Tuesday
March 3, 2015

Posts by Reiny


Total # Posts: 29,207

Math Help!!!
If you meant √-75 , then you can't have a real number thus to ask for the nearest integer would be silly So you must have meant -√75 = -8.66025... = -9 to the nearest integer (look at the number on a number line)
November 21, 2014

Math
Brackets are essential here .... h(x) = (3x+2)/(7x-6) or y = (3x+2)/(7x-6) step 1 of finding the inverse is to interchange the x's and y's x = (3y + 2)/(7y - 6) 7xy - 6x = 3y + 2 step 2 : solve this for y 7xy - 3y = 6x + 2 y(7x - 3) = 6x + 2 y = (6x + 2)/(7x - 3) , ...
November 21, 2014

Algebra 2
from the type of problem that you posted, you surely MUST know how to solve quadratic equations. Steve took you as far as 5x^2 - 16x + 6 = 0 and made the same assumption I made. I suggest using the quadratic formula. (you will get two irrational answers)
November 21, 2014

MATH
proceed this way: f(g(x)) = f(2x^2 - 1) = 2/(2x^2 - 1) test it for some number e.g. let x = 3 g(3) = 18-1 = 17 f(g(3)) = f(17) = 2/17 in my answer: 2/(2x^2 - 1) = 2/17 This does not 'prove' that my answer is correct, but there is high probability that it is. Had my ...
November 21, 2014

math
old rate --- $x new rate --- $ x+2 wage per week at old rate = $ 32x wage per week at new rate with more hours = 40(x+2) 40(x+2) - 32x = 200 easy to solve
November 20, 2014

Math Help
Think about it .... if perimeter of little square is 16, each side is 4 for the larger, each side is multiplied by 7, or , each side is 28 so perimeter of larger is .....
November 20, 2014

algebra. help!
How can I check your work if you did not supply any of your choices
November 20, 2014

math
your solution is correct to check, you must go back to the original equation LS = log4 (19-3) = log 4 (16) = 2 -----> what must be exponent on 4 to get 16 ? = RS so x = 19
November 20, 2014

Math
Let his original number of pens be x then his original number of pencils is 30 - x So for every pen he gets 2 pencils so x pens will yield him 2x pencils but he already had 30-x pencils, so 2x + 30-x = 48 x = 18 So, originally he had 18 pens and 12 pencils check: 12+18 = 30 , ...
November 20, 2014

math
of course not distribute ... -36 - 6x - 6x - x^2 = .... add like terms
November 19, 2014

math!!!!!!
just distribute ... x(x+y+2) = x^2 + xy + 2x
November 19, 2014

Algebra
I will assume you mean (1/25)^(x+2) = 125^-x or else we got ourselves one doosey of a problem (5^-2)^(x+2) = (5^3)^-x 5^(-2x-4) = 5^(-3x) then -2x-4 = -3x x = 4
November 19, 2014

Algebra
m-7 < 6 add 7 to both sides, (just like you would for an equation) m < 13 Do the other two the same way
November 19, 2014

math
P(1 + .07/4)^28 = 30000 solve for P
November 19, 2014

math!
GCD(722,2413) = 19 then GCD(19,209) = 19 so GCD(722,2413,209) = 19
November 19, 2014

Algebra Help! Please
Did you not read the 3 conditions I outlined for you? Especially this one: "- if the variable drops out, and you get a true statement, there will be an infinite number of solutions " so you got 0=0, which is true, thus there will be an infinite number of solutions
November 19, 2014

ALGEBRA Help Please
1st: 2(x-3) = 2x 2x - 6 = 2x -6 = 0 -----> contradiction, thus no solution 4th: 4(x+3) + 2x = x - 8 4x + 12 + 2x = x - 8 5x = -20 x = -4 -----> One solution in general - if you get ?x = ? , there will be one solution - if the variable drops out, and you get a true ...
November 19, 2014

Math
#1, you can decide for yourself if (-5,-1) is correct by subbing in those values into both equations. You should be able to do this mentally. -- A quick mental calculation shows that your answer does not work in either equation from the 2nd: x = 2y + 10 plug that into the 1st...
November 19, 2014

MATH HELP
When testing if a number is prime, you would only try primes as divisors until you reach the last prime < √(the number) e.g. is 71 prime try: 2, 3, 5, 7 none divided exactly, so 71 is prime (did not have to go for 11 , since 11 > √71 so for 1881 ... √...
November 19, 2014

maths
Once around is one circumference. The circumference of a circle is 2πr or πd, d the diameter. So 5 times around would be ...... Plug in your values
November 19, 2014

math
I assume you meant to say, " ... travels 180 cm farther than ... " let the distance to the point of the minute hand be r cm In one hour the minute hand has gone around one rotation or 2πr in one hour the 'hour hand' has gone (1/12)(2π60)) or 10π...
November 19, 2014

Maths
Take a sheet of printer paper and try it. Doesn't the circumference of your tube equal the long side ? So.... 2πr = 20 r = 10/π
November 19, 2014

Math- Combinations
You are choosing 4 from 19 = C(19,4) = 19!/(15!4!) = 3876
November 18, 2014

Math
correct
November 18, 2014

Math
Retype in English please, and tell me what C is.
November 18, 2014

AP CALC
let the point of contact on the cosine curve be (x,y) So the perimeter of the rectangle = P = 2x + 2y = 2x + 2cos 2x dP/dx = 2 - 4sin 2x = 0 for a max/min of P 4sin 2x = 2 sin 2x = 1/2 I know sin π/6 = 1/2 so 2x = π/6 x = π/12 then y = cos π/6 = √3/2 ...
November 18, 2014

algebra
Let Jena time alone be x hrs let Cindy's time alone be 2x hrs let the two rates be 1/x and 1/(2x) combined rate = 1/x + 1/(2x) = 3/(2x) 1/(3/(2x)) = 10 2x/3 = 10 hrs = 2x = 30 or x = 15 Jena will take 15 hrs to do the house alone
November 18, 2014

ap calc
There are many variations of this same question,. Hint: let TP = x then OP^2 = x^2 + 64 OP = (x^2 + 64)^(1/2) I think you are missing the length of TR, we need that to find PR Just for arguments sake, lets say TR = 12 miles then PR = 12-x cost = 90000(x^2+64)^(1/2) + 54000(12-...
November 18, 2014

ap calc
Your graph looks like a W and I assume you want the rectangle placed inside the centre part. Let the two other vertices be (x,y) and (-x,y) So the length is 2x and the height is y Area = 2xy = 2x(x^4 - 2x^2 + 1) = 2x^5 - 4x^3 + 2x d(area)/dx = 10x^4 - 12x^2 + 2 = 0 5x^4 - 6x^2...
November 18, 2014

sixth grade ratios and rates
Here is another way of looking at Morgan's solution. Morgan found the percentage to be 25% or 1/4 of the marbes are blue. So 1/4 of Jasper's marbles must be blue , it said they have the same percentage of blue marbles. Let the total of Jasper's marbles be x then (1...
November 17, 2014

Math
f(x)= -x^2 + 2x = -1(x^2 - 2x +1 - 1 ) = -( (x-1)^2 - 1) = - (x-1)^2 + 1
November 17, 2014

college, math
If I were Sears I would sue the publisher of this textbook for associating their name with such a fraudulent practice . Anyway, according to this criminal plan .... cost after sales tax = 1656.9 "add-on interest" = 1656.90(.12)(3) = 596.484 amount to be "...
November 17, 2014

algebra
let's just plug in t = 10 T(10) = 65 + 115 e^-.42 = 140.56 = 141° to the nearest degree. b) we want 110 = 65 + 115 e^(-.042t) e^(-.042t) = (110-65)/115 = .391304... take ln of both sides -.042t = ln .391304.. t = 22.34 minutes or 22.3 minutes
November 17, 2014

math
x^2 = (-16 ± √196)/10 = (-16 ± 14)/10 x^2 = -1/5 or x^2 = -3 x = ± i/√5 or x = ± √3 i All four roots are imaginary
November 17, 2014

Math
only x= 0 so y= 0 x= 1 so y= -3 is correct, the others are not Perhaps, if you show how you are doing the calculations, I can see where you are going wrong. I will do one for you ... if x = -4 y = (-4)^2 - 4(-4) = 16 + 16 = 32
November 17, 2014

Math
So this question is essence establishes the quadratic equation formula hint: give yourself an equation such as 3x^2 + 12x + 2 = 0 and whichever step you perform on this equation, do the same thing for a parallel solution to ax^2 + bx + c = 0 Of course you know what you are ...
November 17, 2014

Algebra Work Check
correct or (x^2+4)(x^2-4) = 0 x^2 + 4 = 0 --> no real solution or x^2 - 4 = 0 (x+2)(x-2) = 0 x = ±2
November 17, 2014

Pre-Calc/Trig
let f(x) = 5x^3 - 119x^2 - 10x + 16 now try some f(x) , where x = ±1, ±2, ±4, ±8 ... hopefully to get a zero took some some, but f(8) = 0 so (x-8) will be a factor now by synthetic division , I got 15x^3-119x^2-10x+16 = (x-8)((15x^2 + x - 2) = 0 ...
November 17, 2014

algebra
speed of current --- x mph time to go 217 miles with the current = 217/(29+x) time to go 189 againts current = 189/(29-x) 217(29+x) = 189/(29-x) cross-multiply, solve for x
November 17, 2014

Calculus
everything happens starting at t=.5 a = -10 v = -10t + c when t = .5 , v = 20 20 = -10(.5) + c c = 25 v = -10t + 25 , for t ≥ .5 s = -5t^2 + 25t + k when t = .5 , the car goes goes another 20(.5) or 10 m so when t = .5, the remaining distance is 20 m 20 = -5(.5)^2 + 25(....
November 17, 2014

maths
original number --- x after epidemic --- .98x are left 14% of those leave, leaving (.86)(.98x) .86(.98x) = 2107 x = 2107/(.86(.98)) = 2500
November 17, 2014

maths
I am sure you meant A=p(1+r/n)^(nt) for yours r/n = .12/12 = .01 and nt = 12t (our unknown) so 500000(1.01)^(12t) = 1000000 1.01^(12t) = 2 take log of both sides log 1.01^(12t) = log 2 12t log1.01 = log2 12t = log2/log1.01 = 69.6607 t = 5.8 years
November 17, 2014

math
If I understand correctly there would have been 4 transactions. let the amount that each child has originally be x first transaction: 1st child -- x-9 each of remaining 9 children has x+1 2nd transaction: 1st child -- x-9 2nd child -- x+1 - 8 = x-7 each of remaining 8 children...
November 17, 2014

proportion test
new machine, defect rate is 85/820 = .1037 or 1037% draw you conclusion from that
November 16, 2014

Math
The question was to "find all possible roots" so you would try f(1), f(-1) , f(2) ...., f(±12) so you must try all of these unfortunately, none are equal to zero, so you have no rational roots.
November 16, 2014

Math
It is a 4th degree equation, so at most you could have 4 roots How can you possible get 6 of them ?
November 16, 2014

math
√(31-9x) = 5 - x square both sides 31 - 9x = 25 - 10x + x^2 x^2 - x - 6 = 0 (x-3)(x+2) = 0 x = 3 or x = -2 BUT, since we squared, we must verify ALL answers if x = 3 LS = 3 + √4 = 5 RS = 5, YEahh if x = -2 LS = -2 + √49 = -2 + 7 = 5 = RS, YEAHH x = -2 or x = 3
November 16, 2014

MATH 101
using the difference of cubes factoring x^2 - 8 = 0 (x-2)(x^2 + 2x + 4) = 0 x = 2 or x = (-2 ±√-12)/2 = (-1 ± 2√3 i )/2 = -1 ± √3 i for 3 solutions, one real, two complex
November 16, 2014

MATH 101
not enough information. is f(x) linear ? we must assume that, since you only have 2 points, namely, (3,0) and (-4,0) slope = 0/-7 = 0 so we have a horizontal line and f(x) = 0 f(x) is the x-axis
November 16, 2014

math
let's look at x^2 + 2x + 4 = 0 by completing the square, (in this case the easiest way to solve it) x^2 + 2x = -4 x^2 + 2x + 1 = -4+1 (x+1)^2 = -3 but anything squared cannot be negative, so there is no real solution consider y = x^2 + 2x + 4 this parabola never touches or...
November 16, 2014

Math
let f(x) = 3x^3 + 2x^2-1 f(1) = 3 + 2 - 1 ≠ 0 f(-1) = -3 + 2 - 1 ≠ 0 f(1/3) = 1/9 + 2/9 - 1 ≠ 0 f(-1/3) ≠ 0 So there are no "nice" roots looking at the graph, there appears to be a real solution at appr x = 0.5 and two complex roots (the graph...
November 16, 2014

CAL
y = x^3/x- x would reduce to y = x^2 - x and (1,-2/3) would NOT lie on this curve. So there is something wrong with the way you typed it Use brackets to establish the correct form Otherwise this question is bogus.
November 16, 2014

CAL
could be the way you typed your equation. The way you typed it, why not just simplify x^3/x to x^2 ? That is why I am suspicious about the way it was typed. Did you mean y = x^(3/x) - x ?
November 16, 2014

Derivative
But, to even attempt this question, you MUST know the derivatives of the basic trig functions. in this case, use the quotient rule dy/dx = ( (1+sinx)(-sinx) - cosx(cosx) )/(1+sinx)^2 = (-sinx - sin^2 x - cos^2 x)/(1+sinx)^2 = (-sinx -1)(1+sinx)^2 = -(1+sinx)/(1+sinx)^2 = -1/(1...
November 16, 2014

calculus
#1, your dy/dt is correct b) correct, to the right when v(t) > 0 but they probably want to know when that happens look at your derivative, the denominator will always be positive, since it is something squared. So the ± of your v(t) is only determined by the ...
November 16, 2014

Calculus Help
It is not a matter of "choosing" here, you must calculate it. f ' (x) = cos(7-5x)(-5) = -5cos(7-5x) f '(π) = -5cos(7-5π) = 5cos(-8.7078..) = 3.770 Did you set your calculator to radians in your DRG mode ?
November 16, 2014

Pre Albergra
Just put on my tin-foil hat and got a message of 3.4 cm How did I do ?
November 16, 2014

Calculus
let x = √5 then x^2 - 5 let y = x^2 - 5 y' = 2x Newton said: newx = x - y/y' = x - (x^2 - 5)/(2x) = (2x^2 - x^2 + 5)/2x = (x^2 + 5)/(2x) x newx 3 2.3333.... 2.333... 2.23809... 2.23809... 2.23606... could have stopped here 2.23606.. 2.236067878 2.236067978.. 2....
November 16, 2014

Trig
The primary function is ln(...) we can only take logs of positive numbers now look at the sine curve only, and note where it lies above the x-axis so the intervals would be 0 < x < 90° or 360° < x < 450° or 720° < x < 810° or ... how about...
November 16, 2014

Math
first , because of the negatiave outer exponent = 1/(16x^2)^3/4 since (ab)^x = a^x * a^x we get 1/( (16^(3/4 ) * x^(3/2) now 16^(3/4) = (16^(1/4) )^3 = 2^3 = 8 so finally = 1/(8 (√x)^3 )
November 16, 2014

math
Volume of cylinder = π r^2 h you are given r and h, plug in the values and evaluate
November 16, 2014

Elementary Math
Ricardo --- x years Miriana ---- x+4 Ten years ago: Ricardo --- x-10 Miriam --- x+4 - 10 = x-6 x-6 = 3(x-10) easy to solve ... let me know what you get
November 16, 2014

Math
One would think that after trying this for two days, you might realize that you don't have enough information. e.g. If your tank is a large rectangular tank of 10 ft by 10 ft the water level would rise more than if your "tank" had been a swimming pool.
November 16, 2014

Math
PV = 800( 1 - 1.09^-10)/.09 Wow, let me know which bank pays you 9% in 2014.
November 16, 2014

Advanced Algebra (Infinite Geometric Series)
8.690909.... =8.6 + .09 + .0009 + .000009+... = 86/10 + .09/(1-.01) = 86/10 + .09/.99 = 86/10 + 9/99 = 86/10 + 1/11 = 478/55
November 15, 2014

Math
2 / ((cos(r^2 - s^2) / (sin(r^2 - s^2)) = 2 * (sin(r^2 - s^2) / (cos(r^2 - s^2) = 2 tan (r^2 - s^2)
November 14, 2014

Math Please Assist
sin^3 x + sinx cos^2 x = cosx sinx(sin^2 x + cos^2 x) = cosx sinx (1) = cosx sinx/cosx = 1 tanx = 1 x = 45° or x = 225° but you wanted to be between 0 and 180 so x = 45°
November 14, 2014

math
since you want cos 2Ø in terms of x from x+5 = 9sinØ bringing the 5 over would make things worse ... and no, you would not distribute the 9 over the 9sinØ - 5 I would proceed this way: sinØ = ( x+5)/9 now you will have to use one of the half-angle ...
November 14, 2014

Pre-Calc/Trig
quadratic --- x^2 term makes it that linear ----- x term makes it that cubic ------ from the x^3 term the highest exponent term establishes what kind it is
November 14, 2014

Algebra
slope = (-3-1)/(1-3) = 2 so it has to be one of the last two of your choices sub in (1,3) into y = 2x+5 ---> doesn't work sub in (1,3) into y = 2x - 5 ----> Yeahhh! so y = 2x-5 that is what bob had suggested to you, that is, try the points in the equations.
November 14, 2014

math
so in effect the ship went 41 + 15 or 56 north and 23 east. so d^2 = 56^2 + 23^2 = 3665 d =√3665 = 60.5 km
November 14, 2014

math probability
since the code > 400, your choice for the first digit is 6, you can put 10 different digits in the 2nd spot, and 10 different digits in the 3rd spot number of possible codes = 6x10x10 = 600 this would include 400, which cannot be used, since it must be greater than 400 so ...
November 14, 2014

Math
to the nearest 10 13---> 10 46 ---> 50 87 ---> 90 sum = 150 if you added them up like you did to get 146 , you have the actual answer, why bother estimating ? Besides, 146 rounded to the nearest tens is 150, not 160
November 14, 2014

math probability
I don't understand the question. In your first sentence, you are saying that there are only 9 dollars in the box.
November 14, 2014

Intermediate Algebra
simple interest formula: I = PRT, lets plug in our values 85 = 6000(R)(1/12) multiply both sides by 12 1020 = 6000R divide both sides by 6000 R = 1020/6000 = .17 or 17% You had the correct answer, but you should not just piece-meal bits and pieces from the equation.
November 14, 2014

Intermediate Algebra
sloppy use of the decimal place and your solution makes absolutely no sense. if x is the amount loaned at 6% ... .06x + .14(15000-x) = 1500 .06x + 2100 - .14x = 1500 -.08x = -600 x = 600/.08 = 7500 So $ 7500 was loaned at 6% and $7500 at 14% check: .06(7500) + .14(7500) = 1500
November 14, 2014

MATH
true if both are positve, or if both are negative. depends if one is + , the other - e.g 8/5 - 9/7 = 11/35 but 15/4 - 3/2 = 9/4 , still a mixed number
November 13, 2014

Geometry
let the size of the cut-out be x by x inches length of base = 24-2x width of base = 24-2x height = x V = x(24-x)^2 = x(576 - 48x + x^2) =576x - 48x^2 + x^2 dV/dx = 576 - 96x + 3x^2 = 0 for a max of V x^2 - 32x + 192 = 0 (x - 24)(x - 8) = 0 x - 8 or x = 24, but if x = 24, we ...
November 13, 2014

Probability.. HELP!
what is 36x35x34 ? Do you know why ?
November 13, 2014

Math, Please Help!
I will assume we are not distinguishing between small and capital letters. I will do one: TENNESSEE - 9 total, 2 N's , 4 E's, 2 S's total number of ways = 9!/(2!4!2!) = 3780 Can you see what I did ? OHIO ----> 4!/(2!) = 12 try the others.
November 13, 2014

College Algebra
If you mean (-10-6i) /( -9+9i) , then the brackets are essential (-10-6i) /( -9+9i) = (-10-6i) /( -9+9i) * (-9-9i)/(-9-9i) = (90 + 90i + 54i + 36i^2)/(81 -81i^2) = (54 + 144i)/162 = 1/3 + (8/9)i
November 13, 2014

College Algebra
type it this way: (-6 - √10)/(3 + 8√10) I will assume you are rationalizing (-6 - √10)/(3 + 8√10) = (-6 - √10)/(3 + 8√10) * (3 - 8√10)/(3 - 8√10) = (-18 + 48√10 - 3√10 + 80)/(9 - 640) = ( 62 + 45√10)/-631 = (-62...
November 13, 2014

Calculus
are you using the usual notation so that a(t) is acceleration, v(t) is velocity and s(t) is distance ?? I will assume you are a(t) = t^2 - 8t + 5 v(t) = (1/3)t^3 - 4t^2 + 5t + c s(t) = (1/12)t^4 - (4/3)t^3 + (5/2)t^2 + ct + k s(0) = 0 0-0+0+0+k=0 k=0 s(1) = 20 1/12 - 4/3 + 5/2...
November 13, 2014

algebra
looks like we are dividing by -2 each time, so ....
November 13, 2014

algebra
So a is always positive and b is always negative. What is a positive divided by a negative ?
November 13, 2014

Algebra
if f(x) = 4x^7+x^5+3x^2-2x+c f(-1) = -4 -1 + 3 +2 +c = 0 c = 0
November 13, 2014

math
Since the area of each time is 16 in^2, each side of the tile must be 4 inches the table is 6 ft by 6ft or 72 inches by 72 inches so we need 72/4 or 18 tiles along a side. since the table is square, the number of tiles needed = 18(18) 324 tiles
November 13, 2014

Math
I usually get rid of nasty decimals ... .1g+3.75m=7.36 --> 10g + 375m = 736 --> g = (736-375m)/10 8.2g+21m=73 ----> 82g + 210m = 730 10g +375m = 736 -times 410 --> 4100g + 153750m = 301760 82g + 210m = 730 -times 50 --> 4100g + 10500m = 36500 subtract them: ...
November 13, 2014

math
I think Bob has a typo in dividing x+y+z by 2 instead of 3 x+y+z+ (x+y+z)/3=360 3x+3y+3z + x+y+z = 1080 4x+4y+4z = 1080 x+y+z = 270
November 13, 2014

Algebra 2
3x^2 - 24x + 45 = 0 remember Steve told you about all that "zero stuff" ? divide each term by 3 x^2 - 8x + 15 = 0 can you think of 2 numbers that add up to -8 and multiply to get 15 ? I am thinking -3 and -5 so (x-3)(x-5) = 0 x-3=0 ----> x = 3 or x-5 = 0 ----> ...
November 13, 2014

math
Proof for all values: let a+b+c+d+e = S let M be the average M = S/5 5M = S then S/M = 5/1 or S : M = 5 : 1
November 13, 2014

Math
correct
November 13, 2014

algebra. help!
first one: y = 2^x why did you possible pick c) not a single one of the pairs given satisfies that equation. It is clearly y = (x+3)^2 , that is, d)
November 13, 2014

Algebra
number of $1 --- n number of $2 --- n+11 number of $3 --- n-18 now for the "value" : 1n + 2(n+11) + 3(n-18) = 100 n+2n+22 + 3n-54 = 100 6n = 132 n = 22 then n+11 = 33 n-18 = 4 so 22 $1 bills , 33 $2 bills and 4 $3 bills check: 22 + 66 + 12 = 100 Yeahh
November 13, 2014

Algebra
surely you can replace x with 2 and add 2+6
November 13, 2014

Algebra
in h(x) = −9x^3+3x^2−2x+2 they are in order of decreasing degree
November 13, 2014

Algebra
h(x) = −9x^3+3x^2−2x+2 why did you put commas between terms in your answer ?
November 13, 2014

math
cost = 16m + 1895 , where m is the number of miles and cost is in cents 16m + 1895 = 5000 16m = 3105 m = appr 194 miles check: 194(.16) + 18.95 = 49.99
November 13, 2014

Algebra 2
As Morgan pointed out, your left side is a perfect square (x+4)^2 = 16/9 x+4 = ± 4/3 x = 4/3 - 4 = -8/3 or x = -4/3 - 4 = -16/3 your signs were wrong
November 13, 2014

algebra
tom has x stickers Matt has 6x stickers there must have been a total of 140 stickers x + 6x = 140 7x = 140 x = 20 Tom has 20 and Matt has 120 So Matt has to give 50 of them to Tom check: Tom: 20+50 = 70 Matt: 120-50 = 70 Yeahhh
November 13, 2014

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