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Posts by Reiny

Total # Posts: 38,645

Math
let f(x) = x^3 + kx - 4 if x-2 is a factor, then f(2) = 0 f(2) = 8 + 2k - 4 = 0 2k = -4 k = -2

Grade 6: money and measures
combined rate is 15 litres per minute. amount in 6 min = 6(15) = 90 litres. volume in tank = 2400h cm^3, where h is the height = 2.4h litres, since 1000 c^3 = 1 litre so 2.4h = 90 h = 90/2.4 cm = 37.5 cm <--- the depth of water after both taps ran for 6 minutes b) Does the ...

algebra
let the time form 11:00 to the time of overtaking be t hrs distance gone by the truck = 54t distance gone by the van = 64(t-1) but they went the same distance, so ... 54t = 64(t-1) solve for t, and add it to 11:00

math
3s + 4j = 360 s + 3j = 220 -----> s = 220 - 3j sub that into the first and solve for j then find s

algebra
Plane's speed --- x mph wind speed ----- y mph 2(x-y) = 180 x-y = 90 1(x+y) = 180 x+y = 180 add them: 2x = 270 x = 135 back in x+y= 180 135+y=180 y = 45 state a proper conclusion.

Algebra
"and" usually suggests addition, e.g. what is 5 and 6 ? let the number be n "the sum of 4 times a number and 30" --> 4n+30 now twice that ---> 2(4n+30) = 8n + 60

Cal 1
S(-3) = 6(-27) + 8(9) + 5 = -85 S(-1) = 6(-1) + 8 + 5 = 7 avg velocity = (7 + 85)/(-1 + 3) = 46

Math-Geometry
Good job, you have 1. shown that opposite sides are parallel 2. adjacent sides form a right angle.

Math-Geometry
I would first of all plot the points. That would give you an idea which sides would form the rectangle. Since in a rectangle: 1. opposite sides are parallel, you can show this by finding the slopes 2. slopes of adjacent sides are negative reciprocals of each other. Use your ...

Math
or number of bags needed --- n amount of peanuts he bought 2n lbs number of bags he needs to buy = 2n/(5/6) = 12n/5 <---- must be a whole number the smallest number of n to make it so, is n = 5 number of bags needed = 5

Math
all 3 digit number divisible by 6: 102 108 114 120 126 132 138 144...978 984 990 996 How many of those are there ? (996-102)/6 + 1 = 150 or: An AG with a=102, d = 6, term(n) = 996 term(n) = a+(n-1)d 996 = 102 + 6(n-1) 6n-6 = 894 6n = 900 n = 150 Of those which ARE divisible by...

math
so shaded part = 6/20 = 3/10 or 30%

math
prob(yellow) = 1/6= x/36, so x = 6 , 6 yellows prob(orange) = 3/4 = y/36, so y = 27, 27 orange remaining 3 must be orange or 1/6 + 3/4 = 11/12 leaving 1/12 for the purple (1/12)(36) = 3 purple

Maths
midpoint of (-5,12) and (-1,-12) = ( (-5-1)/2 , (12-12)/2 )) = (-3, 0) I will use vectors to find the points of trisection i.e. in the ratio of 1:2 one point = (1/3)(7,10) + (2/3)(-8,-5) = (7/3, 10/3) + (-16/3 , -10/3) = (-9/3 , 0) = (-3,0) which is the midpoint of above other...

Math
In your sketch that you made, you will notice that the diagonals right-bisect each other, creating 4 congruent right-angled triangles. Each of them has angles 30:60:90 degrees the ratio of sides for such a triangle is 1:?3:2 where 2 is the hypotenuse Our hypotenuse is 8 so the...

math
I am sure you meant: f(x) = e^x b) f(6) = e^6 f(4) = e^4 avg rate of change from x=4 to x=6 = (e^6 - e^4)/(6-4) = ... , use your calculator

Algebra
invested at 2% --- x invested at 3% --- 7000-x .02x + .03(7000-x) = 184 carry on

Trigonometry
When you say "a 10 inch wheel" I will assume you have a radius of 10 arc length = rØ, where Ø is in radians 225° = 5?/4 radians 450 = r(5?/4) r = 360/? inches = appr 114.59 inches (big wheel) A point on the smaller wheel has to move 450 inches as ...

Algebra
4^4 x 8^8 x 16^16 are all powers of 2 = (2^2)^4 x (2^3)^8 x (2^4)^16 = 2^8 x 2^24 x 2^64 = 2^96 so what do you think?

Algebra
looks pretty standard to me. Perhaps you mean: |y|-2=0 |y| = 2 y = 2 or y = -2

college algebra
from your data, if h is the height above the water h = -4.9t^2 + 28t + 38 set h = 7 4.9t^2 - 28t - 31 = 0 use the quadratic formula to solve for t, use the positive result

college math
At a time of t hours after the action started, - distance remaining for the northbound car before reaching intersection is 3 - 20t - distance remaining for the westbound car before reaching the intersection is 4 - 30t let d be the distance between them d^2= (3-20t)^2 + (4-30t...

Algebra (answer check)
y = -x^2 + 2x + 5 the x of the vertex is -b/(2a) = -2/(-2) = 1 plug in x = -1, y = -1+2+5 = 6 vertex is (1,6) -4x^2+7x+5=0 4x^2 - 7x - 5 = 0 x = (7 ± ?129)/8 = appr (7±11)/8 = appr 18/8 or -4/8 or appr 2.5 or -1/2 your choice is good 5x^2 - 20 = 15x x^2 - 3x - 4...

Math; Calculus
from the given data: h = -16t^2 + 55t + 6 this is a parabola, we need its vertex. the t of the vertex is -b/(2a) = -55/-32 = 55/32 seconds plug that into equation to find max height it is in the air for h > 0 let's see when h = 0 0 = -16t^2 + 55t + 6 16t^2 - 55t - 6 = 0...

Algebra
speed of current --- y speed of swimming ---- x x+y = 5 x-y = 2 solve, I suggest adding them, etc

Algebra
amount of cashews --- x lbs amount of raisins ---- 4.5 - x lbs 2.5x + 1.25(4.5-x) = 2(4.5)

math
let the second be x ft long then the first is x+4.25 the third is x+2.24 x + x+4.25 + x+2.24 = 10 carry on

math
cost price = 525 18 eggs = 1.5 dozen selling price = 23.5(26) = ... profit or loss = selling price - 525 = .... percent profit = ....

math
collins meant: (a+b+c)/2 = s

number base help plz
Steve is simply using the definition of a number with a different base. Just like 57810 = 5(10^2) + 7(10^1) + 8(10^0) 1234 = 1(4^2) + 2(4) + 3 = 16 + 8 + 3 = 24 + 3 ---> Steve noticed the multiples of 8 = 3(8) + 3 = 338

Math
Say what ?

algebra
your function is a straight line - from your equation we can tell that the slope is -2 and the line passes through (-8,7) All you need is another point and you can draw it. Why not pick something nice like x = 0 So we get: y-7 = -2(8) y = -16+7 = -9 take over

Calculus
A rough sketch of the two functions y = x , and y = 1+sinx will show that y = x clearly crosses y = 1 + sinx only once. So your statement is not correct. evidence: http://www.wolframalpha.com/input/?i=solve+x%3D1%2Bsin(x)

Algebra
x/3 + 5 = 3x/2 times 6. 2x + 30 = 9x 7x = 30 x = 30/7 check: (1/3)(30/7) + 5 = 45/7 3/2(30/7) = 45/7 my answer is correct

math
They do not intersect at (3,4) (3,4) does not satisfy g(x) = 2^x - 1 RS = 2^3 - 1 = 7 LS = 4, no good (3,4) work in f(x) = -5/3x + 9 RS = -5/3(3) + 9 = 4 So it does work in the other equation. did you mean g(x) = 2^(x-1) ?? RS = 2^2 = 4 = RS you must have meant that! so ...

math
Did you make a sketch?? The difference in their connection points is 4 m. and you have a triangle with base 10, height 4 and missing hypotenuse x^2 = 4^2 + 10^2 carry on

Math
Maria "guessed" correctly, I got the same answer. So none of the answers supplied are correct. Either typo or misprint.

Matj
I will assume the difference to be between pairs of coupons possible cases: 5,1 6,1 6,2 7,1 7,2 7,3 8,1 8,2 8,3 8,4 9,1 9,2 9,3 9,4 9,5 10,1 10,2 10,3 10,4 10,5 10,6 total 21 number of pairs = C(10,2) = 45 prob(of your event) = 21/45 = 7/15

math
Hint: The diagonals of a rhombus right-bisect each other. Another hint: Make a sketch. What type of triangles do you see? Do you know the legs of those triangles?

Math
What is the LCM of 2, 6, and 9 ?

algebra
time spent cyling --- x hrs times spent running --- (2.5 - x) hrs 10x + 6(2.5-x) = 21 carry on

math
Scott is absolutely right, if you had taken the 10 seconds to complete his calculations.

n
Let's use a sine curve, we could use a cosine as well amplitude is 10, so h = 10sin kt the period is 6 minutes, so 2?/k = 6 ----> k = ?/3 sofar: h = 10sin (?/3 t) this has a min of -10, but our min is to be +1, so we have to raise everything up by 11 so far: h = 10sin...

Math
Number of Yen remaining = 110682 - 87438.78 = 23243.22 $1100US = 110682 Yen 1 Yen = 1100/110682 = $.009938382 so 23243.22 Yen = .009938382(23243.22) = $231 or 1100/110682 = x/23243.22 x = 231

math
correct, only a = 0 if x = 0 then in x/y=2 0/y = 2, which cannot be, so x ? 0 if y = 0, we would be dividing by zero to get 2, which is rather silly, so y ? 0 if a = 0, x/y =2 has nothing to do with it, but x*y*0 = 0, which is true

math
size of original piece of material: x cm by x cm after cut-out base is (x-8) by (x-8) height = x V = x(x-8)^2 = 576 x^3 - 16x^2 + 64x - 576 = 0 Nasty equation to solve. Have you learned any methods to solve a cubic? Newton's Method is probably the best way, but you have to...

Algebra
x=3, so Alysia is 3 and Adam is 33 3+33 = 36

Algebra
Ms. Sue meant to say: x + 30+x = 36

Algebra 1
Yes, except since this is money in dollars you would round it to the nearest cent. $500,637.91

Algebra 1
What is 20000(1.05)^66 ?

Math
rate of first ---- x rate of 2nd ---- y 1500(3)x - 1500(3)y = 13.50 x-y = .003 the difference is .3%

polynomial
I don't understand how looking at the graph of y=2x³+x²+x+8 , which does not have a "nice" rational solution, will help you in solving y = 2x^3 + x^2 - x + 5. The latter also has an irrational solution. http://www.wolframalpha.com/input/?i=y%3D2x%C2%B3%...

Maths
you are solving, 6750(1.05)^t = 8000 1.05^t = 1.185185.. take log of both sides, and use log rules t = log 1.185185.../log 1.05 = 3.482239 so that is 3 years and .482239 years multiply the decimal part by 12 to get 3 years, 5.7868.. months so 3 years, 5 months and .7868 months...

maths
graphing utility?? why? 6sinx + 3cosx = 0 divide by cosx 6sinx/cosx + 3 = 0 6tanx = -3 tanx = -1/2 we know that the tangent is negative in II or IV and we know tan (.4636) = +.5 x = ?-.4636 = appr 2.678 or x = 2? - .4636 = appr 5.820 If you insist: http://www.wolframalpha.com/...

Math
12.5 litres takes the car 168.75 km then 1 L takes the car 168.75/12.5 km then 15 L will take the car .....

Math
Why do you think this question might deal with the concept of a Lowest Common Multiple ?

Math
How many square cm are there in 1 square metre? - then how many in 1/2 square metre ?

Math
simplify and re-arrange ... y-5 = (2/7)(x-11)

Math
of course it isn't right x = 3 would be a vertical line. A quick sketch will show you that your 2 points do not lie along a vertical line slope = m = (-8-8)/(5-3) = -16/2 = -8 equation: y-8 = -8(x-3) re-arrange to whatever form you learned.

Slopes
slope = m = (7-4)/(-5-0) = ... once you find m, replace it in the equation y-4 = m(x+6) arrange into the form that you are familiar with.

Algebra II
Don't understand your question. Don't understand your answer.

Math
p5^y + 5^-y = 5 p5^y + 1/5^y = 5 now replace px + 1/x = 5 times x px^2 + 1 = 5x px^2 - 5x + 1 = 0 which is what we want

calculus
V= (4/3)? r^3 dV/dt = 4? r^2 dr/dt when V = 64 64 = (4/3)? r^3 48/? = r^3 r = (48/?)^(1/3) = appr 2.4814 ---> I stored the 10 decimal answer in dV/dt = 4? r^2 dr/dt 20 = 4?(2.4814..)^2 dr/dt dr/dt = appr .2585 inches/min

Math
You must know the binomial expansion and the general term of the expansion!! 5th term = C(9,4) (4^4)(-x/5)^5 = 126 (256)(-x^5)/3125 = -32256/3125 x^5 oops, just did in descending powers, so C(9,5) 4^5 (-x/5)^4 = 126(1024)(x^4/625) = 129024/625 x^4 , in ascending order

Maths
distance at original speed = (1/4)(60 km = 15 km time at reduced speed = 15/36 hours = 5/12 hr = 25 minutes

Geometry
clearly the largest circle will have a diameter of 4 ft, or a radius of 2 ft area = ?(2^2) = 4? ft^2 = ...... In this time of calculators, using 3.14 for ? and then rounding off that rounded constant is rather silly. Most calculators have a special key for ?, use it.

Maths
correct your spelling and incomprehensible gibberish

Math
Yes, could have been easily checked by taking 20% of it.

Math
regular price ---- x it said the 20% discount came to $15 well, .2x = 15 x = 15/.2 = ......

Aice Math
(5-x/2)^6 I assume you know how to expand using the binomial theorem. (5-x/2)^6 = 5^6 + 5^5(-x/2) + 5^4(-x/2)^2 + ... = 15625 - (3125/2)x + (625/4)x^2 + ... so matching up terms: -3125x/2 = px ----> p = -3125/2 (625/4)x^2 = qx^2 ----> q = 625/4

Math
Using the binomial expansion (x^2-b/x)^4 = (x^2)^4 + 4(x^2)^3 (-b/x) + 6(x^2)^2 (-b/x)^2 + 4(x^2) (-b/x)^3 + (-b/x)^4 = 4x^8 - 4x^6 (b/x) + 6x^4 b^2/x^2 - ... = 4x^8 - 4x^5 b + 6x^2 b^2 - ... so the term containing x^2 is 6x^2 b^2 , which is equal to 294 6v^2 = 294 b^2 = 49 b...

Math
I = PRT you told me I = 1/9P --> P = 9I you told me r = t, where r is a stated percent I = 9I(r/100)(r) 1 = (9/100)r^2 r^2 = 100/9 r = 10/3 = 3.3333.. the rate is 3 1/3% check: suppose we have $1000 for 10/3 years at 3 1/3 % I = 1000(10/3)(10/300) = 111.11 and 1/9 of 1000...

algebra
Compare this question to your previous one. What is your answer ?

algebra
The product of 5 and 6 = 30 the product of 7 and 8 = 56 the product of 31 and g = 31g

Math
Your post makes absolutely no sense to me.

Maths
equation: x^2 - bx + c roots: ?a and ?b sum of roots = ?a + ?b = b product or roots = ?a?b = c --> ab = c^2 ?a + ?b = b square both sides (?a + ?b)^2 = b^2 a + 2?(ab) + b = b^2 then a+b = b^2 - 2?(ab) = b^2 - 2c DONE a^2 + b^2 = (a+b)^2 - 2ab = (b^2 - 2c)^2 - 2c^2 treat ...

correction - Algebra 1
Eddie's answer is not correct after 8 months, x = 8 y = 3(2^8) = 3(256) = 768 or: 3 6 12 24 48 96 192 384 768 now: 3 after 1 month -- 6 ---> 3(2^1) after 2 months -- 12 --> 3(2^2) ... after 8 months -- 768 = 3(2^8)

Math
(w^-2 j^-4) ^-3 (f^7 f^3) = (w^6)(j^12)(f^10)

Math
3 apples + 2 oranges + 2 apples - 1 orange = 5 apples + 1 orange 3x + 2y + 2x - y = 5x + y 3?3 + 2?5 + 2?3 - ?5 = 5?3 + ?5

Ms. Sue! Math
You should know that linear functions can be written in the form y = mx + b , (the y-intercept form), except vertical lines which have the form x = c so let's pick any slope from -1 to 0. How about m = -1/4 Equations with such a slope are y = (-1/4)x + 7 or y = (-1/4)x + 3...

Algebra
Extraneous roots mostly occur after squaring an equation. Since you verified your solution by subbing it back into the original equation, there are no extraneous roots LS = x/(5x+4) = (-6/7) / (5(-6/7) + 4) = (-6/7) / (-2/7) = (-6/7)(-7/2) = 42/14 = 3 = RS

maths equation too hard
you mean Newton's "iterative" method sure, why not? x^3 = 3^x let y = x^3 - 3^x dy/dx = 3x^2 - ln3(3^x) newx= x - (x^3 - 3^x)/(3x^2 - ln3 (3^x) ) start with x = 2.9 newx = appr 3.0471... using that newx = appr 3.0081... using that newx = appr 3.00006996 , not bad

maths equation too hard
Steve did this for you earlier. What did you not like about his reply? http://www.jiskha.com/display.cgi?id=1486532823 You could graph: y = x^3 and y = 3^x and see where they cross

Maths
prob(defect) = .05 prob(no defect) = .95 a) I read that as exactly 10 out of the 100 = C(100,10) (.05)^10 (.95)^90 = appr .0167, according to my calculator b) unreasonable question, you would have to do prob(exactly 0 defective) + prob(1 effective) + ...+ prob(10 defective) If...

Mathematics
case 1: the circumference of the cylinder is 30, and the height is 18 2?r = 30 r = 15/? V = ?(15/?)^2 (18) = 4050/? case 2: the circumference is 18 and the height is 30 2?r = 18 r = 9/? V = ?(9/?)^2 (30) = 2430/? volume of case1 : volume of case2 = 4050/? : 2430/? = 5 : 3 Just...

math
I read that as area = -x^2 + 7x + 30 this has to be positive, so -x^2 + 7x + 30 > 0 x^2 - 7x - 30 < 0 (x - 10)(x+3) < 0 so you know that -3 < x < 10 that is, x must be between -3 and 10 Possible values : let x = 1, then area = -1 + 7 + 30 = 36 the rectangle is 1...

Continuity Calculus Help
limit ?( (x^2 - 64)/(x-8)) as x -->8 = lim ?( (x-8)x+8)/(x-8) , as x ---> 8 = lim ?(x+8) , as x---> 8 = ?16 = 4

Math
I used to illustrate this problem to my students by taking a cone-shaped drinking cup from a water dispenser and cutting it open to show just that kind of a sector. It was easy to see that the arc of that sector becomes the circular base of the cone, so .... since the angle is...

Calculus-derivatives
Bob forgot to find the derivative first dy/dx = 12x + 4 12x+4 = -2 12x = -8 x = -8/12 = -2/3 f(-2/3) = 6(4/9) + 4(-2/3) - 9 = -25/3 We have a parabola shown below with a tangent at (-2/3 , -25/3) having a slope of -2 http://www.wolframalpha.com/input/?i=plot+y%3D6x%5E2%2B4x-9

Math interest
So the interest on your $5000 should amount to $5000 5000(.05)t = 5000 t = 1/.05 = 20 or, interest for 1 year = 5000(.05)(1) = $250 Since that stays constant (simple interest), it would take 5000/250 or 20 years

physics/calculus
h = -16t^2 + 12t + 600 a) sub in t=6 b) set -16t^2 + 12t + 600 = 0 divide by -4 4t^2 - 3t - 150 = 0 use the formula to find t = .... (use the positive answer only) c) v = -32t + 12 plug in your answer from b)

math
father's age ----- x Mark's age ---- x-32 x + x-32 = 72 easy to solve for x

Maths
first term is 3+2a common difference = d = 3+4a - (3+2a) = 2a term(5) = first term +4d = 3+2a + 4(2a) = 73 10a = 70 a = 7 check: d = 14 terms are: 17, 31, 45, 59, 73 all looks good

Math
sum of interior angles of a hexagon = 180(6-2) = 720 , from 180(n-2) 5x + 155 = 720 5x = 564 x = 113°

Maths
taking differences 1 2 1 5 3 2 11 6 3 1 21 10 4 1 the third differences are constant, so we could represent it as a cubic function. Lots of work, so I went to Wolfram: http://www.wolframalpha.com/input/?i=pattern+%7B1,2,5,11,21,....%7D

Algebra
1st term --- a 15th term = a + 14d = 9a 14d = 8a d = 4a/7 sum(35) = (35/2)(2a + 34d) = (35/2)(2a + 34(4a/7) = (35/2)(150a/7) = 375a

Algebra
a=10 a+(n-1)d = 62 10 + nd - d = 62 nd-d=52 n=(52+d)/d or d = 52/(n-1) sum(n) = (n/2)(2a + (n-1)d) = (n/2)(20 + (n-1)(52)/(n-1)) = (n/2)(20 + 52) = (n/2)(72) = 36n sum(n) = 36n so sum(n) varies directly as the number of terms

Math
33750 = 50*25*27 = 2*3*3*3*5*5*5*5 So the question becomes: in how many ways can these digits be arranged We have 8 digits , of which 4 are the same and another 3 are the same number of arrangements = 8!/(3!4!) = 280 e.g. 23535355 would be one of them

Math
please use t^2 to show exponents. the * symbol is traditionally used for a multiplication sign h = -16t^2 + 40t + 3 , note the - sign! dh/dt = -32t + 40 = 0 for a max of h 32t = 40 t = 40/32 = 1.25 seconds when t = 1.25 h = -16(1.25)^2 + 40(1.25) + 3= 28 when it hits the ...

Algebra
3b = a(B + b) 3b = aB + ab 3b - ab = aB (3b - ab)/a = B

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