Posts by Reiny
Total # Posts: 40,239

Algebra
You will have to use "completing the square". y = 2x^28x+11 = 2(x^2  4x+ .... ) + 11 < took out the coefficient of the square term from the first two terms = 2(x^2  4x + 4  4) < took half of the coefficient of the x term, then squared it, added it ... 
math
It always helps to make a sketch before you start a problem. In this case, notice that RS is a horizontal line, so it is easy to that RS = 5 let's make RS the base, then since T is 6 units below that line, the area = (1/2)(base)(height = .... 
maths
Each rotation is 1.4? m so number of rotations = 1100/(1.4?) = ... 
Pre algebra
X/4+1=5 x/4 = 6 x =24 
Calculus
looks like Steve and I have the same answer 
Calculus
using the quotient rule, by first line derivative is y' = (1/3)[(5z+6)/(39z)]^(2/3) [ (5(39z)  (9)(5z+6) ]/(39z)^2 = (1/3)[(5z+6)/(39z)]^(2/3) [ 69/(39z)^2 ] = 23 (39z)^(2/3) / (5z+6)^2/3 [ 1/(39z)^2 ] = not getting your answer let's try the product rule y... 
Algebra
i = .0645/12 = ..... n = 8(12) = 96 paym = p p( 1  (1+i)^96 )/i = 45000  you should know that formula as the PV , present value, formula Once you have the payment p , use your Amount formula to find the amount of 96 payments of p 
Maths
So wouldn't the length be reduced by 8 cm, and the width reduced by 8 cm ? mmmmhhhh? What is the new area vs the old area ? show me your work. 
algebra
We had a very similar question yesterday /display.cgi?id=1512043982 In that one, I had found the slope Using (30,14) as a point, find the equation in the form y = mx + b then sub in 45 for x to get the number of gallons 
math
from the first: 2x6y=26 > x = 3y + 13 sub into the 2nd and away you go .... 
Math
obviously x + y ? 1000 and just as clearly: 2x + 5y ? 3000 Now show me the efforts you made in the next problem. 
prealgebra
just plug in the numbers.. m/n +m/2p = (4/7) / (5/3) + (4/7) / (16/5) = (4/7)(3/5) + (4/7)(5/16) = 12/35 + (20/112) = 12/35  5/28 now 35 = 5 x 7 and 28 = 4 x7 so the LCD = 5x4x7 = 140 carry on from here 
algebra
Simplest way to understand this is to make a table of values. Pick any x to find the matching y, then plot those points the ... anything .. simply means to take the positive result of 'anything' e.g. 5 = 5 , 5 = 5 your graph should look like this: http://www.... 
algebra
Whenever you have a direct variation of something like (.....y....) varies directly with (.....x.....) we can say y = kx Usually you will be given one case where that is true, in your case x = 5 and y = 15. So sub that in ... 15 = 5k k = 3 so now we know the variation equation... 
Algebra
775.5 is the correct answer. Trust yourself and Ms Sue. 
MATH
nope, Use Pythagoras ... x^2 + 5^2 = 13^2 etc 
Geometry
Steve and I answered this same question way back in 2011 /display.cgi?id=1324327824 
Math
let the length be x let the width be x/2 let the height be x5 x(x/2)(x5) > 1125 x^2(x5) ? 2250 let's solve x^2(x5) = 2250 with the help of Wolfram http://www.wolframalpha.com/input/?i=solve+x%5E2(x5)+%3D+2250 x = 15 x(x/2)(x5) < 3000 x^2(x5) = 6000 and that ... 
Geometry
good! You got it 
Geometry
You are correct, but do you understand why not ? 
Math
Woahh there. looking at the function, it will have a maximum of 37+25 or 62 and a minimum of 37+25 or 12 Since this is apparently Alaska, those units can only be in Fahrenheit units and not Celsius. The units I was talking about are "radians" vs "angles ... 
Math
btw, make sure your calculator is set to radians, and not degrees 
Math
just plug in 342 for the x, and grind it out. let me know what you get. Here is a graph to help you check your answer. http://www.wolframalpha.com/input/?i=plot+y+%3D+37sin%7B2%CF%80%2F365(x%E2%88%92101)%7D%2B25 
Math
nope rate of draining = (914)/(6030) = 5/30 gallons/sec or 1/6 gallons/sec the negative shows the volume is decreasing or "draining" remember, slope is (the difference in the y's)/difference in the x's I think you had it backwards, and also ignored the ... 
Math
You first must define your ordered pairs. let my general ordered pair be (time, volume) secondly, make sure you have the same units, e.b. seconds or minutes. I would have: (30,14) and (60,9) now find the slope, and your answer would be gallons/second let me know what you get. 
geometry
I am sure you made a sketch let triangel APC = x then triangle PBC = 3x the whole triangle ABC = 4x Since M is the midpoint, triangle BPM = (1/2) of 3x = 3x/2 ratio of ?BPM : ?ABC = 3x/2 : 4x = 3/2 : 4 = 3 : 8 you had C, so correct 
Math
speed downstream = x+2 speed upstream = x2 4(x+2) = 6(x2) solve for x, then sub into 4(x+2) to get your distance 
math
A: cost = 25 + .8x B: cost = 44 + .6x set them equal to find out when the cost is the same. then decide when A is cheaper 
Calculus
take the derivative, set it equal to zero and solve for x Plug that x back into P(x) to get your maximum profit. b) ?x^2+36x?26 ? 40 x^2  36x + 66 ? 0 let's use the = sign x^2  36x + 66 = 0 use the quadratic formula, you will get two positive x's lower ? x ? larger ... 
Math
No, there is a solution .... 4  t = (t  1) 5 4  t = t  1  5 2t = 64 2t = 10 t = 5 
Algebra pleaseee helppp
Thanks Steve, you are right, I missed the duplications I was thinking something along the lines of dividing by 2^52 , since we have pairs 52 times. I don't know enough about jokers. Are the all the same or distinct? I did count them in my 108 = 2x52+4 If they are the same... 
Algebra pleaseee helppp
so you want 11 of the 108 cards, which would be C(108,11) = appr 3.4 x 10^14 quite a few i would say 
Math
so our x = 20 set your calculator to radians and find 50 cos(60) + 75 = appr 27 rabbits Strange question. The max population would be 125 and the minimum would be 25 repeatedly during that time, and it would go from a max to a min in a period of (1/2)(2?/3) years or appr. ... 
Algebra
15 correct 16 the discriminant is b^2  4ac for yours we get 164(1)(32) = 144 which is a positive number and a perfect square, so we have to different rational xintercepts. Remember if the discriminant is > zero , you have two real roots if the discriminant is = zero, ... 
math
let the point be P(x,y) you don't say if AP : PB = 2 : 3 or 3 : 2 I will assume the first. If otherwise it is very easy to change If you make a sketch and draw the rightangled triangles, you can see .... for the x: (x2)/(18x) = 2/3 3x  6 = 36  2x 5x = 42 x = 8.4 find ... 
algebra
Just did this for you in your earlier post 
Math
.77..... = 7/9 test with your calculator 
math
But I want you to factor the bottom, and my hint was that one of the factors is (x2) so (x^2 + 3x  10) = (x2)( ...... ) and the x2 will cancel 
math
You will definitely need brackets to properly show these expressions, I will assume you meant: (3x6)/(x2) = 3(x2)/(x2) = 3, x ? 2 You take over to do (x2)/(x^2 +3x10) hint: become very suspicious that perhaps one of the factors in the bottom might be (x2) 
Algebra
1. slope = (y2  y1)/(x2  x1) so , please recalculate the slope, it is not a I think you have it "upside down" 2. correct 
math
6. ?75 + ?3 = ?25?3 + ?3 = 5?3 + ?3 = 6?3 7. ?7(?14 + ?3) = ?98 + ?21 = ?49?2 + ?21 = 7?2 + ?21 
Math
correct I would have preferred if you had said, "I know the answer is A" 
Math
Wow, what garbled language !! Fortunately, I am guessing you are talking about perfect numbers. As far back as Euclid it was know that if if p is prime, then 2^p  1 is a prime number, then (2^p 1)(2^(p1) ) is a perfect number. e.g. p = 2 >(2^2  1)(2^(21)) = 3(2) = ... 
college algebra
similar to your other question let the amount invested at 6% be x then the amount at 7% is 2x let the amount invested at 4% be y so x + 2x + y = 24900 y = 24900  3x .06x + .07(2x) + .04(249003x) = 1412 proceed as before 
Algebra 1
Just translate, if her present rate is x mph, then 2(x+15) > 3x 
college algebra
first equation: x+y = 6600 or y = 6600x .09x + .055y = 468 how about multiplying each term by 200 18x + 11y = 93600 use substitution: 18x + 11(6600x) = 93600 carry on .... 
Algebra
step 1 multiply each term by 6 to eliminate the fraction 6y = x + 24 step 2 rearrange to the form required. 
Geometry
easiest way: Since the slopes must be negative reciprocals of each other, the new equation must look like this y = (1/2)x + b plug in your point (4,7) 7 = (1/2)(4) + b 5 = b y = (1/2)x + 5 
math
Sure looks like we are dividing a term by 4 to get to the next one, so ..... 
math
If the average of the original 20 men is 50 years, what is the total sum of their ages? What is the total sum of the new 5 men ? Find the total sum of the ages of the 25 men, which will lead you to the average age of all of them. 
math
since the time is 6 years, I will assume you are using compound interest, simple interest normally would not be used for that length of time Let the interest rate be i 1500(1+i)^6  1200(1+i)^6 = 90 isolate (1+i)^6 take the 6th root of both sides and you have it 
algebra
good grief, this is as fundamental as it gets. Parallel lines have the same slope. In y = mx + b form, which your given line and all choices are shows as, the slope is m I see only one of the choices having the same slope. 
algebra
for the 6 and 3, it would be 6 for the a and a^2 , it would be a^2 for the b and b^2, it would be b^2 so ....... 
Mathematics
by "easy enough" ole means that you have similar rightangled triangles, so use ratios. 
Algebra
major error from 6000=3000 (1+.10/12)^12t to 60003000=30003000(1+008333333)^12t which in turn is NOT equal to the next line 3=1.008333333^12t propter steps: 6000 = 3000(1.0083333)^t, where t is in months 2 =1.0083333^t take ln of both sides ln2 = t ln1.083333. t = ln2/ln1.... 
Algebra
I agree, assuming the question was, "how long would it take for money to double at 10% compounded continuously?" ( In the good ol' days we had something called the rule of 72. Money doubles approximately if you multiply the time by the rate and you get 72. So 72/... 
Math
If by e you mean the Euler number 2.718281828... and your x is a multiplication sign, then 3e = 8.154845... 
math
number of advance  x number of same day  y x+y = 55 y = 55x 40x + 20y = 1800 40x + 20(55x) = 1800 continue strange price for tickets, usually at the door they are more expensive 
Math
You will have to use your distance formula three times. Add the lengths of PQ , QR, and RS I will do QR, you do the other distances , PQ and RS Q(1,2), R(1,1) QR = ?( (11)^2 + (12)^2 ) = ?( 0 + 9) = 3 units Just noticed that all your trips are either horizontal or vertical... 
ALGEBRA
First of all they should have reduced your given 3x+6y=9 to x + 2y = 3 quickest way: since the new equation is perpendicular to the old one, it should be 2x  y = c , (realizing that for ax + by = c, the slope is a/b ) plug in your point (4,2) 8  2 = c c =10 new equation... 
Math
I did this same question /display.cgi?id=1511672005 
Algebra
suppose they were all positive: 2,1,4,7,10,13,16 that general term would be 3n5, from the second term on It looks like the first term is an outlier if I make that change, let's hope it works out but we want to make the terms alternate between + and  this can be done by... 
geometry
Ok, I saw you diagram, a pyramid with a square base of sides a, and height h, with h1 as the height of each of the 4 triangles. given : (1/3) a^2 h = V, where V is a constant h = 3V/a^2 SA = total surface area covered by marble = 4(1/2) a h1 = 2(a)(h1) I can also see that : h1... 
Math
yes, the pennies might be off slightly depending on the calculator. I did: .10/12 = +1 = y^x 480 = x 100000 = 5,370,066.31 
Math
for your given starting value of 100,000 n = 40(12) = 480 i = .10/12 = .008333... amount = 100000(1.008333...)^480 = .... use your calculator, and yes, you can retire quite nicely. 
Linear Algebra
let Q(x,y,z) be that closest point. then vector PQ = <x+5 , y1 , z+4 > we also know the given line has direction vector <3, 2, 1> The shortest distance is when PQ is a perpendicular which means that the dot product between the two vectors is zero <x+5, y1, z+... 
algebra 2
The ((2)/(3)) part is just (1/3)(2) so we can write it as [ 27^(1/3) ]^2 > 27^(1/3) is the cube root of 27 or 3 = 3^2 = 1/3^2 = 1/9 
math
let the quarterly rate be j (you will have to multiply j by 4 at the end to get the annual rate) 8700(1+j)^52 = 11100 (1+j)^52 = 1.275862.. take 52nd root, that is 1+j = 1.275862^(1/52) = ..... I matched one of your choices 
Math
what is 100(1.085)^100 ?? 
math
since we are estimating, by the rule of 72 time = appr 72/7.3 = 9.86 so what is your estimation? 
Math
Since M is the midpoint, area AMC = area BMC , they have the same height and base so BMC = (1/2)(56) = 28 now look at triangles AMD and CMD, they have the same height and their bases are in the ratio of 2 : 5 so triangle AMD = (2/7)(28) = 8 and triangle CMD = (5/7)(28) = 20 
math
Jim's share  15x Jack's share  30x Tom's share  3(15x) = 45x 15x+30x+45x = 360 90x = 360 x = .... find x, sub back into my definitions 
math
sum to infinity = a/(1r) but a/(1r) = 4a divide both sides by a 1/(1r) = 4 continue 
@Emily  Calculus
Damon had answered this and 4 others for you, why are you switching names? I pointed out your error here. /display.cgi?id=1511687459 
Calculus
Where did you get 4500 from ? Damon correctly found w = 5 and his cost equation was c = 4500/w + 18 w^2 = 4500/5 + 18(25) = 1350 
math (correct my work to see if it's right please?
This is a complicated question. To use our general formulas, the payment period must coincide with the interest period. With your data it doesn't. Your payments are made semiannually, while the interest is compounded biweekly. I will take the definition of "biweekly... 
Math
it asked "how many square feet are added to the area" square feet are the units for area ! 
Math
find the area of the original square ..... your new square will be 12 by 12 find that new area. by how much has the area increased ? 
math gr 10
Either you or your teacher are in error. 
math gr 10
The rule of 72 is a very rough approximation of the relation between interest rate and time for any amount of investment to double. e.g. For Jordan's money to double in 8 years rate x 8 = 72 rate = 72/8 = appr 9% I do not see the operation of 72/8 in your choices. actual ... 
Algebra
Does that answer make any sense to you? number = 23500(1.08)^7 = ..... your formula is incorrect 
Arithmetic
Again, use your definitions. What two equations would you get ? 
Arithmetic
use your definitions: "The sum of three consecutive terms of a geometric progression is 42" > a + ar + ar^2 = 42 a(1 + r + r^2) = 42 ** "their product is 512"  a(ar)(ar)^2 = 512 a^3 r^3 = 512 (ar)^3 = 8^3 ar = 8 *** divide ** by *** (1+r + r^2)/r... 
probability
odds that she will pass the test = 12:13 so probability she will pass the test = 12/25 check to see which choice matches that. Make sure you fully understand the difference between odds and probability and how they are related. 
MATH
x(1 + .05(9/12) ) = 700 solve for x 
Math (Complex Numbers)
I started off the same way as Steve and then ... ....you never know with complex numbers, as it stands, I noticed a real silly error on my part. I dropped the 20i  15i in the 3rd line. No fun correcting and seeing where it leads me 
Math (Complex Numbers)
I assume we are solving for z. when we multiply conjugates we are to get a real number (z+23i)(z+5+10i) = z^2 + 5z + 10iz + 2z + 10 + 20i  3iz  15i  30i^2 = z^2 + 7z + 7iz + 40 let z = a+bi z^2 + 7z + 7iz + 40 = (a^2 + 2bi + b^2 i^2) + 7(a + bi) + 7i(a+bi) + 40 = a^2 + 2bi... 
Algebra
You are cutting off squares of 6 cm from each end. So the length is 6 cm less on one end, and 6 cm off the other end. Or, 12 less from both the length and the width. Make a sketch of a rectangle the corners cut off, and you will see . 
Algebra
Ok, let's go with your definitions. original length  l original width  w so lw = 1500 w = 1500/l new length = l12 new width = w12 , you are cutting 6 cm off on each end new height = 6 volume = 6(l12)(w12)= 3456 (l12)(w12) = 576 lw  12l  12w + 144 = 576 1500... 
Algebra
What were your equations, and what are your steps? 
Algebra
let's test your answers by graphing the equations. http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E2+8,++x%2By%3D1 hover your cursor over the intersection points, and it shows that you are incorrect. x+y=1 > y = 1 x y = x^2  8 x^2  8 = 1  x x^2 + x  9 = 0 x... 
Mathematics
Hey, I found one: 15317 is divisible by 17, ends in 17, and the sum of the digits is 17 I made up a very crude computer program using a computer language I taught in the 1980's , too complicated to explain here. 
Mathematics
clearly it can't be a 2 digit number, since it is to end in 17 make a list of multiple of 17 past 100 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, .... mhhh ok, if it ends in 17 and the sum of the digits is also 17, the sum of the missing digits must be ... 
Álgebra
You started well. Ok, up to 3n+7n = v+4 , you have like terms in n 10n = v+4 n = (v+4)/10 so the longer piece is 7n or 7(v+4)/10 or (7/10)(v+4) 
green Field academy math
If you know half of something, what would you do to find the whole ? e.g. If I told you that half of the money in my pocket is $15, how much money would I have in my pocket ? 
Math
In this GP, a = 10, r = 4/5 remember that S(n) = a(1  r^n)/(1r) Just like in your last question, find n so they are equal, then bump it up to the next whole number. 
Math
Again, use your definition. you know S(n) = (n/2)(2a + (n1)d ), so (n/2)(2a + (n1)d ) > 100 and you know both a and d remember that n has to be a whole number, and you will end up with a quadratic inequality. (n/2)(2a + (n1)d ) = 100 , sub in your values, solve the ... 
Math
Just use your definitions. Isn't the definition of 5th term (a + 4d) and that of the first term a ? so a+4d = 6a 4d = 5a d = 5a/4 > ** Also : sum(6) = (6/2)(2a + 5d) 99 = 3(2a + 5(5a/4) ) 33 = 2a + 25a/4 times 4 132 = 8a + 25a continue to solve for a, then sub it ... 
math
Well, this is a far cry from what you made me do yesterday after you posted this: /display.cgi?id=1511439208 btw, give yourself a nickname instead of "anonymous" to find your posts easier. 
math
Thanks, the math part made me look too. Even though we already celebrated our Thanksgiving a month ago up here in Canada, I want to wish all the US students and tudors a Happy Thanksgiving.