Sunday
August 2, 2015

Posts by Reiny


Total # Posts: 30,519

Algebra
let the border be x cm wide picture is (30-2x) by (36-2x) (30-2x)(36-2x) = 480 1080 - 132x + 4x^2 - 480 = 0 4x^2 - 132x + 600 = 0 x^2 - 33x + 150 = 0 solve using the quadratic equation,
March 22, 2015

Advanced Algebra
It would simply be 10 x 9 x 8 x 7 or 5040 ways This is the same as P(10,4) = 10!/(10-4)! = 10!/8! = 5040
March 22, 2015

Math
Set them equal or R(x) - C(x) = 0 2x + 10 = -5x^2 + 21x 5x^2 - 19x + 10 = 0 x = .6311 thousand or appr 631 or x = 3.169 thousand or appr 3169 check: if x = .6311 , R(.6311) - C(.6311) = .00053.. , not bad if x = 3.169 , ...... = .001805 both answers are valid
March 21, 2015

Pre-Calculus
It is considered "better form" to have your quadratics start with a positive x^2 term So for #2, I would write: 6x^2 - 25x + 24 = 0 , (just switch all the signs, like multiplying by -1) Each of your roots satisfy your equations, but each of your quads should have a ...
March 21, 2015

algebra
Is y = -3x^2 - 4x + 3 supposed to be your answer ? Can't be right, since (0,-4) clearly does not satisfy your equation. Method1: let the equation be ax^2 + bx+c = y for (0,-4), 0+0+c=-4 , c = -4 for (-2,-20), 4a-2b - 4 = -20 4a - 2b = -16 2a - b = -8 for (4,-20), 16a + 4b...
March 21, 2015

Calculus
V = (4/3)π r^3 dV/dt = 4π r^2 dr/dt so when r = .5, dr/dt = .01 just plug it in... dV/dt = 4π(.25)(.01) = ..... cm^3/day
March 21, 2015

maths
fourth term is 11 ---> a+3d = 11 sixth term is 17 ----> a+5d = 17 subtract them 2d = 6 d = 3 back in a+3d = 11 a + 9 = 11 a = 2 tenth term = a+9d = 2+9(3) = 29
March 21, 2015

math
sub in y = x+k x^2 + y^2 = 25 x^2 + (x+k)^2 = 25 x^2 + x^2 + 2kx + k^2 - 25 = 0 2x^2 + 2kx + (k^2-25) = 0 a = 2, b = 2k, c = k^2-25 discriminant = b^2 - 4ac = 4k^2 - 4(2)(k^2-25) = 4k^2 - 8k^2 + 100 = 100 - 4k^2 now proceed the same way as in the previous post to "Eloise&...
March 21, 2015

MATH
I will assume your "equation" is equal to zero, that is, kx - 10 - 5x^2 = 0 or 5x^2 - kx + 10 =0 your discriminant is b^2 - 4ax, or k^2 - 4(5)(10) = k^2 - 200 to have one real root: k^2 - 200 = 0 k^2 = 200 k = ±√200 or ±10√2 for 2 distinct ...
March 21, 2015

math
so you want the vertex of the parabola the x of the vertex is -b/(2a) = -50/-3.724 = 13.426.. subbing that back int gives a height of 2+50(13.426..) - 1.862(13.426..)^2 = appr 337.66 m above "ground" --> h(t) > 0 , for t ≥ 0 solve 2+50t-1.862t^2 = 0 to ...
March 21, 2015

Math
3x + 2y < 6 2y < -3x + 6 y < -(3/2)x + 3 so the slope is -3/2 and the y-intercept is 3 so start with the y-intercept of 3 , or the point (0,3) slope is rise/run = -3/2 so from (0,3) , drop down 3 , then 2 units to the right. This should bring you to the point (-3,5) ...
March 21, 2015

math
oranges --- x apples ---- x + 32 overripe oranges = (3/5)x overripe apples = (1/3)(x+32) but they are the same .... (1/3)(x+32) = (3/5)x multiply by 15 , the LCD 5(x+32) = 9x 5x + 160 = 9x 160 = 4x x = 40 overripe fruit = (1/3)(x+32) + (3/5)x = (1/3)(72) + (3/5)(40) = 48 check...
March 21, 2015

Algebra
boat's speed in still water --- x mph against the current ----- x-3 mph with the current -------- x + 3 mph time against current = 12/(x-3) time with the current = 12/(x+3) 12/(x+3) + 12/(x-3) = 3 times (x-3)(x+3) or x^2 - 9 12(x-3) + 12(x+3) = 3(x^2 - 9) 12x-36 + 12x + 36...
February 23, 2015

algebra
Let the shorter wire be x m long and let that wire be y m from the base of the pole so x^2= 576 + y^2 ----> x^2 - y^2 = 576 let the longer be x+5 and we have (x+5)^2 = 24^2 + (y+11)^2 x^2 + 10x + 25 = 576 + y^2 + 22y + 121 x^2 - y^2 = 22y - 10x + 672 22y - 10x + 672 = 576 ...
February 23, 2015

Algebra
I agree with all you answers
February 23, 2015

Vectors Math
Anwered here: http://www.jiskha.com/display.cgi?id=1424665237 take a vector (a,b,c) now do (a,b,c) x (a,b,c) to get (0,0,0) by whatever means you have learned. The steps will become your explanation.
February 23, 2015

Math
Maria, as I told you yesterday, you don't have enough information http://www.jiskha.com/display.cgi?id=1424650591
February 23, 2015

Math
amount = 3000(1.02)^8 = ... subtract $3000 from that answer and you got your interest earned.
February 23, 2015

Math
Circumference of the wheel = 1.05π number of turns = 3300/1.05π Btw, on your calculator, key in 3300 ÷ (1.05 x π) = to make sure the order of operations is correct
February 23, 2015

Maths
numbers which when divided by 5 leave a remainder of 1: 6 11 16 21 26 31 36 41 46 .. numbers which when divided by 8 leave a remainder of 1: 9 17 25 33 41 49 ... looks like 41 is the smallest common to both
February 23, 2015

Vectors Math
http://www.jiskha.com/display.cgi?id=1424665199
February 22, 2015

Vectors Math
If using whichever method you have to find the cross-product, if you take (a,b,c) x (a,b,c) you will get (0,0,0)
February 22, 2015

Algebra 2
On here, we write rational expressions this way: (6x^2 + 13x - 5)/(6x^2 -23x + 7) = (3x-1)(2x + 5)/((3x-1)(2x - 7) = (2x+5)/(2x-7) , x ≠ 1/3 (or else I divided by zero)
February 22, 2015

Vectors
I don't know what your method is but I got (59,42,-29)
February 22, 2015

Vectors
done, see your earlier post
February 22, 2015

math
To go from -5 to -1, we moved 4 to the right to go from 4 to -1, we moved 5 to the left, so (x,y) ---> (x+4, y-5) then (-4,5) ---> (0,0)
February 22, 2015

Vectors Math
the projection of vector a on vector b = (a dot b)/|b| = (5-10+9)/√(1+4+9) = 4/√14 or = 4√14 /14 = 2√14/7
February 22, 2015

math
And the question is .... ?
February 22, 2015

Math
cell1 = 50 + 40m cell2 = 0 + 50m when is 50m = 50+40m ??? (seems too easy)
February 22, 2015

Algebra 2
pr = k(1/d) when d = 2, pr = 750000 750000 = k(1/2) k = 1500000 so pr = 150000(1/d) if d = 5 pr = 150000(1/5) = $300,000
February 22, 2015

Mathematics
let f(x) = 7x^6-9x^2+2 f(0) = 2 f(1) = 7-9+2 = 0 , well , isn't that special, we accidentally found a solution So I guess there has to be at least one solution.
February 22, 2015

expected value
If you look at the outcomes, you will see that half of the sums are even, the other half are odd. So prob (even) = 1/2 prob(odd) = 1/2 expected value= (1/2)$10 + (1/2(-$25) = -7.5 Who would possible want to play this game ?
February 22, 2015

math
Not enough information, you need some angles Imagine the shape having pivots or hinges at the vertices. I can "squish" the hexagon, thus changing the area, while keeping all the sides the same.
February 22, 2015

math
prob(both red) = (3/6)(2/5) = 1/5
February 22, 2015

Algebra 2
f(x) = 5x+50 g(x) = x/5 - 10 f(g(x)) = 5(x/5-10) + 50 = x - 50 + 50 = x g(f(x) = (5x+50)/5 - 10 = x + 10 - 10 = x Yup they are check: let f(x) = 5x+50 be written as y = 5x+50 to form the inverse, interchange the x and y x = 5y + 50 now solve this for y 5y = x - 50 y = x/5 - 10...
February 22, 2015

Math Help!
#6 Let the three consecutive odd numbers be n, n+2, n+4 their sum = 3n + 6 = 3(n+2) so the sum is a multiple of 3. but 29 does not divide evenly by 3, so it cannot be 29
February 22, 2015

Math Help!
#5. visualize the number or write them out 123456789101112131415161718192021222324252627282930313233 Now circle all the 3's. By the time you reach 33, you will have counted 8 3's. So to write from 1 to 10 took 11 digits so we have 11 12 ... 33, which is 23 double ...
February 22, 2015

Math Help!
#1. so you have x + (x+2) + (x+4) + .. + (x+18) = 200 ( explanation for term(10) = a+9d = x + 9(2) = x+18) sum(10) = 5(first + last) 5(x + x+18) = 200 2x + 18 = 40 2x = 22 x =11
February 22, 2015

Trigonometry (Logarithmic Function)
or 15 = (10x3÷2) take log of both sides log 15 = log (10x3÷2) = log10 + log3 - log2 = 1 + y - x
February 22, 2015

Math
To obtain the product ab, you are simply choosing pairs of numbers form the 6 different numbers. e.g. (3,-5), (1,-1) etc that would be 6x5 or 30 but isn't (5,3) the same product as (3,5), and don't we have a double choice for each pair like that ? so the number of ...
February 22, 2015

Math
based on the theorem that the area of similar figures is proportional to the square of their corresponding sides, thus also their perimeters. so (p1)^2 : (p2)^2 = 1 : 4 p1 : p2 = √1 : √4 = 1 : 2
February 22, 2015

AP CALC
I agree with Steve, it is 97/3
February 21, 2015

math
the arithmetic looks good. I would insist on an equal sign in front of each new line commission = 100000(.024) + 0.015(280000 - 100000) = 2400 + 2700 = 5100
February 21, 2015

math
what you have is 1+2+3+...+n let S(n) = 1+2+3+...+ (n-2) + (n-1) + n writing this in reverse order S(n) = n + (n-1) + (n-2)+ ... + 3+2+1 add them 2S(n) = (1+n) + (2+n-1) + (3+n-2) +...+(3+n-2) + (2+n-1) + (n+1) = (n/2)(n+1) or = n(n+1)/2 , as required
February 21, 2015

Math
2x-3y ≤ 6 -3y ≤ -2x + 6 y ≥ (2/3)x - 2 so shade in everything above and including the line y = (2/3)x - 2 4x + 4y ≤ 8 x + y ≤ 2 y ≤ -x + 2 now shade in everything below and including the line y = -x + 2 the solution is all the shaded region ...
February 21, 2015

Math
You have to consider the speed of the plane without wind and the speed of the wind itself Let the speed of the plane in still air be x km/h le the speed of the wind be y km/h so going with the wind -- speed is x+y mph going against the wind -- speed is x - y mph 2 equations: 4...
February 21, 2015

maths
I did this last Wednesday http://www.jiskha.com/display.cgi?id=1424295544
February 21, 2015

Math
Clearly, since 3 does not divide evenly into 25, you cannot do this without some marbles left over.
February 21, 2015

Math
∛64 = 64^(1/3) = 4 = 2^2 243^1/5 = 3 so 6 log2 ∛64 +10log3 (243)^1/5) = 6log2 (2^2) + 10 log3 (3) = 6(2 log2 2) + 10 log3 3 = 12 (1) + 10(1) = 22
February 21, 2015

Math
I like Steve's thinking, but sometimes I like to take a hammer to a thumbtack.
February 21, 2015

Math
Yes, you are adding 5+10+15+...+45+50 here a=5 and d = 5 How many terms are there? term(n) = a+(n-1)d 50 = 5 + (n-1)(5) 45 = 5n - 5 50 = 5n n = 10 so we want the sum of 10 terms sum = (10/2)(first + last) = 5(5+ 50) = 275
February 21, 2015

math
Meg's age --- x Jill's age ----- x-2 Beth's age --- x/2 or (1/2)x Of course we could have started by defining: Beth's age --- y Meg's age --- 2y Jill's age -----2y - 2 or , starting with Jill's age ----- z Meg's age ---- z+2 Beth's age...
February 21, 2015

math
If we consider 2004 to be represented by 0, then 2009 would correspond with 5 and we have two ordered pairs (0,14.54) and (5,15.37) slope = (15.37-14.54)/(5-0) = .83 N = .83t + c at (0,14.54) 14.54 = 0 + c , c = 14.54 N = .83t + 14.54 , where t is in years since 2004 and N is ...
February 20, 2015

correction _ Last help Thanks
Argghhh! the odds AGAINST drawing an S = 7 : 3
February 20, 2015

Last help Thanks
prob of drawing an S = 4/11 prob of NOT drawing an S = 1 - 4/11 = 7/11 So the odds in favour of drawing an S = (4/11) : (7/11) = 4 : 7 So the odds AGAINST drawing an S = 3 : 7 I would say, "Karen, read the question carefully"
February 20, 2015

help please
odds in favour of some event = probability of that event happening : probability of the event NOT happening so if the odds of something happening is 3: 4 then the probability of the event happening is 3/7 in general if the odds of something is a : b then prob of that something...
February 20, 2015

math
total amount invested ---- x Fatuma's share = x/4 Ali's share = (2/5)(3x/4) = 3x/10 Hassan's share = (3/2)(x/4) = 3x/8 so far they have: x/4 + 3x/10 + 3x/8 = 10x/40 + 9x/40 + 15x/40 = 37x/40 so they are still short 3x/40 3x/40 < 3x/8 by 60000 3x/40 = 3x/8 - ...
February 20, 2015

math
sinØ= 2/3 , Ø is in quad I in my triangle, x = ? , y = 2, r = 3 x^2 + 2^2 = 3^2 x^2 = 5 x = √5 tanØ = y/x = 2/√5 or, if rationalized, 2√5 /5
February 20, 2015

Math
5 gifts take 1.5 rollos 1 gift takes 1.5/5 rolls 9 gifts take 9(1.5/5) rolls or 2.7 rolls or 9/5 = x/1.5 x = 1.5(9/5) = 2.7
February 20, 2015

Algebra
let the side parallel to the house be y ft let each of the other two sides by x ft so 2x + y = 164 y = 164 - 2x area = xy = x(164 - 2x = -2x^2 + 164x This is a downwards opening parabola, so we need its vertex. Either 1. complete the square 2. use Calculus 3. use " the x ...
February 20, 2015

math.help pls
all you have to look at is B(5,-6,-1) If you are using the standard position of x-axis towards and away from you, the y-axis left and right, and the z-axis up and down, then B ---> 2 units back, 3 units right, and 1 unit up ---> B' (3, -3, 0) , then B'(3,-3,0...
February 20, 2015

Math Help
3u ∙ v = <6,6> ∙ <-3,4> = -18 + 24 = 6 (u ∙ 2v)w = ( <2,2> ∙ <-6,8>)<1,-2> = (-12 + 16)<1,-2> = 4<1,-2>= <4,-8>
February 20, 2015

Math
i = .035/365 = .00009589.. (I store this in my calculator memory so I don't lose any accuracy) amount = 28000(1 + .00009589..)^68 = 28183.16 for the 2nd problem, the 3000 earns interest for 20 + 30 or 50 days the 650 for 10+30 or 40 days then 1200 for 12 days amount = 3000...
February 20, 2015

Math
1. dot product u ∙ v = |u| |v| cosØ, where Ø is the angle between them, so <2,-3> ∙ <1,-2> = √13 √5 cosØ 2+6 = √13√5cosØ cosØ = 8/(√13√5) = .99227... Ø = appr 7.1° do #2 ...
February 20, 2015

Maths
Of course not. It only increases by 3 for this question since this arithmetic series has a common difference of 3 It depends totally on the sequence
February 20, 2015

Maths
Nothing very exciting. It just blows up, getting bigger and bigger You are just adding 3 to each new term added.
February 20, 2015

Math
in general: <a, b> ∙ <c, d> = ac + bd so <0, 3> ∙ <4, -2> = 0 + (-6) = -6 repeat for #2
February 20, 2015

math
either 2 men or 2 women. with no restriction: number of choices = C(5,2) = 10 number choices of 2 women = C(2,2) = 1 number of choices of 2 men = C(3,2) = 3 prob of 2 of same sex = 4/10 = 2/5 prob of 2 of opposite sex = 1 - 2/5 = 3/5
February 20, 2015

math
L1: y-2 = 5(x-1) y-2 = 5x-5 5x - y = 3 L2: x + 5y = c from L1, when x = 4, y = 17 so (4,17) into L2 4 + 85 = c = 89 L2: x + 5y = 89 or y = (-1/5)x + 89/5
February 20, 2015

trignometry
Iwill read that as 1/(1 - cscx) - 1/(1 + cscx) = -2tanx secx LS = (1 + cscx - (1 - cscx))/(1 - csc^2 x) = 2cscx/(-cot^2 x) = -2 (1/sinx)(tan^2 x) = -2(1/sinx)(sin^2 x/cos^2 x) = -2 cscx/cos^2 x = -2 cscx sec^2 x = RS
February 20, 2015

math
90/x = 5^2/10^2 90/x = 25/100 = 1/4 x = 360
February 20, 2015

math
follow the same method I showed you in your other post with a similar concept Except here you have areas instead of volumes Hint: areas of similar shapes area proportional to the square of their corresponding sides.
February 20, 2015

Math
prob of grey = 87/100 number of greys in 220 = (87/100)(220) = appr 191
February 20, 2015

Math
number = (1/50)(750) = 15
February 20, 2015

maths
visualize the box cut open and laid out flat on a table. What do you see ? Calculate the area of each of the 5 rectangles and add them up
February 20, 2015

Math
prob of 4 spades = C(13,4)/C(52,4) = 715/270725 = 11/4165
February 19, 2015

Math
original square is x by x cm new rectangle is x by x/2 2( x + x/2) = 24.9 2x + x = 24.9 x = 8.3 the square piece is 8.3 by 8.3 cm
February 19, 2015

Math
volume of similar solids is proportional to the cube of their corresponding sides 240/x = 92^3/23^3 240/x = 778688/12167 778688x = 12167(240) x = 3.75 or 3.8 to the nearest tenth
February 19, 2015

Math (Probability)
You want the 8 of hearts, then an Ace prob = (1/52)(4/51) = 1/663
February 19, 2015

Algebra 2
t3 = ar^2 = -75 t6 = ar^5 = -9375 divide them r^3 = 125 r = 5 in ar^2 = -75 a(25) = -75 a = -3 term(n) = -3(5)^(n-1)
February 19, 2015

Math
I assume the median is 87 z-score = (91-87)/4.01 = ....
February 19, 2015

math
You are basically going through the development of the formula, using a specific example You seem to have a typo your: 3²+3³+3to the power of 6+...to 20 terms makes little sense I will assume we have S(20) = 3^2 + 3^3 + ... + 3^21 multiply both sides by 3 3S(20) = 3^...
February 19, 2015

MATH
Typo: you have Sn=n/2[a+1] clearly should be : Sn=n/2[a+l] let S(n) = a + (a+d) + (a+2d) + ... +(l-2d) + (l-d) + l , for n terms we could just write this turned around S(n) = l + (l-d) + (l-2d) + ... + (a+2d) + (a+d) + a add these two equations 2S(n) = a+l + (a+d+l-d...
February 19, 2015

MATH
I will assume that you are adding the corresponding terms of each sequence, that is .. new sequence: t1 = a+a t2 = a+d + ar t3 = a+2d + ar^2 etc so a+a = 4 a+d + ar = 20 but d=-2 and r=3 2a = 4 a = 2 So all is known t3 = 2 - 4 + 2(9) = 16 check: AS: 2, 0, -2, -4, .. GS: 2, 6, ...
February 19, 2015

math
Use the formulas for both "sum of terms" and "sum of infinite number of terms" Sum to infinity = a/(1-r) a/(1-r) = 243 , ---- #1 ( I recognized 243 as 3^5) a = 243 - 243r sum(5) = a(1 - r^5)/(1-r) 242 = a(1 - r^5)/(1-r) ---- #2 divide #2 by #1 1-r^5 = 242/...
February 19, 2015

Algebra 2
∑ 2n/(n+4) , where n = 1 to 5 write n=1 underneath the sigma symbol and 5 above it
February 18, 2015

Math Help Please
You must mean: (4x^3 + 5x^2 - 12x + 27)/(x + 3) I did a synthetic division and got 4x^2 - 7x + 9 , which is A since none of the answers had a remainder, you knew the division had to be exact, so it had to look like this (4x^3 + 5x^2 - 12x + 27) = (x+3)(4x^2 .... +9) so it had ...
February 18, 2015

math
going to the theatre C = 12.5n, where n is the number of movies seen buying a player, then renting C = 125 + 1.95n 12.5n = 125 + 1.95n 10.55n = 125 n = 11.8 I will let you interpret that decimal answer
February 18, 2015

algebra
let the side parallel to the barn be y yards then the other two sides are x yards each 2x + y = 25 y = 25-2x area = xy = x(25-2x) = 25x - 2x^2 which graphs as a downwards parabola, so the vertex has to be found. quickest way: the x of the vertex is -b/(2a) = -25/-4 = 6.25 then...
February 18, 2015

ALGEBRA
unless [ ] is defined as something special, f(2) = 2*(-1)^2 = 2*(1) = 2
February 18, 2015

math
reflection of P(-3,5) in the x-axis ----> R(-3,-5) which is in quadrant III P(-3,5) reflected in the y-axis---> S(3,5) , which is in quad I
February 18, 2015

Jonie, Pamela, Spartans - math
Why are you changing names, and what could you not understand about my answer here: http://www.jiskha.com/display.cgi?id=1424281591
February 18, 2015

Math
the resultant vector is (9-1 , 3-11) = (8,-8) This is generally considered in component form check with your textbook how they write the vector. Some authors avoid the standard round brackets ( ..., ...) to avoid confusion with a point. Some use this form [8,-8] others use <...
February 18, 2015

Calculus
not an easy problem follow these steps: http://mathworld.wolfram.com/SphericalCap.html or http://en.wikipedia.org/wiki/Spherical_cap or http://keisan.casio.com/has10/SpecExec.cgi?id=system/2006/1223382199
February 18, 2015

math
I hope Mr. Howard put in the closing brackets. 3(20x + 8) = 60x + 24 4(15x)+6) = 60x + 48 so what is your opinion ?
February 18, 2015

Math
so what did your calculator say? remember the angle could have been in quadrant IV also. so 360-(whatever your calculator said)°
February 18, 2015

Algebra 2
sum(7) = (7/2)(2(26) + 6(18)) = 560
February 18, 2015

Algebra 2
so you want 16+20+24+...100 number of terms = ?? you have an AS, where a = 16 , d=4 term(n) = a+(n-1)d 100 = 16 + (n-1)(4) 84 = 4n - 4 88 = 4n n = 22 so we want S(22) = (22/2)(first + last) = 11(16+100) = 1276
February 18, 2015

Algebra not algabra
(3a+2)^3 = (3a+2)(9a^2 + 12a + 4) = 27a^3 + 36a^2 + 12a + 18a^2 + 24a + 8 = 27a^3 + 54a^2 + 36a + 8 or , using the binomial expansion = 1(3a)^3 + 3(3a)^2 (2) + 3(3a)(2^2) = 1(2^3) = 27a^3 + 54a^2 + 36a + 8
February 18, 2015

Math
N = N(M) + N(S) + N(R) - N(M and S) - N(M and R) - N(S and R) + N(M and S and R) = 36+28+12 - 15 - 12 - 8 + 4 = 45 If the question is, How many did not buy any type of book, then it would be 59-45 or 14 You did not state a question. You could draw a Venn diagram and all ...
February 18, 2015

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