Wednesday
August 20, 2014

Posts by Reiny


Total # Posts: 26,966

Algebra
start with y = mx + b y = (4/5)x + b plug in the point ... -1 = (4/5)(3) + b -1 = 12/5 + b -5 = 12 + 5b ---- I don't like fractions 5b = -17 b = -17/5 y = (4/5)x - 17/5 easier way: y+1 = (4/5)(x-3) 5y + 5 = 4x - 12 4x - 5y = 17 mold this equation into any form you wish, ...
February 12, 2014

math
original price --- x (1/2)x - 6 = 88 x/2 = 94 x = 188
February 12, 2014

Maths
I am not familiar with a "balloon payment" since I am not from the US, but I will take a stab at the math. Amount owing after 30 years = 300000(1.07)^30 - 23500( 1.07^30 - 1)/.07 = $ 63,848.80 Is this the balloon payment? It is appr 3 times the annual payment of 23,...
February 12, 2014

Intermediate Algebra
or y = (9/5)x + 4
February 12, 2014

Intermediate Algebra
The slope of the given line is -5/9 so the slope of the new line must be +9/5 and the new equation will look like 9x- 5y= c plug in the given point (0,4) 0 - 20 = c new equation: 9x - 5y = -20
February 12, 2014

Math
Using the same form of your given line, and since the slope is the same , m = 2 y-7 = 2(x-5) or y = 2x - 10 + 7 y = 2x- 3
February 12, 2014

math
What is 400(3) + 500(-2) ?
February 12, 2014

Calculus I
when x = 3 9+y^2 = 25 y^2 = 16 y = ±4 2x dx/dt + 2y dy/dt = 0 dy/dt = -x dx/dt/y = -3(-8)/±4 = ± 6
February 12, 2014

Geometry
40 cm : 18 mm = 40 cm : 1.8 cm = 40 : 1.8 = 400 : 18 = 200 : 9
February 12, 2014

Maths
Pay( 1.08^18 -1)/.08 = 160000 pay = $ 4272.34
February 12, 2014

math
45000(1.03)^n = 50000 1.03^n = 1.1111... n log 1.03 = log 1.111.. n = 3.5644.. about 3 1/2 years
February 12, 2014

Math
let the present value of the deposit be P P(1.075)^6 = 55000 p = 55000/1.075^+ = $35637.88 (elope, skip the expensive wedding, and use it as a downpayment for a house)
February 12, 2014

Algebra
What? No interest involved? So, let the number of months be n 500 + 95n = 800 + 75n 20n = 300 n = 15 check: 500 + 15(95) = 1925 800 + 15(75) = 1925
February 11, 2014

Bronies
Never heard of that, so I googled it. Does GOOGLE not work on your computer ?
February 11, 2014

Algebra (Age Problem)
present age --- x age five years ago --- x-5 age five years from now -- x+8 "Five years ago Rico's age was half of the age he will be in eight years" x-5 = (1/2)(x+8 times 2 2x - 10 = x + 8 x = 18 Rico is now 18 yrs old check: 5 years ago: 13 8 years from now: 26...
February 11, 2014

Math (Variation)
cost = k r^2 when r = 6, cost = 148 148 = k(36) k = 37/9 cost = (37/9) r^2 so when r = 11 cost = (37/9)(121) = 497.44 or cost1/cost2 = r1^2/r2^2 148/cost2 = 36/121 36cost2 = 148(121) cost = 148(121)/36 = 497.44
February 11, 2014

math
denominator --- x numerator ---- x-6 (x-6)/x = 3/4 4x-24 = 3x x = 24 check: (24-6)/24 = 18/24 = 3/4 , YUP
February 11, 2014

Pre-Alegebra
25/20 = 6/x 25x = 120 x = 120/25 = 24/5 or 4.8 ft
February 10, 2014

maths
time = distance / rate = 300 km/(60 km/h) = 5 hrs
February 10, 2014

algebra 2
since cotØ = 1/tanØ by definition, given the tangent of an angle, just take the reciprocal to find the cotangent of that same angle eg, given tanØ = 4/7 then cotØ = 7/4
February 10, 2014

Math
I would first of all change the ratio from 1/4 in : 6 ft , to 1 inch: 24 ft a) for 18 ft, x in/1 in = 18ft/24ft x = 18/24 = 3/4 inch b) x/1 = 66/24 = 11/4 inches or 2.75 inches c) you do it.
February 10, 2014

Maths
current: number of girls -- 3x number of boys --- 4x after change: number of girls -- 3x+3 numbr of boys --- 4x-1 new ratio of girls to boys = (3x+3) : (4x-1) more data needed to get numerical answer. e.g. if we let x = 5 we had 15 girls and 20 boys, notice 15:20 = 3:4 after ...
February 10, 2014

Probability
Assuming of course that he would try the same password more than once, we want success within 2 attempts ----> He could log in on his first try, or if that fails on his second try. FS for failure, then success is Prob(S) + Prob(FS) = 1/8 + (7/8)(1/7) = 2/8 = 1/4
February 10, 2014

Math
using my favourite normal distribution graphing calculator (same as tables in back of text books) http://davidmlane.com/hyperstat/z_table.html click on "value from an area" then enter: area = .9 (to be in top 10%, 90 must be "below" ) mean = 620 SD = 220 ...
February 9, 2014

math
total now = 24 let the number of oranges to be added be x so (4+x)/(24+x) = 1/4 16 + 4x = 24+x 3x = 8 x = 8/3 8/3 buttons ??? Questions is flawed, check your data or your typing.
February 9, 2014

math
number of rooms rented = 450 - 7x price per room = 750 + 4x revenue = (450-7x)(750+4x) expand, then either find the vertex of the resultiong quadratic function, or differentiate, set equal to zero, and solve for x
February 9, 2014

MATH HELP!!!!!!!!
Do you know how to find the inverse of a 3by3 matrix? I got the following: 28 -51 1 40 -18 -26 4 27 7 each is divided by 192 so multiply the above inverse matrix by 46 12 60 then divide each result by 192 for your x1, x2, x3
February 9, 2014

Algebra 1 (Reiny!)
a) correct b) correct, but do you know why the volume is zero ? c) this will also answer part b) the given volume = c(8.5-2c)(11-2c) in expanded form notice if c = 4.25, the size of the cut-out, you would be cutting away 4.25 on each side of the width but the width is only 8.5...
February 9, 2014

math
do you know Calculus? If so, then dP/dx = -80x + 1000 = 0 for a max of P 80x = 1000 x = 1000/80 = 12.5 I assume you can't make a partial product , so either make 12 or 13 to get the same maximum profit If you don't know calculus .... the x value of the vertex is -b/(2a...
February 9, 2014

math
let magnitude 3 be represented by c then maginitude 4 would be 10c and magnitude 6 would be 10^2 x 10c = 1000c it would be 1000 times as great.
February 9, 2014

algebra
number of quarters --- x number of dimes ----- x + 6 25x + 10(x+6) = 165 solve for x, sub into my definition
February 9, 2014

math
let the amounts be 2x , 3x, and 5x solve 2x+3x+5x = 8000, then sub the x back into the three different definitions (hint: the largest share should be $4000 )
February 9, 2014

math!!!!
9 laps = 9(1/8) or 9/8 miles speed = (9/8) / 2.5 minutes = 1.125/2.5 mpm = .45 miles/min
February 9, 2014

MATH
yellow : red = (3/4) : (5/4) = 3 : 5 y:1 = 3:5 y/1 = 3/5 y = 3/5 He needs 3/5 L of red check: (3/5) : 1 = 3 : 5, the ratio as needed
February 9, 2014

Geometry
Area of a kite = (1/2)product of the diagonals So the width and height would be diagonals let the height diagonal be h (1/2)(15)h = 60 15h = 120 h = 8 , looks like C
February 9, 2014

Maths
I will assume you meant: x^2 = (y^2 - r^2)/y^2 , (or else it becomes a real mess involving a quadratic equation in y^4) Let me know otherwise on my assumption, x^2 y^2 = y^2 - r^2 y^2 - x^2 y^2 = r^2 y^2(1 - x^2) = r^2 y^2 = r^2/(1 - x^2) y = ± r/(√(1-x^2) , where...
February 9, 2014

math
Assume there were no babies in the group number of children --- x number of adults ----- y number of seniors ---- 6-x-y 17x + 27y + 25(6-x-y) = 115 17x + 27y + 150 - 25x - 25y = 115 -8x + 2y = -35 8x - 2y = 35 The left side of this equation is even, the right side is odd, this...
February 9, 2014

pre calculus
.72 = 1 (e^-.000124t -.000124t ln e = ln .72 but lne =1 t = ln .72 /-.000124 = appr 2649 years check my arithmetic
February 8, 2014

pre calculus
i = .10/12 = .008333.. n = ? months 5000(1.008333..)^n = 10000 1.008333..^n = 2 n log 1.0083333..= log2 n = appr 83.5 months or 6 years and appr 11.5 months
February 8, 2014

pre calculus
a) amount = 1000(1.025)^10 = 1280.08 b) amount = 1000 e^(5(.05)) = 1000 e^.25 = 1284.03
February 8, 2014

Math
cos 4Ø = 2cos^2 2Ø - 1) = 2(2cos^2 Ø - 1)(2cos^2 Ø -1) -1 = 2(4cos^4 Ø - 4cos^2 Ø + 1) - 1 = 8cos^4 Ø - 8cos^2 Ø + 2 - 1 = 8cos^4 Ø - 8cos^2 Ø + 1 now let cosØ = x and we have f(x) = 8x^4 - 8x^2 + 1
February 8, 2014

maths
number(baseball OR football) =number(baseball) + number(football) - number(baseball AND football) 29 = 21 + 12 - x x = 4 4 of them play both sports.
February 8, 2014

Math
And exactly what part of Steve' answer and mine did you not like ? http://www.jiskha.com/display.cgi?id=1391831037
February 8, 2014

statistics
W - wrong R - right a) prob RRR = (1/3)(1/3)(1/3) = 1/27 b) prob WWW = (2/3)^3 = 8/27 c) 2 right could be WRR, RWR, or RRW prob(of that) = 3 x (2/3)(1/3)^2 = 6/27 (notice the other case is 2 wrong prob of that = 3(1/3)(2/3)^2 = 12/27 and notice that 1/27 + 8/27 + 6/27 + 12/27...
February 7, 2014

Math
the first line of my explanation should have said: 72 = 2x2x2x3x3 = (2^3)(3^2) Looks like I had 12 on my mind
February 7, 2014

Math
To find the number of factors of a number, list its prime factors. e.g. 12 = 2x2x2x3x3 = (2^3)(3^2) so now we argue as follows: the 2's can be used in 4 ways: that is, we can use none, one, two , or all three of them. similarly the 2's can be used in 3 ways, none, one ...
February 7, 2014

statistics
I use this fantastic webpage for these kind of questions http://davidmlane.com/hyperstat/z_table.html enter the mean and SD, click on "between" and enter 69 and 70 to get .1779
February 7, 2014

LINEAR EQUATIONS
Noting to "solve" here, since you have 2 unknowns there would be an infinite number of solutions. What can you do with it? - perhaps graph it, by ... sub in any x you feel like e.g. let x = 3, then y = -2) ---> point (3,-2) let x = 0 , then y = 4 ---------> ...
February 7, 2014

math
let time taken until they meet be t hrs distance covered by first train = 115t miles distance covered by 2nd train = 105t miles 115t+ 105t = 1200 220t = 1200 t = 5.454545.. hrs or 5hrs and .4545..*60 min = 5hrs and appr 27 minutes (let's hope the trains are on different ...
February 7, 2014

Math
I tried dividing the given number by number that reflect teenagers. That is, I started with 13 61150 = 13*47040 47040 = 14*3360 3360=15*224 224=14*16 so the factors are: 13*14*14*15*16 So there are 5 factors, thus 5 members in the club For the second part, start with 12, then ...
February 7, 2014

math
I must disagree with that answer. There are 2 pizzas, each cut into 10 pieces. So they had 20 pieces, and ate 14 part of the pizzas eaten = 14/20 = .7
February 7, 2014

Algebra 1 (Reiny)
both 8 and 27 are perfect cubes, so the cube root will be exact and 2. (8/27)^(1/3) = 2/3 for (8/27)^(2/3) = [(8/27)^(1/3) ]^2 = (2/3)^2 = 4/9
February 7, 2014

Math
889/12 = 74 with remainder 1 961/12 = 80 with remainder 1 1009/12 = 84 with remainder 1 1189/12 = 99 with remainder of 1 So 12 is it! I am not sure if you know anything about modular arithmetic, so I made up a silly little old-fashioned computer program. Here is a listing of ...
February 7, 2014

Algebra 1 (Reiny)
If you meant: the cube root ∛(8m^3) then you would have = 2m , not both 8 and m^3 are perfect cubes 2. very confusing way of typing it, if you represent the square root correctly with an exponent of 1/3, why not represent the cube root with an exponent of 1/3 so we have...
February 7, 2014

Math:A.P.
for AP: term1 = a term3 = a+2d term9 = a+8d but term7 = 19 = a+6d so a = 19-6d so re-defining: term1 = 19-6d term3 = 19-6d+2d = 19-4d term9 = 19-6d + 8d = 19+2d these 3 are supposed to be a GP, so (19-4d)/(19-6d)= (19+2d)/(19-4d) 361 - 152d + 16d^2 = 361 -76d - 12d^2 28d^2 - ...
February 6, 2014

Math
x=2 is a vertical line, thus not a function the others are non-vertical lines All non-vertical straight lines are functions.
February 6, 2014

Math
The lab would measure 180 inches by 216 inches case 1: longer side of tile along longer side of floor 216/18 = 12 180/12 =15 number of tiles = 12x15 = 180 case 2: shorter side of tile along the longer side of floor 216/12 = 18 180/18 = 10 number of tiles = 10x18 = 180 Of ...
February 6, 2014

Fractions
original number ---- x Juan ate (1/3)x , leaving (2/3)x Maria ate 3/4 of that , leaving (1/4)((2/3)x = (1/6)x (1/6)x = 10 x = 60 There were 60 j-beans check: Juan ate 1/3 of the 60 or he ate 20 , leaving 40 Maria ate (3/4) of the 40 , or 30, which would leave 10
February 6, 2014

Only math nerds should read
If you are estimating to get 2/17, and then using a calculator to divide, why not just divide 204/1700 to get .12 or 12% (Some of us old timers actually had to memorize the 12 times table. I recognized 204 = 120 + 84 120 = 10x12 84 = 7 x 12 so 204 = 17 x 12 then 204/1700 = 204...
February 6, 2014

Math - Alg
Did that one last night http://www.jiskha.com/display.cgi?id=1391650592
February 6, 2014

Math
1. height of tree above her line of sight: h1/44 = tan28 h1 = 44tan28 height of tree below her line of sight: h2/44 = tan36 h2 = 44tan36 height of tree = h1 + h2 = ... (not a good idea to have her view to be below the tree line) 2. make a sketch. Label the top of the tree T, ...
February 6, 2014

math
I suspect a typo If I am more than 1000 and more than 2000, then I am more than 2000 there would be an infinite number of solutions e.g. 3660 5579, 9481,9482,9483,....
February 6, 2014

Math - Alg
amount of pure acid to be added -- x L 1(x) + .3(60-x) = .5(60) 10x + 3(60-x) = 5(60) 10x + 180 - 3x = 300 7x = 120 x = 120/7 or appr 17.14 L
February 5, 2014

Math - Alg
solve for x, the amount of water to be added 0(x) + .8(50-x) = .7(50) 40 - .8x = 35 -.8x = -5 x = 6.25 So they had 43.75 ml of the 80% solution, and by adding 6.25 ml of water they now had 50 ml of a 70% solution.
February 5, 2014

math
You keep changing the question. now we have √(2 + √(1+k) ) = √5 square both sides 2 + √(1+k) = 5 √(1+k) = 3 square again 1+k = 9 k = 8
February 5, 2014

math
see your previous post
February 5, 2014

math
area = 10x40 = 400 square yds number of bags= 400/50 = 8 cost = 8($4.99) = $39.92 ignoring tax HUHH, where does the new lawn come in??
February 5, 2014

math
sure
February 5, 2014

math
I read that as √2 + √(1+k) = √5 √1+k = √5 - √2 square both sides 1+k = 5 - 2√10 + 2 k = 6 - 2√10 or appr -0.325
February 5, 2014

Algebra
Chessville : 50000(1.07)^n Checkervill: 70000(.96)^n when is 50000(1.07)^n = 70000(.96)6n 5(1.07)^n = 7(.96)^n log both sides and use rules of logs log5 + nlog1.07) = log7 + nlog.96 nlog1.07 - nlog.96 = log7 - log5 n(log1.07 -log.96) = log7 - log5 n = ( log7 - log5)/(log1.07 -...
February 5, 2014

quanitative methods
enter your data into http://davidmlane.com/hyperstat/z_table.html click on "below" and enter 40
February 5, 2014

Trigonometry
Just tried you first question again, using cos30° in my cosine law and got 22.6 which is D BUT, according to your wording of N 60° E, the angle between the two paths would be 60, and not 30 So to get your answer it should have been N 30° E
February 5, 2014

Trigonometry
This time I get a triangle with sides 30 and 10 and the contained angle between them is 150° , (90+60) again by the cosine law, dist^2 = 30^2 + 10^2 - 2(30)(10)cos150 = 1519.62 distance = √1519.62 = appr 38.98 nm which is choice B The next question you posted is a ...
February 5, 2014

Trigonometry
looks like a rather straight-forward case of the cosine law. distance^2 = 42^2 + 28^2 - 2(42)(28)cos60 = 1372 distance = 37.04 nm or vector of first leg = (42cos270, 42sin270)=(0, -42) vector for 2nd leg = (28cos30,28sin30) = (24.249, 14) adding them to get (24.249 , -28) ...
February 5, 2014

Math help
What is 6000(1.04)^70 ?
February 5, 2014

math - interest rates
annual payments on a car loan? Never heard of that, but, anyway..... Cash value of car = 5000( 1 - 1.06)^-5)/.06 = 21061.82 a) value of loan after 1 year had you made no payments at all = 21061.82(1.06) = 22325.53 but you just made a payment of 5000 So balance after one year...
February 5, 2014

Math
if y = -x+3 and y = x+4 then x+4 = -x + 3 2x =-1 x = -1/2 and y = -1/2 + 4 = 7/2
February 5, 2014

math
let the width of the walkway be x m area of walkway = (6+2x)(15+2x) - (6)(15) = 46 90 + 42x + 4x^2 - 90 = 46 4x^2 + 42x - 46 = 0 2x^2 + 21x - 23 = 0 (x-1)(2x + 23) = 0 x = 1 or x = -23 which would be inadmissable The border should be 1 m wide check: area of garden = 6x15 = 90 ...
February 4, 2014

oops - precalculus II
go with bobpursley's solution I don't know how my "-" suddenly turned into a + in my third line. should have been: 5^x( x-2 - 5^2) = 0 5^x(x - 27) = 0 5^x = 0 or x = 27 but 5^x = 0 has no solution, so x = 27 , the same as bob had
February 4, 2014

precalculus II
(x-2)5^x - 5^(x+2) = 0 I see a common factor of 5^x 5^x( x-2 + 5^2) = 0 5^x(x + 23) = 0 5^x = 0 or x = -23 but 5^x = 0 has no solution, so x = -23
February 4, 2014

Math
Didn't I just show you that it was ? Did you not look at my answer ?
February 4, 2014

Math
first notice the common factor of x x^3 - 3x^2 - 28x = x(x^2 - 3x - 28) now do the quadratic = x(x-7)(x+4) (notice (-7)(+4) = -28 and -7+4 = -3 )
February 4, 2014

alegebra
In this forum we type powers using the ^ to show exponents e.g 4x^2 , not 4x2 anyway 1. 4x^2 + 12x + 5 = (2x+1)(2x+5) 2. 2x^2 + x - 3 = (x-1)(2x+3) 3. ok 4. 16x^2 - 16x - 12 = 4(4x^2 - 4x -3) = 4(2x+1)(2x - 3) which is D) 5. = 3(x^2 + 7x - 8) = 3(x+8)(x-1) which is A) looks ...
February 4, 2014

Math
no need to do FOIL, just sub in n=11 (n-3)^2 = (11-3)^2 = 8^2 = 64 now just put n=11 into the different choices for answers
February 4, 2014

Math
if n=11, then (n-3)^2 = 64 A) is 17(5) ≠64 B) is 16(4) = 64 ahhhh!!! I assume there is only one answer, but check the others anyway.
February 4, 2014

math
let the three pieces be x , 3x, and 6x 6x - x = 2.5 5x = 2.5 x = .5 three pieces are .5 , 1.5, and 3 ft the piece was x+3x+6x or 10 long so 10x = 10(.5) = 5 ft mmmhh, what about the wood lost due to the sawdust? You must have one of those fancy new laser saws.
February 4, 2014

Finance
I will do the first, you do the others in the same way Let me know what you get. PV = ? Amount = 5000 i = .05 n = 10 PV(1 + i)^n = Amount PV(1.05)^10 = 5000 PV = 5000/1.05^10 = 5000/1.628894627 = $3069.57
February 4, 2014

Algebra 2
Jane, from your wording it is not clear if the first card drawn is returned to the deck or not. Suppose it is not returned could be F4 or 4F = (12/52)(4/40) + (4/52)(12/40) = 3/130 + 3/130 = 3/65 Your answer suggests that the card is returned after it is drawn. Then it would ...
February 4, 2014

trig
Just supposing you meant what you typed cot^2x+csc=x cos^2 x/sin^2 x + 1 sinx = x wolfram shows 4 answers in your domain http://www.wolframalpha.com/input/?i=solve+cot%5E2%28x%29+%2B+csc%28x%29+%3D+x x = appr. 1.211, 2.343, 3.523 and 5.964 When substituted all are within an ...
February 4, 2014

math
Oscar is definitely out of line.
February 4, 2014

Math
draw in an altitude to the base , which would bisect the base. So now you have a right angled triangle, let the equal sides be x cm each sin 43° = 7/x x = 7/sin43 = appr 10.26 cm For the second, I will assume that the 170 yrds is measured along the ski run then sin42 = x/...
February 4, 2014

Algebra
mmmh, have you tried substituting t = 4 into the equation and comparing that answer to your graph result when t = 4 on the horizontal axis ?
February 3, 2014

Algebra
in 5 hours , (from 1:00pm to 6:00pm), he did 5 driveways. (7-2) so he does 1 driveway per hour or he takes 1 hour per driveway.
February 3, 2014

Algebra
it is in that form
February 3, 2014

algebra
y-0 = (-2/3)(x-5)
February 3, 2014

math
treat it as having 2 ordered pairs (28, 8) and (47,17) in the form (m,g) slope = (17-8)/(47-28) = 9/19 using (28,8) g-8 = (9/19)(m-28) 19g - 152 =9m - 252 9m - 19g = 100 or -19g = -9m + 100 g =(9/19)m - 100/19
February 3, 2014

Math
Notice what happens when you state a problem in a misleading way? I interpreted that you wanted the cost after a 40% discount. Steve thought that the $99 was the cost after the 40% discount. Besides, "$99 watch with a 40% discount. ", is a statement, not a question.
February 3, 2014

Math
discount = $ 99(.4) = $39.60 So cost of watch = $ 59.40 (how can you get $ 247 ? . That is 2 1/2 times the original cost !! )
February 3, 2014

algebra
amount needed to rent 5 movies is 3(5) + 10 = $25 He already has $10, so he needs an extra $15
February 3, 2014

Math
The tens place can be filled in 4 ways for each of those, the unit place can be filled in 3 ways number of such numbers = 4 x 3 = 12 (count the numbers that Ms Sue gave you)
February 3, 2014

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