Thursday
February 11, 2016

Posts by Reiny

Total # Posts: 32,937

maths
15x + 12(10-x) = 141 solve for x to get the amount sold at 15
January 25, 2016

math
volume of block of paper = (11)(8.5)(2) in^3 = 187 in^3 so volume of 1 sheet = 187/500 or .374 inches^3
January 25, 2016

maths
Steve gave you the two equations, so use substitution. y = x + 15 x+y = 275 sub 1st into 2nd x + (x+15) = 275 2x = 260 x = 130 back into y = x+15 y = 130+15 = 145
January 25, 2016

Algebra
yup, the sum of cubes.
January 24, 2016

College algebra
let the distance driven be x km speed on first leg = x/8 speed on return leg = x/8 + 18 km/h = (x + 144)/8 km/h distance/rate = time x/((x+144)/8) = 5 8x/(x+144) = 5 8x = 5x + 144 3x = 144 x = 48 so speed on return trip = (48+144)/8 km/h = 24 km/h
January 24, 2016

algebra
That is an example change to ... x+31 > 5 x > -26 shade in everything to the right of the vertical line x = -26 , draw the line as a dotted line.
January 24, 2016

math
or, using the compound interest formula (1 + i)^74 = 3 , where i is the quarterly rate take 74th root of both sides 1+i = 1.01495.. i = .01495.. annual rate compounded quarterly = 4(.01595..) = .0598 or 5.98%
January 24, 2016

trig
My triangle has sides 60 , 20 and 50 km and I am finding the angle opposite the side of 50 by cosine law: 50^2 = 20^2 + 60^2 - 2(20)(60)cosØ cosØ = .625 Ø = appr 51.3°
January 24, 2016

oops - Calculus
go with Damon's I really don't know how my 1/√2 became 1/√3
January 24, 2016

Calculus
I recognize this as Lim ( 1/3 - 1/√x)/(x-9) , as x -->9 But for yours x --->2 Most teachers would tell you that the first step in any limit question is to actually sub in the restricted value into your expression. If you get 0/0, then you have some work to do If ...
January 24, 2016

Math
This is pretty "advanced" stuff Your nail traces out a cycloid, the equation of that path can be written as parametric equations x=r(t−sint) y=r(1−cost) , where t is the angle of rotation, and r is the radius What level of math is this ? http://mathworld....
January 24, 2016

maths
(1/2)(12)height = 38.8 height = 97/15 or 6.466.. assuming your base is BC sin 54° = height /AC AC = height/sin54° take over
January 24, 2016

ggggg
smallest angle --- x one of the others --- 2x third angle = x+2x = 3x thus: x + 2x + 3x = 180 carry on
January 24, 2016

MTH
Did you mean (x+y)^25 ? Do you really expect me to write out all 26 terms ? What is "the porem" ?
January 24, 2016

correction - math
So you have two ordered pairs: (30,2) and (50,6) slope = (6-2)/(50-30) = 4/20 = 1/5 equation: y-2 = (1/5)(x-30) 5y - 10 = x - 30 x - 5y = 20 ----> that's your relationship then if y = 3, x - 15 = 20 x = 35
January 24, 2016

maths
r = 6/(3-x) OR r = (7-5x)/6 6/(3-x) = (7-5x)/6 21 - 15x - 7x + 5x^2 = 36 5x^2 - 22x - 15 = 0 (x - 5)(5x + 3) = 0 x = 5 or x = -3/5 so the common ratio could be 6/3-5) = -2 or 6/(-3/5) = -10 if r = -2, we have -3 + 6 - 12 = -9 if r = -10 , we have -5/3 + 6 - 60 = - 167/3 check ...
January 24, 2016

math
let f(x) = ax + b then f(f(x)) = a(ax+b) + b = a^2 x + ab + b so a^2 = 64 ---> a = ±8 then ab+b=-21 b = -21/(a+1) if a=8 , b = -21/9 = -7/3 if a = -8, b = -21/-7 = 3 f(x) = 8x - 7/3 OR f(x) = -8x + 3 check: if f(x) = -8x + 3 f(f(x)) = -8(-8x+3) + 3 = 64x - 21 if f(x...
January 24, 2016

Math
let the annual rate be i 1+i = (1 + .024/12)^12 = 1.02426 i = .02426 or 2.426 % per annum The difference would be more significant for higher rates of interest.
January 24, 2016

math
I am the one that gave you the answer in your previous post. I am just using the formula for compound interest. Have you learned about compound interest?
January 24, 2016

math
Since we are "doubling" it is easy to use a base of 2 amount = a(2)^(t/1) = a (2)^t , where t ≥ 0, and t=0 ---> now after 1 day we have 2a after 3 days , we have a(2)^3 or 8a after 1 week , we have a(2)^7 = 128a normally we would use base e here we have ...
January 24, 2016

math
assuming your rate is compounded annually, what is 87000(1.045)^8 ?
January 24, 2016

Maths
My money is on Steve's correct answer.
January 24, 2016

Math
Did you make a sketch? The area reached by the horse is 1/4 of a circle with original radius of 6 m that area = (1/4)π(36) = 9π m^2 after lengthening of rope, r = 11.5 m new area for grazing = (1/4)π(11.5)^2 m^2 = 33.0625π m^2 So what is the increase in area ?
January 24, 2016

math
Filling in the given information in a Venn diagram, I got 8 taking all three subjects 7 taking only Chemistry 6 taking only Biology These were the only ones that required calculations, the rest were given. Adding up all the entries in the Venn diagrams only comes to 44, thus ...
January 24, 2016

@ shredder - Maths
Simply stating the answer serves the student no purpose.
January 24, 2016

probstats
number of possible codes = 9x10x10x10x10 = 90000 number starting with 7 and ending in 8 = 1x10x10x10x1 = 1000 prob(your event) = 1000/90000 = 1/90
January 24, 2016

math/trigo
Again, my money is on Steve's answer.
January 24, 2016

math
Make a sketch showing the trapezoid in a side view. Volume = (area of trap) x 8 = (13(2 + h)/2)(8) = 52(2+h) = 286 104 + 52h = 286 h = .....
January 24, 2016

arthmetic sequence
by definition: a+2d = 14 a+8d = -1 subtract ... 6d = -15 d= -5/2 then a+2(-5/2) = 14 a = 19 first 4 terms are 19, 33/2 , 14 , 23/2
January 23, 2016

math
by the cosine law: AC^2 = 8^2 + 24^2 - 2(8)(24)cos60° = 448 AC = √448 = 8√7 now by similar triangles: DE/8√7 = 6/8 DE = 48√7/8 = 6√7
January 23, 2016

Algebra
I agree with Bob
January 23, 2016

Related Rates
from your V= (1/3)π(r)(r)(h) , but r = h V = (1/3)π h^3 dV/dt = π h^2 dh/dt plug in the values .... 10 = π(25) dh/dt dh/dt = 10/(25π) = 2/(5π) I have no idea how you got your derivative.
January 23, 2016

Math
I will let you count the days --- d I = PRT = 4500(.08)(d/365)
January 23, 2016

Maths
that is .... 3000 cm = 30 m you wouldn't measure road distance in cm .
January 23, 2016

math
I am sure you made a sketch. Let the length of his shadow be x By similar triangles..... x/2 = (x+5)/6 6x = 2x+10 carry on
January 23, 2016

Math
amount of mortgage before raise = .23(6000) = 1380 after raise, rate = 1380/6500 = .2123 or appr 21.2%
January 23, 2016

NO - Maths
This is an inverse relation, not a direct proportion i.e. the more artists, the lesser the time "It takes 3 artists 24 days to paint a building" ---> 72 artist-days for 72 artist-days / 6 artists = 12 days
January 23, 2016

algebra
done when you posted this under a different name. look at your other post.
January 23, 2016

Algebra
What part of my solution to the same question did you not like ? http://www.jiskha.com/display.cgi?id=1453557228
January 23, 2016

algebra
just did it, look back
January 23, 2016

algebra
Your first question makes no sense your second: Tn = a + bn T6 = a + 6b = 22 T13 = a + 13b = 71 subtract them 7b = 49 b = 7 a+6b=22 ---> a + 42 = 49, a = 7
January 23, 2016

math
In triangle DRA, draw an altitude DK where K is on RA, to get a 30-60-90° triangle and you should know that the corresponding sides are in the ratio 1 : √3 : 2 So RK/(6√2) = √3/2 x = 3√6 then RA = 6√6 and the perimeter is 24√6
January 23, 2016

maths
rate of smaller tap = 1/45 tanks/min rate of larger tap = 1/30 tanks/min combined rate = (1/45 + 1/30) tanks/min = 1/18 tanks/min time at combined rate = 1/(1/18) min = 18 minutes
January 23, 2016

math
radius of flower bed --- r m 2πr = 66 r = 33/π radius of whole thing = 4+33/π area of whole thing = π(4+33/π)^2 area of flower bed =π(33/π)^2 subtract the two areas to get the area of the path. you do the arithmetic
January 23, 2016

maths
"product" is the result of a multiplication So if the product of 2 numbers is zero, one of them must have been zero since the difference is 6 , the other number must have been 6 Only choice possible for your number : 60
January 23, 2016

math
done ,see you other post
January 23, 2016

Algebra
the way you typed it: (x-2)+1/x+1=2/3 x-2 + 1/x + 1 = 2/3 x + 1/x -1 - 2/3 = 0 times 3x 3x^2 + 3 - 3x - 2x = 0 3x^2 - 5x + 3 = 0 x = (5 ± √-11)/6 no real solution You probably meant: x- 2 + 1/(x+1) = 2/3 times 3(x+1) 3x(x+1) - 6(x+1) + 3 = 2(x+1) 3x^2 + 3x - 6x - ...
January 23, 2016

Maths
my number is x result1 = 8x + 15 result2 = 2x + 81 so 8x + 15 = 2x + 81 can you solve this equation ? test your answer.
January 23, 2016

math
Surely for the 2nd equation Akbar must have meant: 2^(x+2)+3^(y+1)=5 or else why not just add up those constants. (2^2)(2^x) + 3(3^y) = 5 let a = 2^x and let b = 3^y, then we can reduce our equations to ... a+b = 17 4a + 3b = 5 first one by 3 3a + 3b = 51 4a + 3b = 5 a = -46 b...
January 23, 2016

Algebra
did you sub in the point ?
January 22, 2016

math help pls pls
actually it would be all the points above and including the line y = -3x+10 http://www.wolframalpha.com/input/?i=plot+y+%E2%89%A5+-3x%2B10+
January 22, 2016

Math
where are your choices so we can check ?
January 22, 2016

check this - math
Or using a property of quadratic roots: for ax^2 + bx + c = 0 if p and q are the roots p+q = -b/a qp = c/a so for the given equation: p+q = -6/-2 = 3 pq = -7/2 a) for new equation: roots are p/q and q/p sum = p/q + q/p = (p^2+q^2)/(pq) = ( (p+q)^2 - 2pq)/(pq) = (9 - 2(-7/2...
January 22, 2016

Algebra 2 pt 2
Damon did this for you here: http://www.jiskha.com/display.cgi?id=1453466988
January 22, 2016

5th grade math
The value of the 9 in 794256 is 9x10,000 or 90,000 the value of 9 in 12,276,459 is 9x1 and 90000/9 = 10,000 so isn't it 10,000 times the value ?
January 22, 2016

Math
width -- x length -- 3x so x^2 + (3x)^2 = (6√10)^2 10x^2 = 360 x^2 = 36 x = 6 finish it up
January 21, 2016

Algebra
Why not just translate all that English into Math Katie --- x Harry --- x+4 Rachel --- 2(x+4) x + x+4 + 2(x+4) = 36 take over
January 21, 2016

math
since the denominator can never equal to zero and it contains no square roots or other strange operators, domain : x ∊ R I like the "old fashioned" format I used, I always have to look up this "interval notation stuff" I will let you write it your way.
January 21, 2016

Math
f(1) = 1^3 - 3 = -2 f(1+h) = (1+h)^3 - 3 = 1 + 3h + 3h^2 + h^3 - 3 = h^3 + 3h^2 + 3h - 2 avg rate of change = (h^3 + 3h^2 + 3h - 2 + 2)/(1+h - 1) = (h^3 + 3h^2 + 3h)/h = h^2 + 3h + 3 , h ≠ 0
January 21, 2016

Calculus
f(t) = 1/t f(1) = 1 ( 1/t - 1)/(t-1) = 14 , where t ≠ 1 1/t - 1 = 14t - 14 times t 1 - t = 14t^2 - 14t 14t^2 - 13t - 1 = 0 (14t + 1)(t - 1) = 0 t = -1/14
January 21, 2016

Calc
why did you doubt it ?
January 21, 2016

Calc
f(2.01) = √9.03 f(2) = √9 avg rate of change = (√9.03 - √9)/(2.01-2) = .... I get .49958..
January 21, 2016

math
5cm --- 1 km 5 cm --- 1000 m 1 cm --- 200 m what is 250(1.2) ? what is 8(3.25)(4) ?
January 21, 2016

math
Study the reply I just made to Nina and see how critical brackets are. http://www.jiskha.com/display.cgi?id=1453394669 btw, your question factors nicely. Hint: If we want the denominator to cancel wouldn't we expect 2x-5 to be one of the factors of the top?
January 21, 2016

math
I assume you meant: (x^2 - x - 6)/(2x-6) and I assume you want it simplified. = (x-3)(x+2)/(2(x-3)) = (x+2)/2 , x ≠ 3
January 21, 2016

Math
f(1) = 7(1)^2 = 7 f(A) = 7A^2 avg rate of change = (7a^2 - 7)/(a-1) (7a^2 - 7)/(a-1) = 84 7a^2 - 7 = 84a - 84 7a^2 - 84a + 77 = 0 a^2 - 12a + 11 = 0 (a-11)(a-1) = 0 a = 11 or a = 1, but we have to reject a = 1 or else we would be dividing by zero A =11 check: f(11) = 7(121) = ...
January 21, 2016

algebraic fractions
The way you typed it ..... 8/4x-4 = 2x - 4 if you meant: 8/(4x-4) = 8/(4(x-1)) = 2/(x-1) , x≠1
January 21, 2016

algebra
her brother --- x Archie ------- x+12 four years from now: brother = x+4 Archie = x+12 + 4 = x+16 x+4 = (2/3)(x+16) solve for x and sub into original definitions
January 21, 2016

College Calc
find the time taken to go from A to B (220/55) hrs find the time from B to C add up the times divide (total distance/total time) editorial: This is College Calculus???
January 21, 2016

algebra
let the unit be be x then the tens digit is x+2 let the hundreds digit by y x + x+2 + y = 14 2x + y = 12 number: 100y + 10(x+2) + x = 100y + 11x + 20 number reversed: 100x + 10(x+2) + y = 110x + y + 20 but they are to be equal 100y + 11x + 20 = 110x + y + 20 99y = 99x y = x ...
January 21, 2016

Math
since g(x) = x, f(g(x)) = f(x) = sinx
January 21, 2016

math
for a 18 month period, the last term is 18 and the sum is 1+2+3+...+18 ( ----> sum(n) = n(n+1)/2) = 18(19)/2 = 171 Do the others the same way. I recall this rule as something we taught way back in the 60's Here is a challenge for you: Phone any bank, mortgage company, ...
January 21, 2016

maths
by definition term8 = a + 7d sub in our data 3 + 7d = 31 7d = 28 d = 4
January 21, 2016

maths
Area of trap = (1/2)(a+b)(h) where a and b are the two parallel sides and h is the height between them you have one missing unknown, just plug everything in, and solve
January 21, 2016

algebra
so she paid 3/4 of the original. solve (3/4)x = 42
January 21, 2016

trigonometry
You will need brackets to establish the proper order of operations. e.g , the way you have it, the cos^3 Ø would be divided by sinØ, but it probably is divided by (sinØ + cosØ) etc.
January 21, 2016

trigonometry
I just googled your question after fixing the typo, and found all kinds of results. Here is just one of them: http://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.703828.html let Google be your friend
January 21, 2016

trigonometry
tan 3Ø = tan (2Ø + Ø) = (tan 2Ø + tanØ)/(1 - tan 2Ø tanØ) and tan 2Ø = 2tanØ/(1 - tan^2 Ø) let x = tanØ for ease of typing then tan 3Ø = (tan 2Ø + x)/(1 - xtan 2Ø) = ( (2x/(1 - x^...
January 21, 2016

math
treat the 2 as one item, so you are arranging 5 which is 5! but the two students could be interchanged, so number of ways to seat the students = 2(5!) = ...
January 21, 2016

Math
If you want f(g(x)), then .. = f(3-x) = 2^(3-x)
January 21, 2016

math
Did you make a sketch? Shade in the area not reached by the horse The area reached by the horse is 1/4 of a circle with radius of 7 m that area = (1/4)π(49) = 12.25π m^2 Area of the whole square = 100 m^2 So .....
January 21, 2016

math
looks like the x was decreased by 5, and the y was bumped up by 8, so (x,y) ---> (x-5, y+8)
January 20, 2016

math
In the scale drawing, each side is 10 cm , (10^2 = 100) if 1 cm ---> 2 ft then 10 cm ---> 20 ft area of real floor = 20^2 ft^2 = 400 ft^2
January 20, 2016

maths
1. In your GP, a = 2, r = 2 sum(n) < 1500000 a(r^n - 1)/(r-1) > 1500000 2(2^n - 1)/(2-1) > 1500000 2^n - 1 > 750000 2^n > 750001 take log of both sides , and use log rules n log2 > log 750001 n > log 750001/log2 n > 19.5 at n = 19 we won't be there...
January 20, 2016

Finance 101
Time to get a more up-to-date textbook. 10% mortgage?? anyway... monthly rate = .10/12 = .008333... (store in your calculator) n for 5 years = 60 n for 30 years = 360 monthly payment at original rate -- P P(1 - 1.008333...)^-360)/.0083333 = 150000 P = 1316.36 amount if no ...
January 20, 2016

Math
The leg will be the hypotenuse of a right-angled triangle with base 2x and height 6 H^2 = 4x^2 + 36 H = √(4x^2 + 36) = 2√(x^2 + 9)
January 20, 2016

Math
David's marbles --- x Sam's marbles -----x After Sam lost his marbles: Sam --- x-50 David -- x+50 x+50 = 5(x-50) x+50 = 5x - 250 -4x = -300 x = 75 they had 75+75 or 150 marbles between them Your previous post contains the "same" question, just the numbers and...
January 20, 2016

Math
John --- x yrs Mary --- 2x yrs Bob --- 4x yrs in 22 years from now: John: x+22 Mary: 2x+22 bob: 4x+22 4x+22 = 2(x+22) 4x+22 = 2x + 44 2x=22 x=11 So Mary is now 22
January 20, 2016

probability and statistics
Since you state no restriction, I will assume that the plate can start with a 0 first let's select our plate: number of selections = C(2,2) C(4,3) = 4 then each of those can be arranged in 5! ways. number of possible arrangements = 4(5!) = 480
January 20, 2016

Pre-Calc
confirmation by Wolfram: http://www.wolframalpha.com/input/?i=simplify+sin%28arcsinx+%2B+arccosx%29
January 19, 2016

Pre-Calc
arcsinx is an angle Ø so that sinØ = x/1 = x arccosx is an angle Ø so that cosØ = x/1 thus sinØ = cosØ and Ø = 45° sin(arcsinx + arccosx) = sin(45° + 45°) = sin 90° = 1
January 19, 2016

Pre-Calc
secx(sinx/tanx) = (1/cosx)(sinx)(cosx/sinx) = 1
January 19, 2016

algebra
let Jimmy's rate be 1/x Jack's rate = 1/10 combined rate = 1/x + 1/10 = (x+10)/(10x) 1/( (x+10)/(10x) ) = 4.44 10x/(x+10) = 4.44 10x = 4.44x + 44.4 5.56x = 44.4 x = 7.9856 Jimmy alone would take 7.99 hrs or appr 8 hrs combined rate = 1/10 + 1/8 = 9/40 time at combined ...
January 19, 2016

math-linear equations
h + c = 340 h = c + 52 sub the second into the first: h + c = 340 c+52 + c = 340 2c = 288 c = 144 then h = 144+52 = 196 So 144 cows and 196 horses
January 19, 2016

Math
Did not check if the ordered pairs satisfy, but 6x + 10y ≥ 120 is the only correct inequality.
January 19, 2016

Math
2 years ago you were x 2 years ago your mom was 4x 18 years from now, you will be x+20 18 years from now, your mom will be 4x+20 x+20 = (1/2)(4x+20) x+20 = 2x + 10 10 = x 2 years ago, you were 10, your mom was 40 you are now 12, your mom is now 42 check: 2 years ago you were ...
January 19, 2016

math
the number should look like this (x+1)x9 "Those two numbers equal 11" Did you mean that their sum is 11? I will assume thus. x+1 + x = 11 x = 5 your number is 659
January 19, 2016

math help
let y = 2x^4 - 3x^2 - 7x + 1 y ' = 8x^3 - 6x - 7 newx = x - y/y' = x - (2x^4 - 3x^2 - 7x + 1)/(8x^3 - 6x - 7) =(6x^4- 3x^2 - 1)/(8x^3 - 6x - 7) x = 1.75 newx = 1.8162 ---> x newx = 1.8111 ---> x newx = 1.811102 I would call 1.8111 a good estimate
January 19, 2016

Maths
a+6d=11 a+(n-1)d=3 subtract them: 6d - (n-1)d = 8 6d - nd + d = 8 7d - nd = 8 d = 8/(7-n) , it should be noted that n ≠ 7 back in the 1st: a + 48/(7-n) = 11 a = 11 - 48/(7-n) = (77 - 11n - 48)/(7-n) = (29 - 11n)/(7-n) so the terms are: (29 - 11n)/(7-n) , (37 - 11n)/(7-n...
January 19, 2016

math
tan^2 x = 3 tan x = ±√3 we know tan 60° = √3 so x = 60° , 120° , 240° or 300° or in radians x = π/3, 2π/3, 4π/3, or 5π/3
January 19, 2016

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