Thursday

December 18, 2014

December 18, 2014

Total # Posts: 28,246

**Math**

log (10A)/(7B^2) = log(10A) - log(7B^2) = lof 10 + logA - (log7 + 2logB) = 1 + logA - log7 - 2logB
*August 2, 2014*

**college math**

From a Physics point of view, this question is really flawed. First of all, it should be -16t^ (gravity works downwards, not upwards) Secondly, at the moment of jettison of the tanks, the tank still has an upwards velocity, so there should be term in t after the -16t^2 anyway...
*August 2, 2014*

**College math**

-In45=3.80666249 this statement is false should say: In45=3.80666249 then e^3.80666249 = 45 again, I will assume you meant: Log sub.B T^5=W , I read that as: logB T^5 = W by definition: T^5 = B^W
*August 2, 2014*

**College math**

yes it is 1: y = x^3 - 27 ----> x = y^3 - 27 2: x = y^3 - 27 y^3 = -x - 27 y = (-x - 27)^(1/3)
*August 2, 2014*

**College math**

follow same steps as I showed you
*August 2, 2014*

**College math**

Inverse: step 1. switch the x and y variables y = 5/(x+3) -----> x = 5/(y+3) step 2: solve this new equation for y xy + 3x = 5 xy = 5-3x y = (5-3x)/x I was able to find the inverse, but both the original and the inverse have restrictions, so it is not a one-to-one function ...
*August 2, 2014*

**Greg/kat - calculus**

Please stick to one name done in previous post
*August 2, 2014*

**Precalculus**

All you want is the linear equation passing through the two points (0,20000) and (5,10000) slope = (10000-20000)/(5-0) = -2000 So if we let t be the time V = -2000t + 20000 the rate of depreciation is $2000/year
*August 2, 2014*

**Math**

well! , just set 164t - 16t^2 = 400 -16t^2 + 164t - 400 = 0 4t^2 - 41t + 100 = 0 (t-16)(4t - 10) = 0 t = 10 or t = 10/4 or 2.5 seconds So it will reach that height first at 2.5 seconds, (and again after 10 seconds on its way back down)
*August 2, 2014*

**Math**

As you can see from the many similar questions, this poorly worded question comes up again and again with just a change of numbers We must assume that the width is the same for the kitchen and the dining room let the dining room be x by x area of dining room = x^2 area of ...
*August 2, 2014*

**math**

let the mileage be m 65 + .7m < 114 + 0m .7m < 49 m < 70 so for m> 70 miles, company A is cheaper check: if m = 50 company A charges $114 company B charges 65 + .7(50) = 100 if m = 71 company A charges $114 company B charges 65+.7(71) = $114.70 . which is more btw...
*August 2, 2014*

**math**

assuming neither of the two given sides is the hypotenuse, make a sketch to see that tan B = 960/490 angle B = appr 63°
*August 2, 2014*

**math**

if GP , then (2x-4)/4 = (21x+2)/64 128x-256 = 84x + 8 44x = 264 x = 6 check: 4, 8, ... , 64, 128 YUP, common ratio of 2
*July 30, 2014*

**typo - Math**

In all that lengthy typing, I just noticed an error. When I stated De Moivre's Theorem, it should of course have been: then z^n = r^n( cos (nØ) + i sin (nØ) ) I did use it correctly in my work.
*July 30, 2014*

**Math**

How did I get 171.9 ? from tanØ = -1/7 I know that the tangent is negative in II and IV by the CAST rule but <-7,1> ends up in quadrant II so I took tan-inverse of 1/7 to get 8.13° , had it been in quad I in quad II we have 180-8.13 = appr 171.9
*July 30, 2014*

**Math**

Jane, you will have to be able to change a complex number from standard form to trig form in general a + bi = (√(a^2 + b^2) [cosØ + isinØ] where Ø is such that tanØ = b/a e.g. change 3 + 4i to trig form = √(3^2+4^2) (cosØ + isin&...
*July 30, 2014*

**Math**

2nd: let z = 0 + 8i = 8( 0 + i) we need 0+i in the form cosØ + isinØ we need Ø, so that cosØ = 0 and sinØ = 1 mmmmhhh, Ø = 90 comes to mind so z = 8(cos90° + isin90°) so the cube root, and using De Moivre's z^(1/3) = 8^(1/3...
*July 30, 2014*

**Math**

For the 2nd: are you familiar with D' Moivres Theorem? let me know, and I will go through with this one 3rd: make a sketch and use the cosine law 35.1^2 = 32.7^2 + 20.2^2 - 2(20.2)(32.7)cosØ ( see if you get Ø = 100.7° )
*July 30, 2014*

**Math**

I assume <2,1> and <-1,1) are vectors then -2A + 3B = <-4,-2) + <-3,3) = <-7,1> magnitude = √(49+1) = √50 or 5√2 direction: let the angle be Ø tanØ = -1/7 Ø = appr 171.9° with the x-axis
*July 30, 2014*

**Alegbra1**

You will have to use brackets to show where the square root ends I suspect it is f(x) = √(-x+2) - 1 , or else why not combine the +2-1 ? then the number under the square root must not be negative, that is ... -x + 2 ≥ 0 -x ≥ -2 x ≤ 2
*July 30, 2014*

**math**

job/rate = time --> rate = job/time let the fathers rate = job/x let the son's rate be job/2x combined rate =job/x + job/2x = 3job/(2x) combined time = job ÷(3job/2x) = job (2x/3job) = 2x/3 but 2x/3 = 6 2x = 18 x = 9 It would take 9 hrs for the father to work ...
*July 30, 2014*

**math**

Making the first 3 as small as possible, they would have to be 1, 2, and 3 let the 4th be x and the 5th be y then 1+2+3+x+y = 90 x+y = 84 remember, y has to be the largest we want x to be as large as possible but still be less than y x y .. .. .. .. 40 44 41 43 42 42 --->...
*July 30, 2014*

**maths**

2(x^2 - 4x + ... ) + 2(y^2 + (5/2)y + ... ) = -10 2(x^2 - 4x + 4 ) + 2(y^2 + (5/2)y + 25/16 ) = -10+ 8 + 25/8 2(x-2)^2 + 2(y+ 5/4)^2 = 9/8 (x-2)^2 + (y+5/4)^2 =9/4
*July 30, 2014*

**Algebra**

let's work on the bottom 6^(2n+1) = 3^(2n+1)* 2^(2n+1) = 3^n * 3^(n+1) * 2^n * 2^(n+1) = 3^n * 2^n * 6^(n+1) now the 3^n would cancel the 3^n on top, leaving you with 1/(2^n * 6^(n+1) )
*July 30, 2014*

**Math; Alegbra**

If r = 3 Volume of sphere = (4/3)π r^3 = 36π volume of a cone = (1/3)π r^2 h =3π h 3π h = 36π 3h = 36 h = 12
*July 30, 2014*

**mathematics**

H = (1/28)L L = 28H L + H = 116 28H + H = 116 29H = 116 H = 4 then L = 112 one number is 16 let the other number be 4x then : 16 = 4*4 4x = 4*x 16x = 112 x = 7 and 4x= 28 The other number is 28 check: 16 = 2*2*2*2 28=2*2*7 LCF = 2*2 = 4 HCM = 2*2*2*2*7 = 112 is 4 equal to 1/28...
*July 30, 2014*

**early morning oops - Math**

But .... if the second derivative is linear, the original function must be a cubic. y'' = 6x y' = 3x^2 + a at x = 1 we have y = 5 - 3x is a tangent, so y' = -3 when x=1 -3 = 3(1) + a a = -6 y' = 3x^2 - 6 then y = x^3 - 6x + b at (1,2) 2 = (1)^3 - 6(1) + b b...
*July 29, 2014*

**Math**

ARrgghhh, really? Matrices for such a simple system? ok .... we need the inverse of 4 -2 7 1 I will assume you know how to find the inverse of a 2by2 I get 1/18 2/18 -7/18 4/18 now if we multiply that by 4 -2 7 1 we get 1 0 0 1 on left and the column matrix 33/18 3/18 on the ...
*July 29, 2014*

**Algebra**

from 3x = 4y ---> x = 4y/3 from 12y = 5z --> z = 12y/5 so z/x = (12y/5) / (4y/3) = (12y/5)(3/4y) = 9/5
*July 29, 2014*

**Calculus**

direction of the given line is (1,1) so if Ø is the angle it makes with the x-axis, then tanØ = 1/1 Ø = 45° so a line which makes an angle of 60° with the given line would have an angle of (45°+60°) or 105° or -15° now tan 105°...
*July 29, 2014*

**Calculus**

A normal to r is (0,1,1) cross (-1,0 3) or (3, -1, 1) , (I assume you know how to find a cross-product) So the plane must look like, 3x - y + z = c , where c is a constant from the line (x-3)/2 = (y+1)/-3 , z=1 the point (3,-1 ,1) must lie on the line, so it must also lie in ...
*July 29, 2014*

**Math**

Ok, starting to make sense now So I will assume you are given: sin(alpha+beta)=(sin alpha)(cos beta)+(cos alpha)(sin beta) and cos(alpha+beta)=(sis alpha)(cos beta)+(sin alpha)(sin beta) I will use A and B for easier typing You must also know that 1. sin(-A) = -sinA 2. cos(-A...
*July 29, 2014*

**Math**

That's not what you said originally, look at your post. So which identity are we deriving ?
*July 29, 2014*

**Math**

so you want us to use the identity: sin(A - B) = sinAcosB - cosAsinB to prove sin(A - B) = sinAcosB - cosAsinB ? mmmhhh? did you mean sin(A+B) ??
*July 29, 2014*

**Math**

let the time taken since 10:00 am till they meet be t hrs at 10:00 am , train will have already gone 130 miles when they meet, they both will have traveled the same distance, so ... 90t = 130 + 65t 25t = 130 t = 5.2 hrs or 5 hrs and 12 minutes that would put the time at 10:00...
*July 29, 2014*

**Math**

1 ---> 4 = 2^2 2 ---> 8 = 2^3 3 ---> 16 = 2^4 4 ---> 32 = 2^5 mmmhhh, look at the exponent of 2 and compare it to your input value. isn't it always one greater ? so .....
*July 29, 2014*

**error - Algebra**

Whoahh there Sheenybeany if the inequality is y/6 > 10 then y > 60 Why did you reverse the inequality sign? It is reversed only if you multiply or divide by a negative. Since we simply multiplied by 6, it stays the same. Since y > 60 is not one of the choices, we ...
*July 29, 2014*

**geometry**

mmmh, I guess that explains why he is still a bachelor
*July 29, 2014*

**arggg! ... Geometry**

How did I possible see 4 of equal sides ? but... my algebra worked out sooo nice! Reminds me of the classic StarTrek episode where Cpt Picard is tortured by the Kardashians and sees 4 lights. https://www.youtube.com/watch?v=moX3z2RJAV8
*July 29, 2014*

**Geometry**

let the sides be a, b, and c We know: 4a +4b + 4c = 24 ----> a+b+c = 6 and 4ab + 4ac + 4bc = 22 2ab + 2ac + 2bc = 11 The length of the diagonal is √(a^2 + b^2 + c^2) by algebra, we know (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc subbing in 6^2 = a^2 + b^2 + c^2 +11...
*July 29, 2014*

**math**

The way it is written, I must agree with Steve
*July 29, 2014*

**Math**

start at (-3,-4) and mark it since slope = rise/run = 2/3 the rise is 2 and the run is 3 so from the point (-3,-4) go to the right 3 (run of 3), then go up 2 (rise of 2) mark this new point, join with a line and you are done Easy, eh ??
*July 28, 2014*

**Math**

you replaced the y with -8 , but not the x with -3 Why not? -8 = -2(-3) + b -8 = 6 + b -14 = b so y = -2x - 14
*July 28, 2014*

**Math**

done below
*July 28, 2014*

**math**

1. can you think of two numbers which when multiplies yields -36 and when added is 16 how about 18 and -2 ???? (x+18)(x-2) 2. can you think of two numbers which when multiplies yields 9 and when added is -10 how about -1 and -9 (x^2 - 1)(x^2 - 9) now we have the difference of ...
*July 28, 2014*

**Math**

Natalie, use the method I showed you in your previous post slope of lines parallel to 8x + 4y = 7 = -8/7 slope of perpendicular lines = + 7/8
*July 28, 2014*

**math**

profit = 12.50 - 8.00 = 4.5 percentage profit = 4.5/8 = .5625 or 56.25%
*July 28, 2014*

**math**

I will assume from your poorly worded question that the sale price is $10.00 so if the original is $x .8x = 10 x = 10/8 = 12.50 Now, do you need the profit percentage before or after the sale? You decide
*July 28, 2014*

**Math**

use a two step process 1. take all terms except the y term to the right side 4x + 5y = 3 ----> 5y = -4x + 3 2. divide each term by the coefficient of the y term 5y = -4x + 3 y = (-4/5)x + 3/5 now you have it in the form y = mx + b, where m is the slope, so the slope is -4/5
*July 28, 2014*

**Calculus**

if F' (x) = -7x then F(x) = -(7/2)x^2 + c but F(0) = 1 1 = 0(-7/2) + c c = 1 F(x) = (-7/2)x^2 + 1
*July 28, 2014*

**math**

Johnny, looks like "homework dumping to me" How about showing us what steps you have taken in these problems or indicate where your difficulties lie.
*July 28, 2014*

**math**

I suppose we could do this .... 12V = 3W V = 3W/12 = W/4 then 2W - 8V = 2W - 8(W/4) = 2W - 2W = 0
*July 28, 2014*

**Geometry**

I agree with Bob My understanding of a trifoil has been this: http://www.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/9/9d/Trefoil-Architectural.png&imgrefurl=http://commons.wikimedia.org/wiki/File:Trefoil-Architectural.png&h=218&w=231&tbnid=...
*July 28, 2014*

**general math**

This is how I would have expected my students to write up the solution to this equation 5x − 2 = 2x + 7 5x - 2x = 7 + 2 3x = 9 x = 3
*July 28, 2014*

**Maths (differentiation)**

the way you typed it, Wolfram read it as http://www.wolframalpha.com/input/?i=+Y+%3D+1%2FSinX%5E2 and y = (sinx)^-2 dy/dx = -2(sinx)^-3 (cosx) = -2cotx /sin^2 x or = -2cotx csc^2 x if you meant: y = 1/ sin(x^2) then y = sin(x^2)^-1 dy/dx = -1sin(x^2)^-2 cos(x^2) (2x) = -2x cot...
*July 28, 2014*

**Math**

number of tests before the last one ---> x total marks at that point = 84x then (84x + 100)/(x+1) = 86 86x + 86 = 84x + 100 2x = 14 x = 7 So there were 8 tests, including his perfect test at the end.
*July 27, 2014*

**Maths**

Kelvin --- x Ken ----- x+6 average of Kelvin and Ken = (2x+6)/2 = x+3 David = (x+3) + 6 = x+9 (x + x+6 + x+9)/3 = 42 3x + 15 = 126 3x = 111 x = 111/3 = 37 David is 37+9 = =46 check: Kelvin --> 37 Ken----> 43 David ---> 46 average of Kelvin and Ken = (37+43)/2 = 40 Is ...
*July 27, 2014*

**math**

number of girls = 3x number of boys = 4x (check: total is 7x) total weight of all children = 7x(36) = 252x total weight of all the girls = 3x(32) = 96x so the weight of all the boys = 252x-96x = 156x average weight of boys = 156x/(4x) = 39 kg
*July 27, 2014*

**Maths**

Did you make a sketch? If so, you can see that cosØ = 2/6 = 1/3 Ø = cos^-1 (1/3) = appr 70.5°
*July 27, 2014*

**math**

Let the salaries of A, B, and C be 2x, 3x, and 5x respectively. then 3x + 5x = 8000 8x=8000 x = 1000 A's is 2000 C's is 5000 we don't really have to find their actual salaries amount that C has more than A is 5x-2x = 3x Percentage of that of A = 3x/2x = 3/2 = 1.5 ...
*July 27, 2014*

**math**

breadth --- x length ---- 1.2x 2(x+1.2x) = 88 x+1.2x = 44 2.2x = 44 x = 20 area = x(1.2)x = 1.2(20^2) = 480 m^2
*July 27, 2014*

**correction - calculus 2**

∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9 should be ∆x = (6-1)/10 = 5/3 , so ∆x/3 = 5/30 = 1/6 and the 5/3 in front of the big brackets should be 5/30 or 1/6
*July 26, 2014*

**calculus 2**

I assume that you know the formula .... in case you don't, here is the method http://www.mathwords.com/s/simpsons_rule.htm ∆x = (6-1)/3 = 5/3 , so ∆x/3 = 5/9 interval = (6-1)/10 = 1/2 then we have (5/9)[ f(1) + 4f(1.5) + 2f(2) + 4f(2.5) + 2f(3) + 4f(3.5) + 2f(4...
*July 26, 2014*

**calculus 2**

fix your equation first
*July 26, 2014*

**math**

since the function is linear, the slope must be constant for any pair so (12-a)/(1-0) = (b-12)/(2-1) 12-a = b-12 24 = a+b
*July 26, 2014*

**Math**

number of increases of one unit of money (pesos ? or dollars ?) be n price = 10+n number sold = 200-10n revenue = R = (10+n)(200-10n) = 2000 + 100n - 10n^2 completing the square = -10(n^2 - 10n + 25 -25) + 2000 = -10(n-5)^2 + 2250 vertex is (5,2250) price should be 15 max ...
*July 26, 2014*

**math**

so -9x^2 + 9x + 5 = 0 9x^2 - 9x - 5 = 0 Don't see any obvious facors, so let's use the formula x (9 ± √261)/18 = appr 1.4 or -.4 looks like d)
*July 26, 2014*

**Calc**

let each of the 2 equal sides by x let yeach of the 3 equal sides by y xy = 1,500,000 y = 1500000/x let the length be L L = 2x + 3y = 2x + 4500000/x dL/dx = 2 - 4500000/x^2 = 0 for a min of L 2x^2 = 4500000 x^2 = 2250000 x = 1500 then y = 1500000/1500 =1000 so L = 2(1500) + 3(...
*July 25, 2014*

**math**

Since no choice of 3 points forms a straight line, you are simply finding the number of ways to choose 3 of the 5 points, which is C(5,3) or 5!/(3!2!) = 10
*July 25, 2014*

**good observation - Trigonometry**

Bosnian, thanks for catching that The question used feet as its units, and I just did the math without really thinking about that height. I think the linear units should have been metres and not feet. Both of our numerical values were correct, you also had 171.7 I recall ...
*July 25, 2014*

**Trigonometry**

I use a slightly different method. In my sketch , I labeled the top of the monument P and the bottom Q By properties of the sum of angles in a triangle, in triangle ABP , angle A = 32°, angle ABP = 142, and angle APB = 6° using the Sine Law: BP/sin32 = 55/sin6 BP = ...
*July 25, 2014*

**Math**

I made a sketch, letting the top of the building A I drew in the tower, called the top P and the bottom Q I drew a line from A to B, AB parallel to the ground thus QB = 16 , the same height as the building. We now have two right angled triangles, ABP and ABQ in triangle ABQ, ...
*July 25, 2014*

**maths**

I know math is heavenly, but triangles have angels ?? If the smallest angle is x, then the largest is 5x If they are in AP, then the middle angle must be 3x (note: 3x - x = 5x - 3x , using the common difference relationship) then x + 3x + 5x = 180 9x = 180 x = 20 the angles ...
*July 25, 2014*

**math**

pieces on disc = 3 + 4 + x = x+7 prob of picking one of the 4 ballads = 4/(x+7) but we are told 4/(x+7) = 1/4 x+7 = 16 x = 9
*July 24, 2014*

**Math 221*revised***

This is a poorly worded question. " y=x+4 and the parallel must past through this given point (-7, 1) " y = x+4 does not pass through (-7,1) and you cannot make it do it, unless you change its slope or y-intercept. If you merely want a new line which is parallel to y...
*July 24, 2014*

**MATH**

He can use the 2 pennies in 3 ways, take none, take 1 or take 2 He can use the 3 nickels in 4 ways, take none, take 1, etc the dime in 2 ways, and the quarters in 3 ways total number of ways = (3)(4)(2)(3) = 72 but that includes taking none of any coins, so number of ways to ...
*July 23, 2014*

**Math**

1. find what percentage of the trip Keith drove, then his wife must have driven the remaining percentage 2. 1.5J = (1/2)K 3J = K divide by K 3J/K = 1 divide by 3 J/K = 1/3 3. with radius r, area = πr^2 reduce radius by 10% ---> new radius = .9r new area = π(.9r)^2...
*July 23, 2014*

**MATH**

What choices did you pick? Where are your difficulties? I will do the first one, you try the others If A is 125% of B ----> A = 1.25B B = (1/1.25)A = .8A so B is 80% of A
*July 23, 2014*

**Algebra**

When it hits the ground , h(t) = 0 , so -16t^2 + 40t + 5 = 0 16t^2 - 50t - 5 = 0 Now solve this quadratic using the method that you learned. One of the answers will be negative, you would reject that one.
*July 23, 2014*

**math**

8 hrs, 15 minutes = 315 minutes total minutes available for the experiments = 8(315) = 2520 minutes 84 experiments take 2520 minutes 1 experiment takes 2520/84 or 30 minutes
*July 23, 2014*

**geometry**

areas of similar figures are proportional to the square of their sides area1 : area2 = 3^2 : 9^2 = 9 : 81 = 1 : 9
*July 23, 2014*

**math**

You must have meant: area is 2x^3+5x^2-x-6 if so, then it factors nicely into (x-1)(x+2)(2x+3) and the width of 2x^2 + x - 3 factors to (2x+3)(x-1) then (2x^3+5x^2-x-6) ÷ (2x^2+ x-3) = (x-1)(x+2)(2x+3)/( (2x+3)(x-1) ) = x+2 or you could do a long algebraic division as ...
*July 23, 2014*

**algebra 2**

Is this supposed to be the solution to finding the inverse of y = 1/3x - 5 ??? I suggest a 2-step process 1. interchange the x and y variables ----> x = 1/3y - 5 (you had that) 2. now solve this new equation for y x = 1/3y - 5 x+5 = 1/3y times 3 3x + 15 = y so f^-1 (x) = 3x...
*July 22, 2014*

**Algebra**

what do you think ? I just answered it for you in your previous post
*July 22, 2014*

**Algebra**

I would say it is A it simplifies to -x + 3 = 0 , which is linear and not quadratic. If you force the issue and make it look like a quadratic, it would be 0x^2 - x + 3 = 0 so a=0 , b=-1 and c = 0 BUT, in the formula we are dividing by 2a which in this case would be dividing by...
*July 22, 2014*

**math**

if AP , then d = 2k/3 - k = 2k/3 - 3k/3 = -k/3 term 6 = a+5d = k + 5(-k/3) = -2k/3
*July 22, 2014*

**Math**

2160 = 2*2*2*2*3*3*3*5 1344 = 2*2*2*2*2*2*3*7 1440 = 2*2*2*2*2*3*3*5 HCF = 2*2*2*2*3 = 24 2. let their income be x x/10 + x/3 + x/5 + 1320 = x times 150 , the LCM 15x + 50x + 30x + 198000 = 150x 198000 = 55x x = 3600
*July 22, 2014*

**algebra**

(3+2x)^5 = 3^5 + 5(3^4)(2x) + 10(3^3)(2x)^2 + 10(3^2)(2x)^3 + 5(3)(2x)^4 + (2x)^5 =243 + 810x + 1080x^2 + 720x^3 + 240x^4 + 32x^5 by simple observation that a negative base raised to an odd exponent is negative .... (3-2x)^5 = 243 - 810x + 1080x^2 - 720x^3 + 240x^4 - 32x^5 (3+...
*July 22, 2014*

**algebra 2**

use your formula for S(n) S(n) = a(r^n - 1)/(r-1) 405 = a(3^4 - 1)/(3-1) 405 = a(81 - 1)/2 405 = 40a a = 405/40 = 81/8
*July 22, 2014*

**math**

8+4+2+1+1/2+1/4+...+1/32 = 1/32 + 1/16 + ... + 4 + 8 sum = ∑ 2^(n - 6) for n= 1 to 9
*July 22, 2014*

**math**

sum(n) = (n/2)(first + last) sum(11) = (11/2)(1+6) = 77/2
*July 22, 2014*

**math**

volume = lwh = 18(3)(1/3) = 18 cubic feet
*July 22, 2014*

**coordinate algebra**

I don't see any choices, but it would have to be c = 4h
*July 22, 2014*

**trigonometry**

write it as y = -3sec 2(x-π/6) period = 2π/2 = π no vertical translation phase shift π/6 units to the right
*July 22, 2014*

**Maths**

a = b+2 c = b-11 )a+b+c)/3 = 70 a+b+c = 210 b+2 + b + b-11 = 210 3b = 219 b = 73 a = 75 c = 62 check: (73+75+62)/3 = 70 all looks good
*July 22, 2014*

**Math**

the wonders of Wolfram http://www.wolframalpha.com/input/?i=pattern+%2831%2C30%2C27%2C22%2C15%29 actual work did you notice that consecutive differences are -1, -3, -5, -7 ? this forms an arithmetic sequence, so a quadratic will act as the defining function. let the sequence ...
*July 22, 2014*

**Algebra**

e.g. x^2 - 6x = 0 add 9 to both sides x^2 - 6x + 9 = 9 (x-3)^2 = 9 x-3 = ±3 x = 3 ± 3 = 6 or 0 check: by factoring, x(x-6) = 0 x = 0 or x = 6 , as above
*July 21, 2014*

**Algebra**

I betcha I can solve any quadratic equation by completing the square.
*July 21, 2014*

**math**

#2 number of green = x number of marbles after 5 reds are added = x+5 prob of picking red = 1/7 5/(x+5) = 1/7 x+5 = 35 x = 30 there were 30 marbles
*July 21, 2014*

**math**

#1 g/(b+g) = 1/3 3g = b+g b = 2g (g+1)/(b+g+1) = 3/7 7g + 7 = 3b+3g+3 4g - 3b = -4 4g - 6g = -4 g = 2 then b = 4 , which is choice d. #3 1 million is an even number all prime numbers are odd, except the first one, which is 2, thus even so we have the sum of 999,999 odd numbers...
*July 21, 2014*

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