Wednesday
June 29, 2016

Posts by Reiny

Total # Posts: 35,090

math
original fraction : x/y new fraction : (.5x)/(.75y) = (2/3) (x/y) so the new fraction is 2/3 of the old one, thus it was decreased by 1/3
April 30, 2016

math
According to your wording: - you wanted the percentage increase , so my answer is correct 3.5/.432 = 8.102 so the new price is 810% of the old one, but the increase is 710% e.g. suppose the cost of a coat went from $100 to $120 so it increased by 120%, but the percentage ...
April 30, 2016

math
number of dozen in the bucket = 450/12 = 37.5 so cost price per dozen = 16.20/37.5 = .432 So they bought them at $ 0.432 per dozen and sold them at $3.50 per dozen percentage increase = 3.5/.432 - 1 = 7.102 or 710%
April 30, 2016

consumer math
I will assume you are using compound interest and the monthly rate is .13/12 or i = .0108333... n = 15 payment = p p( 1 - 1..0108333..^-15)/.0108333... = 1380 I get p = 100.17
April 30, 2016

Maths
I see that you corrected your post, and inserted a time of 2 hours So go back to my previous reply to the same question, replace t with 2 and repeat the steps. (or just plug t=2 into my answer for x)
April 30, 2016

Maths
"how far are apart" ? After what time ? Let the time passed since they left be t hours My diagram shows a triangle with sides 5t and 7.5t and an angle of 134° between those sides. If the distance between them is x, by the cosine law: x^2 = (5t)^2 + (7.5t)^2 - 2(...
April 30, 2016

Calculus
Make a sketch and draw in the rectangle. Let the top-right point be P(x,26-x^2) and the bottom-right point be Q(x, x^2 + 2) So the width of the rectangle is 2x and the height is 26-x^2 - x^2 - 2 = 24 - 2x^2 area = 2x(24-2x^2) = 48x - 4x^3 d(area)/dx = 48 - 12x^2 = 0 for a max ...
April 29, 2016

Math
2x - 1 = x+3 x = 4 , then y = 7 the solution is (4,7) which is not listed The wording is poor. "No solution" implies that there is no answer to our intersection, but there is! It should have said "none of the above"
April 29, 2016

Algebra
let's rephrase the question. For what values of k will the quadratic x^2 - kx + k^2 = 0 have 2 solutions when b^2 - 4ac > 0 k^2 - 4(1)(k^2) >0 -3k^2 > 0 k^2 < 0 any number squared is always positive, so there is no value of k for which the graph will cross the ...
April 29, 2016

Geometry
cosine law: DE^2 = 70^2 + 50^2 - 2(70)(50)cos54° = .. carry on
April 29, 2016

math
number of men --- x number of men --- 3x men wearing glasses = (3/5)x number of women wearing glasses = (1/3)(3x) = x x - (3/5)x = 120 times 5 5x - 3x = 600 2x = 600 x = 300 people at concert = x + 3x = 4x = 1200
April 29, 2016

College Algebra
#1 4 - 3(x+1) = 2x 4 - 3x - 3 = 2x -5x = -1 x = -1/-5 = 1/5 #2 15x^2=x=2 , assuming you meant 15x^2 + x=2 since the = and + sign are on the same key 15x^2 + x - 2 = 0 which factors to (3x-1)(5x+2) = 0 x = 1/3 or x = -2/5 by formula: x = (-1 ± √121)/30 = 1/3 or -2/...
April 29, 2016

@Steve
Thanks Steve Had an inkling thats what he was doing, but then it was contradicted in how he worked the last one. btw, was it overkill in my solution to http://www.jiskha.com/display.cgi?id=1461944692 Almost gave up on it, but found some clues on a webpage.
April 29, 2016

College Algebra/pre-calculus
#1 How did you get -2 ?? log 6^(1/36) = (1/36) log 6 = appr .0216 #2 ln(1/e^4) = ln1 - ln e^4 = 0 - 4lne = 0 - 4(1) = -4 #3 log 7^1 = log 7 = appr .845 #4 log 4^64 = 64 log4 = appr 38.532 #5 log 10^8 = 8log10 = 8 #6 --- the only one you got right
April 29, 2016

Trigonometry
One of my all-time favourite topics in Math is the Golden Ratio of (1 + √5)/2. I happen to know that cos 36° = (1+√5)/4 Notice also that in a regular pentagon , we have interior angles of 108° , and if we draw in some diagonals, we have all kinds of 36, 72 ...
April 29, 2016

Math
When they meet, they both would have traveled the same time. Let that time be t hrs so 60t + 80t = 210 140t = 210 t = 1.5 hrs take over
April 29, 2016

algebra
given: 8l = 15w then w = 8l/15 Perimeter = 2l + 2w 2l + 2(8l/15) = 230 times 15 30l + 16l = 3450 46l = 3450 l = 75 then w = 8(75)/15 = 40 the yard is 40 ft by 75 ft check: is 15(40) = 8(75) ??? YES is 2(40) + 2(75) = 230 ?? , YES
April 29, 2016

Math
Your question makes no sense. Must be reach a certain amount before withdrawing?
April 29, 2016

Math
correction: on this good earth of ours the equation would be h(t) = -16t^2 + 35t + 1 I assume you had a typo. the t of the vertex (instead of the normal x) = -b/2a = -35/-32 so h(35/32) = -16(35/32)^2 + 35(35/2) + 1 = appr 20.14 (exact answer is 1289/64)
April 29, 2016

College Algebra Help?!
number of choices = C(20,2) x C(32,2) = 190(496) = 94240 ways
April 29, 2016

Math (Probability)
1) prob(r,r) = (12/20)(8/13) = 24/65 ----> B 2) prob = (6/20)(2/19) = 3/95 ----> C 3) you want (1/2)^12 = 1/4096 ----> A
April 29, 2016

Algebra
So we need the vertex of the parabola h(t) = -16t^2 + 293t + 7 the t of the vertex is -b/(2a) = -293/-32 = 293/32 seconds or in 9.15625 seconds plug that into h(t) = ... = appr 1348.4 ft your next two questions have just been answered
April 29, 2016

sails math
amount of the 70% solution --- x L amount of the 45% solution--- 300-x L .70x + .45(300-x) = .65(300) time 100 70x + 45(300-x) = 65(300 70x + 13500 - 45x = 19500 25x = 6000 x = 240 So 240 L of the 70% stuff, and 60 L of the 45% stuff check: .7(240) + .45(60) = 195 .65(300) = ...
April 29, 2016

alg
f(x) = 4(x^2 - 6x + 9 - 9) + 20 = 4( (x-3)^2 - 9) + 20 = 4(x-3)^2 - 36 + 20 = 4(x-3)^2 - 16
April 29, 2016

math
1. π --- irrational √3 --- irrational √2 --- irrational 1.333.... = 4/3 ---- Rational 2. If n is your symbol for π then your choice if a) is correct
April 29, 2016

math
yes, notice that 300, 400, and 500 is simply a multiple of 3,4, 5 3,4,5 would form the smallest right-angled triangle with integer sides.
April 29, 2016

math
Just good ol' Pythagoras .... L^2 = 300^2 + 400^2 L = .....
April 29, 2016

Math Help
Wolfram shows that x = -π/12 and π/36 are intersection values and the region forms a closed area. area = ∫(cos 12x - sin 6x) dx from -π/12 to π/36 = (1/12)sin 12x + (1/6)cos 6x | from -π/12 to π/36 = .. take over
April 29, 2016

Error - Geometry
This question makes no sense. You don't have a right-angled triangle , since 6^2 + 4^2 ≠ 7^2 from sinA = 6/7 , A = appr 59° from cosA = 4/7, A = appr 55° Which one is it ?
April 29, 2016

math
avg vel = total distance / total time find the time from 2:00 pm to 5:45 pm, write it as a decimal and go for it.
April 28, 2016

Algebra
ummmhh, if the points don't form a straight line, then the function is not linear.
April 28, 2016

math
I don't see any choices. y = 2x^3 - 4x + 1 dy/dx = 6x^2 - 4 at x = -1, dy/dx = 6-4 = 2 y = -2 + 4+1 = 3 so we have slope = 2, point is (-1,3) equation of tangent: y - 3 = 2(x + 1) dress it up to whatever form you need.
April 28, 2016

math
those codes don't work here, I read that as: C(x) = x^2 + 2 R(x) = 2x^2 - x equate them: 2x^2 - x = x^2 + 2 x^2 - x - 2 = 0 (x-2)(x+1) = 0 x = 2 or x = -1 if x=2, y = 6 if x = -1, y = 3 you had (2,-6) , don't see how you got y = -6 C(x) can never be negative, you are ...
April 28, 2016

geometry
Assuming that the peak of the house is in the centre of the width. tanØ = 40/15 = 8/3 Ø = appr 69°
April 28, 2016

Math
since both are expressed as y = ... we can equate them: x^2 + 2x = 3x + 20 x^2 - x - 20 = 0 (x-5)(x+4) = 0 x = 5 or x = -4 if x = 5, y = 3(5) + 20 = 35 if x = -4, y = 3(-4) + 20 = 8 x=5, y = 35 x = -4, y = 8 check: http://www.wolframalpha.com/input/?i=solve+y%3Dx%5E2%2B2x,++y%...
April 28, 2016

Alias robert
a = 2 v = 2t + c, where t is in seconds when t=0, v = 0 , (it started from rest) 0 = 0 + c, c = 0 v = 2t s = t^2 + k when t = 0, s = 0 , (hasn't gone anywhere) after 10 seconds v = 20 m/s s = 100 m now goes for 20 s, at 20 m/s, covering 400 m so it can covered 500 m, and ...
April 28, 2016

Algebra
In a multiplication of a number and a variable, we write the variable last, so Cost = 2a + 4c
April 28, 2016

math
done, look back at your other post
April 28, 2016

math
Assuming people are sitting on the ice while the Rangers are losing, .... area = π(202)^2 ft^2 = 40,804π ft^2 number of square ft per spectator = 40804π/20234 = appr 6.34 ft^2
April 28, 2016

Math
let the original amount be x he spent 3x/8, leaving him with 5x/8 he spends half of that , leaving him with 5x/16 5x/16 = 6.25 5x = 100 x = 20 He started with $20.00 check: he spends (3/8)(20) or $7.50, leaving him with $12.50 He has 1/2 of that left or (1/2)(12.50) = $6.25 My...
April 28, 2016

math
no, you have to use trig, or else know that the ratio of sides of the 30-60-90 triangle is 1:√3:2 So if the short side is 2, the sides are: 2 : 2√3 : 4 or make a sketch, mark the shortest side adjacent to the 60° angle as 2 and the hypotenuse as h cos60° = ...
April 28, 2016

Math
The product of distance x mass on both sides of the fulcrum must be the same, so 100d1 = 10d2 10d1 = d2
April 28, 2016

centimeter dot grid
Here is page full of printable graphpaper, many of which are metric. https://images.search.yahoo.com/search/images;_ylt=AwrB8qEruSJXTCoAA2KJzbkF;_ylu=X3oDMTBsZ29xY3ZzBHNlYwNzZWFyY2gEc2xrA2J1dHRvbg--;_ylc=...
April 28, 2016

Math
integral 10x/(x^2 + 1) dx from 0 to 5 = 5ln(x^2 + 1) | from 0 to 5 = 5ln 26 - 5ln1 = 5 ln 26 - 0 = 5 ln 26
April 28, 2016

math
PV = ?? Amount = 12500 i = .12/4 = .03 n = 4(12) = 48 PV(1.03)^48 = 12500 PV = 12500/1.03^48 = 3,024.99
April 28, 2016

Plz do help..GEOMETRIC SEQUENCES
You are looking at a GS with a = 32000 r = 1.04 term(n) = a r^(-1) term(n) = 32000(1.04)^(n-1) 32000(1.04)^(n-1) = 40000 1.04^(n-1) = 1.25 take logs of both sides and use log rules (n-1)log1.04 = log1.25 n-1 = log1.25/log1.04 = 5.689 n = 6.689 The question does not say when ...
April 28, 2016

Algebra
brackets are essential here don't you want to say x ≠ instead of x = ??? A 1/(6-x) , x ≠ 0,6 2nd one: 5(7+x) , x ≠0,-7 ----> choice A
April 28, 2016

Math
length = area/width = (2/3) / (1/2) = (2/3)(2/1) = 4/3 km check area = (4/3)(1/2) = 4/6 = 2/3 all is good
April 28, 2016

,math
let y = x^2 + 10x + 12 = (x^2 + 10x + 25 - 25) + 12 = ( (x+5)^2 - 25) + 12 = (x+5)^2) - 25 + 12 = (x+5)^2 - 13 we have found the vertex to be (-5,-13), which for a parabola would be the turning point.
April 28, 2016

maths
number of children -- c number of sweets per child -- s sc = 60 or c = 60/s 2nd scenario: number of sweets per child = s-1 (s-1)(c+2) = 60 sc+ 2s - c - 2 = 60 60 + 2s - c - 2 = 60 2s - c = 2 2s - 60/s = 2 2s^2 - 60 = 2s s^2 - s - 30 = 0 (s+5)(s-6) = 0 s = 6 or s is a negative ...
April 28, 2016

8th grade math - system of equations
#23 The larger number is three more than the smaller ---- l = s + 3 you had "the larger is 3 times the smaller" l - s = 3 l + s = 27 add them 2l = 30 l = 15 and 15+s= 27 s = 12 24. 5% ---> .05, so .05x + .09y = 380 multiply by 100 5x + 9y = 38000 ** first equation...
April 27, 2016

algebra
larger x smaller y x+y = 83 x - 3y = 19 subtract them: 4y = 64 y = 16 , then x = 67 larger is 67, the smaller is 16
April 27, 2016

matc
The $5,500 is irrelevant, all you want is the annual rate equivalent to 6% per annum, compounded monthly let that annual rate be i 1+i = (1 + .06/12)^12 1+i = 1.005^12 = appr 1.06168 the equivalent annual rate is 6.168 %
April 27, 2016

algebra, how to do fractions?
Don't let the fractions scare you .... slope = (15/32 - 1/4)/(5/8 - 1/3) = (15/32 - 8/32)/(15/24 - 8/24) = (7/32) / (7/24) = (7/32)(24/7) = 3/4 so y - 15/32 = (3/4)(x - 5/8) y - 15/32 = (3/4)x - 15/32 times 32 32y - 15 = 24x - 15 24x - 32y = 0 3x - 4y = 0
April 27, 2016

math
1(1.045)^n = 3, where n is the number of half-years. using logs ... n log 1.045 = log 3 n = log3/log1.045 = 24.95888 or 25 half-years. I would say 12.5 years.
April 27, 2016

PreCalc
when t=0 , temp = 35 when t = 12, temp = 50 Period = 24 hours or k = π/12 how about Temp = 7.5cos (π/12)(t + 12) + 42.5 check: when t = 0, Temp = 7.5cos(π) + 42.5 = 35 when t = 12, Temp = 7.5cos(2π) + 42.5 = 50 You try it with a sine curve, be aware that ...
April 27, 2016

prealgebra
#1, ok #2 .245 = 24.5% , move decimal 2 places to right, tag on the % sign #3 28% = .28 = 28/100 = 7/25, so C #4 .367 -----> .367 36.5% --- > .365 9/25 -----> .36 so what do you think?
April 27, 2016

Probability
prob = (18/30)(17/29) = 51/145 = appr .352
April 27, 2016

MATH PLS HELP
I can't quite see your work for this assignment.
April 27, 2016

Trig
h/23 = tan 40 h = 23tan40 = ....
April 27, 2016

Math
Logy=1/3(logx-log27) logy = 1/3 log (x/27) log y = log (x/27)^(1/3) antilog it y = (x/27)^(1/3) or y = (1/3)x^(1/3)
April 27, 2016

math
Just translate it to Math 2(x+7) < x by 19 2x + 14 = x-19 x = -33 check: add 7 to -33 ---> -26 double it -----> -52 19 less than the number = -33-19 = -52 YEAH
April 27, 2016

math
a = 1.6 b = 2 c = 2.5 x = (-b ± √(b^2 - 4ac)/(2a) (you MUST memorize this formula) x = (-2 ± (√(4 - 4(1.6)(2.5))/3.2 = (-2 ± √-12)/3.2 This is a complex or imaginary number, so there is no REAL solution. Is that your problem? Have you ...
April 27, 2016

pre-calculus
so arccos(?) is an angle, so let arcos(x/2) = θ that means cosθ = x/2 that is cosθ = adjacent / hypoenuse = x/2 so we are looking at a right-angles triangle with angle θ, adjacent = x, hypotenuse =2 Make a sketch, then x^2 + y^2 = 4 y^2 = 4-x^2 y = √(...
April 27, 2016

Math
let the initial population be 1 or 100% after 10 years: pop= 1(2)^(-10/7) = .3715 or 37.15%
April 27, 2016

Help Steve or Damon, Solid Mensuration
Am I overthinking this ???? volume of water in cylinder being upright = π(2^2)(41/12) inches^3 , (arrhhhg -- non-metric units) = (41/3)π in^3 Now lay it on its side, and make a diagram of the cross section Shade in the water which is a segment of the circle, label ...
April 27, 2016

calculus
How does this question relate to your two previous questions, let's see.... Let the base be x by x inches, and the height be y inches V= x^2 y 27 = x^2 y y = 27/x^2 material = 2x^2 + 4xy = 2x^2 + 4x(27/x^2) = 2x^2 + 108/x d(material)/dx = 4x - 108/x^2 = 0 for a min/max of ...
April 27, 2016

calculus
see my previous reply to this same idea.
April 27, 2016

calculus
width --- x length -- y 2x+2y = 320 y = 160-x area = xy = x(160-x) = -x^2 + 160x this is a downwards opening parabola with a vertex at (80, 6400) (I assume you know how to find the vertex) the max area is 644 m^2 , when x = 80m that is, when the rectangle is a square, which ...
April 27, 2016

Math
After giving to his son, he has 3x/8 left after giving to his daughter he has 3x/16 left 3x/16 = 150 3x = 2400 x = 800 check: first gift = (5/8)(800) = 500 amount left = 300 2nd gift = (1/2)(300) = 150 amount left = 150 Editorial: Looks like sexism in continued in math ...
April 27, 2016

algebra
width --- y length --- 3y area = y(3y) or 3y^2
April 27, 2016

math
most scientific calculators have the ! function built in on mine I press: 5 2ndF 4 -----> on mine the ! is with the 4 key = 120
April 27, 2016

Maths
x = 2cos t y = 2sin t dx/dt = -2sin t dy/dt = 2cos t slope = dy/dx = (dy/dt) / )dx/dt) = 2cost/-2sint = -cost/sint when t = pi/6 sint = 1/2 cost= √3/2 slope = (-√3/2)/(1/2) = -√3 point: (2cos pi/6, 2sin pi/6) or (√3 , 1) So now you have m = -√3, ...
April 27, 2016

algebra
let the first 4 terms of the AP be a-d, a , a+d, and a+2d new sequence is a-d+1, a+2, a+d + 7, and a+2d+20 so (a+2)/(a-d+1) = (a+d+7)/(a+2) (a+2)^2 = (a-d+1)(a+d+7) a^2+4a+4 = a^2+ad+7a-ad-d^2-7d+7a+d+7 -4a = -d^2 - 6d + 3 4a = d^2 + 6d - 3 ** (a+d+7)/(a+2) = (a+2d+20)/(a+d+7...
April 27, 2016

maths
I will assume you meant: 3 log9 9^2 = 6 log9 9 = 6(1) = 6
April 27, 2016

maths
did you mean: log √(x+1) + 9logx ?? then = log √(x+1) + log x^9 = log ( x^9 √(x+1) )
April 27, 2016

maths
I will assume you meant: log(x^2 y^3) then: = log x^2 + log y^3 = 2logx + 3logy = .... take over
April 27, 2016

math
y + 2x - 12 = 0 or y = -2x + 12 has a y-intercept of 12 5x + 12y = 8 has a slope of -5/12 so your new line is y = (-5/12)x + 12
April 27, 2016

math
Interest = 100,000(.06)(30) = 180,000 (This is a completely meaningless answer. Nobody would charge simple interest for such a period of time. The formula assumes that there is always 100,000 owing, but aren't there payments made in a "house loan", generally ...
April 26, 2016

PreCal
I am missing the speed of the wind.
April 26, 2016

PRECALC
#1, look how I did this similar problem, and follow the same steps http://www.jiskha.com/display.cgi?id=1461697741 #2 2 cos(θ) tan(θ) + tan(θ) = 1 + 2 cos(θ) 2cosθtanθ - 2cos + tanθ - 1 = 0 2cosθ(tanθ - 1) + (tanθ -1) = 0 by ...
April 26, 2016

mathh
y - 67/36 = (1/4)(x - 4/9) expand, then multiply each term by 36, the LCD
April 26, 2016

precalc
square both sides cos^2 x + 2sinxcosx + sin^2 x = 1 1 + 2sinxcosx = 1 sin (2x) = 0 2x = 0 or 2x = π or 2x = 2π x = 0, x = π/2, x = π the period of sin 2x is π, so adding multiples of π will yield more answers so in the domain 0 < x < 2π...
April 26, 2016

Calculus
let the height of the water be h m let the radius of the water level be r m Make a sketch of the cross-section. By similar triangles: r/h = 40/10 r = 4h or h = r/4 V = (1/3)π r^2 h = (1/3)π(4h)^2 h = (16/3)π h^3 dV/dt = 16π h^2 dh/dt plug in the given ...
April 26, 2016

Math
What is 22,000(.94)^6 ??
April 26, 2016

Calculus
V = (4/3)πr^3 dV/dt = 4πr^2 dr/dt when r = 5 and dr/dt = 2 dV/dt = 4π(25)(2) = 200π cm^3/min SA = 4πr^2 d(SA)/dt = 8πr dr/dt = 8π(5)(2) = 80π cm^2/min
April 26, 2016

Geometry
Remember that for each chord , a perpendicular from the centre will right-bisect the chord so if you let the height to the shorter chord be h1, and the height form the centre to the longer chord be h2 you have two right-angled triangles, the first one sides 6, h1, and ...
April 26, 2016

maths
Look carefully, Damon had .75 not 75 45 minutes = 3/4 hour = .75 hours
April 26, 2016

Mathematics
number of boys --- x number of girls --- x+36 x/(x+36) = 2/5 5x = 2x + 72 3x = 72 x = 24 so we have 24 boys and 60 girls for a total of 84 adults/children = 5/6 adults/84 = 5/6 6adults = 420 adults = 70 All is known
April 25, 2016

Math
Prob = (1/2)(1/2)(1/2) = 1/8
April 25, 2016

Math
Since we can only add "like" terms, wouldn't we have to add x^3 + 5x^3 ?? And that would give us ..... ?
April 25, 2016

Math PLZZZ HELP ME!!!!!
look back at your previous post of this question.
April 25, 2016

Algebra
x^2+6x=-7 x^2 + 6x + 9 = -7+ 9 (x+3)^2 = 2 x+3 = ± √2 x = -3 ± √2
April 25, 2016

Math
The mathematical probability of rolling a 5 on a die is 1/6 so the number of times you would get a 5 in 300 rolls = (1/6)(300) = 50 so your "experimental" probability had to be different from the mathematical one. And you didn't state the experiment, so I can'...
April 25, 2016

Math
Let me try to wade through this quagmire of a sentence. A four digit decimal number lies between 10 and 20. ---> 1x.yz My tenths digit is twice my tens digit. ---> 1x.2z The sum of my tenths and my ones digit equals my hundredth digit. ---> 2+x=z ** The sum of all my ...
April 25, 2016

Math(Quadratic Functions)
For days ???? since the x-intercepts of a function are the same as the roots of the corresponding equation x=7 ----> a factor of (x-7) x=-2 ---> a factor of (x+2) so f(x) = a(x-7)(x+2) we are told that (0,5) lies on it, so 5 = a(-7)(2) a = -5/14 f(x) = (-5/14)(x-7)(x+2) ...
April 25, 2016

Roots, complex numbers
This question must be a popular one. Did it yesterday http://www.jiskha.com/display.cgi?id=1461490844
April 25, 2016

Math
A = 800(3)^3.12 = appr 24644 bacteria
April 25, 2016

Math
90000 = 45000(1.075)^n 2 = 1.075^n log both sides log 2 = nlog1.075 n = log2/log1.075 = appr 8.58 years
April 25, 2016

Calculus
let the height along the wall be y m let the distance from the wall along the ground be x x^2 + y^2 = 6^2 2x dx/dt + 2y dy/dt = 0 x dx/dt + y dy/dt = 0 when x = 4 16 + y^2 = 36 y = √20 , and dx/dt = 1 4(1) + √20 dy/dt = 0 dy/dt = -4/√20 m/sec the negative ...
April 25, 2016

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