%252Ft2.gstatic.com%252Fimages%253Fq%253Dtbn%253AANd9GcTP5OK2B8xVEFseHgCh5S25ao2K4pX-fClEpupY9ltfPRK6cZC8NA%253B332%253B265%...
June 17, 2014

MATH
if you divide the 2nd by 2, all your equations start with 2x. That is good, since we could add or subtract them to eliminate the x 2x+y-3z=4 2x+z=10 -2x+3y-13z=-8 subtract 1st from the 2nd -y + 4z = 6 , #4 add the 2nd and 3rd 3y - 12z = 2 , #5 #4 times 3---> -3y + 12z = 18...
June 17, 2014

algebra
Did you mean, are the lines through each pair of points parallel or perpendicular to each other ?
June 17, 2014

Angles,Lines and Triangles
let the angles be x and y x+y = 116 x-y = 24 add them 2x = 140 x = 70 then y = 46 one angle is 70°, the other is 46° leaving 64° for the third angle
June 17, 2014

math
use a simple ratio ... miles/7 = 64/80 miles = 7(64/80) = 5.6
June 17, 2014

Math
since it is parallel to y=x/2 + 4 it will differ only in the y-intercept, so let y=x/2 + b plug in the point(10,12) 12 = 5+b b = 7 y = x/2 + 7
June 16, 2014

algebra 2
Since you labeled it algebra rather than Calculus, I will use an algebraic solution, completing the square h(t) = -16(t^2 - 9t + 81/4 - 81/4) + 24 = -16( (t - 9/2)^2 - 81/4) + 24 = -16(t - 9/2)^2 + 324 + 24 = -16(t-9/2)^2 + 348 this is a downwards-opening parabola with vertex...
June 16, 2014

Math
#1 and #2 are the same type as the ones I just did for you Give them a try #3 a=2 , d=4 a+(n-1)d = term(n) 2 + (n-1)(4) = 106 2 + 4n - 4 = 106 4n = 108 n = 27 term(27) = 106
June 15, 2014

Math
common difference = 4+p - (6-p) = 4+p - 6 + p = 2p - 2 term(101) = a+100d = 6-p + 100(2p-2) = 6-p + 200p - 200 = 199p - 194
June 15, 2014

Math
a+32d = -2p a+ 60d = 26p subtract: 28d = 28p d = p a + 32p = -2p a = -34p
June 15, 2014

Maths
R(t) = e^kt, where R(t) is the percentage remaining after t t years, k is a constant given: when t = 50 , R(50) = .6 .6 = e^(50k) ln both sides ln.6 = 50k lne k = ln.6/50 R(t) = e^( (ln.6/50) t)
June 15, 2014

Math
volume = h(50-2h)^2
June 15, 2014

add maths
OP /PA = 1/3 3OP = AP now follow the same method I just showed you in your previous post
June 14, 2014

add maths
let the point be P(x,y) then PA = 2PB √( (x-1)^2 + y^2) = 2√( (x+2)^2 + y^2) square both sides and expand x^2 - 2x + 1 + y^2 = 4(x^2 + 4x + 4 + y^2) x^2 - 2x + 1 + y^2 = 4x^2 + 16x + 16 + 4y^2 3x^2 + 18x + 3y^2 = -15 x^2 + 6x + y^2 = -5 complete the square: x^2 + ...
June 14, 2014

Word Problem
let the length and width be 4x and 3x old area = (4x)(3x) = 12x^2 new length = 4x+4 new width = 3x + 2 new area = (4x+4)(3x+2) = 12x^2 + 20x + 8 12x^2 + 20x + 8 = 2(12x^2) = 24x^2 12x^2 - 20x - 8 = 0 3x^2 - 5x - 2 = 0 (x-2)(3x + 1) = 0 x = 2 or x = -1/3, which is not ...
June 13, 2014

lehman
number of $30 units ---- x number of $20 units ---- 2x number of $10 units ---- 40000-x-2x = 40000-3x 30x + 20(2x) + 10(40000-3x) = 800000 30x + 40x + 400000 - 30x = 800000 40x = 400000 x = 10,000 so 10,000 of the $30 units 20,000 of the $20 units 10,000 of the $10
June 13, 2014

lehman
amount invested at 10% --- x amount invested at 8% ---- 3x amount invested at 9% ----- 700,000-x-3x = 700,000-4x .1x + .08(3x) + .09(700000-4x) = 60500 times 100 10x + 8(3x) + 9(700000-4x) = 6050000 34x + 6300000 - 36x = 6050000 -2x = -250,000 x = 125,000 amount borrowed at 10...
June 13, 2014

math
Here is the "magic" square, where not only are your diagonals equal to a sum of 15, but so are each row and column 8 1 6 3 5 7 4 9 2
June 13, 2014

UGRENT HELP, math
They used the < sign should have used the ≤ for the ones that are equal
June 13, 2014

UGRENT HELP, math
number = 80(3)^(8/2) = 6480 C is obviously the biggest, followed by A B and D are the same none of the answers match, after you find the typo, I will let you figure it out
June 13, 2014

finance
first let the 50,000 and the 100,000 ride for the 12 years. Amount = 50000(1.05)^12 + 100000(1.10)^12 = 403,635.65 PLus our annuity of 30,000 for 12 years at 10% = 30000(1.1^12 - 1)/.1 =641,528.51 for a total of $1,045,164.17 Last part: let the rate be i 1,045,164.17 = 102,000...
June 13, 2014

maths
All four sides are equal, so each side of the rhombus is 8 cm get angle Ø , opposite the 10 cm diagonal 10^2 = 8^2 + 8^2 - 2(8)(8)cosØ cosØ = 7/32, then sinØ = 5√39/32 area = 8(8)sinØ = ... you take over
June 13, 2014

MAth
4+√(4+x^2) = x √(4+x^2) = x-4 square both sides 4+x^2 = x^2 - 8x + 16 8x = 12 x = 12/8 = 3/2 since we squared the equation, we MUST verify the answer LS = 4 + √(4 + 9/4) = 4 + √(25/4) = 4 + 5/2 = 13/2 RS = 2/3 LS ≠ RS so actually there is no ...
June 12, 2014

Math
prob(blue, then red) = (10/24)(1/23) = 5/276
June 12, 2014

College Algebra
from vertex, y = a(x+9)^2 + 8 but (9,4) lies on it, so 4 = a(18^2) + 8 324a = -4 a = -4/324 = -1/81 etc you messed up here: 4=a(18)^2+8 4=a(332) , you added 8 to 324a , you can't add unlike terms
June 12, 2014

College Algebra
from the given vertex, the equation must be y = a(x+2)^2 + 4 but (0,2) lies on it, so 2 = a(0+2)^2 + 4 2 = 4a + 4 4a=-2 a = -1/2 y = (-1/2)(x+2)^2 + 4
June 12, 2014

Math please help
let y = 3/x + 4(1-x) = 3/x + 4(1-x)^-1 dy/dx = -3/x^2 -4(1-x)^-2 (-1) = -3/x^2 + 4/(1-x)^2 = 0 for a max/min of y 4/(1-x)^2 = 3/x^2 4x^2 = 3(1-x)^2 2x = ± √3(1-x) 2x = √3 - √3x 2x + √3x = √3 x = √3/(2 + √3) = appr .4641 or 2x...
June 12, 2014

algebra
D : B = 27 : 16 = D : 64 D/64 = 27/16 D = 64(27/16) = 108
June 12, 2014

Math
$1 = 82.8/12 francs so he has 12 + 25 or $37 $37 = 37(82.8/12) francs = appr 255.3 francs Time to update that ancient texbook your school is using. France has been using the Euro since 1999
June 12, 2014

Math
2nd angle --- x 1st angle ---- 4x 3rd angle ---- x+84 x + 4x + x+84 = 180 6x=96 x = 16 1st angle = 4x = 4(16) = 64°
June 12, 2014

ALgebra
adults --- x children -- 3x solve: 975x + 525(3x) = 30600
June 12, 2014

math
In terms of cosx cos 3x = 4 cos^3 x - 3cosx , and cos 2x = 2 cos^2 x - 1 so cos 3x = cos 2x 4 cos^3 x - 3cosx - 2cos^2 x + 1 = 0 let cosx = y so we need 4y^3 - 2y^2 - 3y + 1 = 0 I tried y = 1 and sure enough that was a solution. then by synthetic division ... 4y^3 - 2y^2 - 3y...
June 12, 2014

math
i = .08 n = 40 years a) amount = 3000 ( 1.08^40 - 1)/.08 = appr $777,170.00 b) change the exponent from 40 to 30
June 12, 2014

geometry
second angle --- x first angle ------ 4x third angle ----- x+84 x + 4x + x+84 = 180 you finish it
June 11, 2014

Math
dimes--- x quarters -- x+2 nickels --- 3(x+2) = 3x + 6 10x + 25(x+2) + 5(3x+6) = 180 10x + 25x + 50 + 15x + 30 = 180 50x =100 x = 2 so 2 dimes and 4 quarters and 12 nickels check: 10(2) + 4(25) + 5(12) = 180 all is good
June 11, 2014

Introductory Algebra
Ummmh, isn't it about your school updated those old textbooks? France hasn't used the franc for years, they use the Euro.
June 11, 2014

algebra
cost of pound of copper ---- x cost of pound of tin -------- x+2 3(x + 2) + 7x = 10(3.85) 3x + 6 + 7x = 38.5 10x = 32.5 x = 3.25 copper sells for $3.25 per pound, and tin sells for $5.25 per pound
June 11, 2014

Math
I would write it as y = (8x^3)(3x-2)^(-1/2) and use the product rule dy/dx = (8x^3)(-1/2)(3x-2)^(-3/2) (3) + 24x^2 (3x-2)^(1/2) I will let you clean it up a bit
June 11, 2014

Math
yes, f(-6) = -18-5 = -23 f(4) = 12 - 5 = ........ f(8) = ........ range = { -23, ..... , .... }
June 11, 2014

trig
3secØ = 5 secØ = 5/3 then cosØ = 3/5 , since secA = 1/cosA Ø = arccos 3/5 = appr53.13° but you wanted the obtuse angle, so Ø = 360-53.13 = 306.87° , because the cosine is positive in quadrant I and IV to the nearest degree it would be...
June 11, 2014

Algebra
to get the y-intercept, let x = 0, that would leave you with y = 3 for the x-intercept, let y = 0 , that would leave you with x = 3 if the equation is of the form Ax + By = C do the same thing, usually you can do it your head e.g. 5x + 3y = 20 x-intercept is 4 y-intercept is 20/3
June 11, 2014

Algebra
of course
June 11, 2014

Algebra
treat it like two ordered pairs (1,295) and (2,272) slope = (272 - 295)/(2-1) = - 23 so equation in the form y = mx + b would be count = -23x + b , were x is the day number so using (1,295) 295 = -23(1) + b b = 318 count = -23x + 318 so on day 3 , x =3 count = -23(3) + 318 = ...
June 11, 2014

data management
a) z-score for 6 days = (6-7)/2 = -1/2 = -.5 b) go to your table at z = -.5 and find the corresponding probability , multiply by 8000 ( I got 2468 c) repeat the above for 4 days I found this website a great replacement for tables http://davidmlane.com/hyperstat/z_table.html
June 11, 2014

math (please check answer)
prob = (6/20)(2/19) = 3/95 you were right
June 11, 2014

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