Saturday
August 27, 2016

Posts by Reiny

Total # Posts: 35,561

Analytic geometry
Name your points A(-8,8) and B(-2,2) So you want PA = 2PB Use you distance between points formula: √( (x+8)^2 + (y-8)^2 ) = 2√( (x+2)^2 + y-2)^2 ) square both sides (x+8)^2 + (y-8)^2 = 4( (x+2)^2 + y-2)^2 ) I will leave it up to you to expand and simplify the equation
July 6, 2016

math
Ahh, I see you fixed the problem from your earlier post. a) 20 men, 12 women, choose 5, with exactly 3 men = C(20,3) x C(12,2) = 2053(66) = 135498 b) at least 4 women ---> 4 women or 5 women = C(20,1) x C(12,4) + C(20,0) x C(12,5) = 20(495) + 1(792) = 10692 check my arithmetic
July 6, 2016

Math
Since the room is square, its side is √350 = 5√14 m your carpet is only 5√14 by 3√14 So clearly you will need an extra 2√14 m
July 6, 2016

math
your wording is gibberish. How can you have a committee of 5 people "if exactly three men must be on each committee and at least four women on each committee" Are there two different questions here?
July 5, 2016

Prealgebra
correct about the conversion to start. 3 m = 300 cm 2 m = 200 cm, (isn't the metric system great??) but 300/10.5 = 28.5 , so you will need 29 one way, and 200/10.5 = 19.04.. darn!, you will have to have 20 along the width So you will need 20x29 or 580 tiles. ( in reality ...
July 5, 2016

math
Area of ellipse = abπ where a and b are 1/2 of the axes respectively, that is, a = 7, b = 5
July 5, 2016

Pre Calculus
so you want: y = log3 (127) or 3^y = 1/27 , by definition of logs 3^y = 3^-3 y = -3 f(1/27) = -3
July 5, 2016

Pre Calculus
recall that ln 1 = 0 so x-3 = 1 x = 4
July 5, 2016

Pre Calculus
Where does the b come from in all your answers? Where does the 19 come from in all the answers? I suspect a typo
July 5, 2016

Math of investigation
Same post answered by Steve http://www.jiskha.com/display.cgi?id=1467634318
July 4, 2016

Pre-Calculus 11
∛5*5*5*3/4 = 5∛3/4 , assuming the 4 is not part of the cube root
July 4, 2016

Pre Calculus
I will try to show my synthetic division, the .... are spaces: 6+√6 | 1 ........ -11 ........ 18 ........ 32 .................... 6+√6 .... √6-24 .... -30 ............ 1 ..... √6-5 ..... √6-6 ........ 2 showing that: x^3-11x^2+18x+32 = (x-6-√...
July 4, 2016

maths
the time taken would be inversely proportional to the number of men, that is , the men we have working the less time it takes. t = k/m k = tm given: 8 men take 6 months k = 6x8 = 48 when m = 12 t = 48/12 = 4 or number of "man-months" = 48 time for 12 men = 48/12 = 4 ...
July 4, 2016

MATH
area of whole flag = 9000 cm^2 width of thin stripe --- x width of thicker stripe --- 2x area of stripes = 2x(90) + x(100) - 2x^2 ( we have to subtract the intersection of the stripes or else we would count it twice) = 280x - 2x^2 4500 = 280x - 2x^2 2x^2 - 280x + 4500 = 0 x^2...
July 4, 2016

math
You know how to find the area of a square if you know the sides, right? area = (5x+3y)^2 m^2 = (25x^2 + 30xy + 9y^2) m^2
July 4, 2016

math
which digits? at the left of what? at the right of what?
July 4, 2016

maths
unit digit --- x tens digit --- x+7 10(x+7) + x = 10(x + x+7) 10x + 70 = 20x + 70 10x = 0 x = 0 so the number is 70
July 4, 2016

maths
unit digit --- x tens digit -- 4x the number is 10(4x) + x or 41x the number reversed is 10x + 4x or 14x 41x - 14x = 54 27x = 54 x = 2 the original number is 82 check: 82-28 = 54 , all is good.
July 4, 2016

math
original number ---- x/(x+7) new number: (x+17)/(x+7-6) = (x+17)/(x+1) (x+17)/(x+1) = 2 2x + 2 = x+17 x = 15 the original number was 15/22
July 4, 2016

math
There are billions and billions of those. Some of them are: 3 and 5 6 and 10 30 and 50 5.4 and 9 6√3 and 10√3 -9 and -15 .... etc
July 4, 2016

Math
amount of original money ---- x (1/5)x + (1/4)(4/5)x + 360 = x x/5 + x/5 + 360 = x times 5, the LCD x + x + 1800 = 5x 3x = 1800 x = 600 check: he spent 1/5 of 600, or 120 , leaving him with 480 he spend 1/4 of 480 on food, leaving him with 360
July 4, 2016

Maths
V = (4/3)π r^3 dV/dt = 4π r^2 dr/dt when V = 2000 (4/3)πr^3 = 2000 r^3 = 1500/π r = (1500/π)^(1/3) = 7.8159... I stored in my calculator's memory so in dV/dt = 4π r^2 dr/dt 125 = 4π (7.8159...)^2 dr/dt dr/dt = .1628618 rate of change of ...
July 3, 2016

MATH
The hexagon is made up 6 equilateral triangles with sides of 9 ft Area of one of them = (1/2)(9)(9)sin60° = (81/2)(√3/2) = 81√3/4 area of whole hexagon = 6(81√3/4) = 243√3/2 area of whole hexagonal prism = 2(243√3/2) + 6(9)(6) = (243√3...
July 3, 2016

math
find the slope, then use the steps I showed you in your first post
July 3, 2016

math
Since your new line is parallel to the given line, it will differ only in the constant, so it will be -7x + 6y = c plug in the given point: -7(-1) + 6(-4) = c c = -17 new equation: -7x + 6y = -17 or 6y = 7x - 17 y = (7/6)x - 17/6
July 3, 2016

math
from what I had: y+6 = 8x + 40 y = 8x + 34 ---> this is correct standard form: 8x - y = -34 ---> this is correct general form: 8x - y + 34 = 0 ---> this is correct
July 3, 2016

math
y+6 = 8(x+5) I will leave it up to you to change it to the required form.
July 3, 2016

Math
let the amount of money be m let the number of people sharing be x let each persons share be y then xy = m second case: number of people = x+8 share of each person = y-1 then m = (x+8)(y-1) = xy + 8y - x - 8 thus: xy+8y-x-8 = xy x = 8y - 8 , where y > 0 , and y is a natural...
July 3, 2016

Math
If the new line is to be parallel to y = 4x +1, it will differ only in the constant, so let it be y = 4x + b, plug in the given point, find b, and you are done
July 3, 2016

math
bend = k mass given: 10 cm = k 4 kg k = 10/4 cm/kg or (5/2) cm/kg if mass = 7kg bend = (5/2)(7) = 17.5 cm
July 3, 2016

maths
let the total number be x (4/5)x are boys (1/5)x are girls, but (1/5)x = 100 x = 500 So we have 100 girls and 400 boys
July 3, 2016

college algebra
amount = (1/2)^(t/23), where t is in minutes .1 = (.5)^(t/23) log both sides log .1 = (t/23)log .5 t/23 = log.1/log.5 t = 23log.1/log.5 = appr 76.4 minutes check: after 23 minutes, 50% would be left after 46 minutes, 25% would be left after 69 minutes 12.5% would be left my ...
July 3, 2016

math
4/11 - x/3 = 24/25 I would multiply each term by 825 , the LCD
July 3, 2016

Maths
convert each to a decimal, then compare
July 3, 2016

Math
fill in all the fields of your Venn diagram. Place 10 in the intersection. Put 4x - 10 in the "math only" field Put 5x - 10 in the "science only" field then 4x-10 + 5x-10 + 10 + 15 = 95 9x = 90 x = 9 Now you know each of the entries in the Venn diagram.
July 3, 2016

maths
Stated simply: In an AP, the sum of the first 8 terms is 128 3 times the difference between the 2nd and 5th term is 36. 4(2a + 7d) = 128 2a + 7d = 32 3(a+d - a - 4d) = 36 -3d = 12 d = -4 in 2a + 7d = 32 2a - 28 = 32 2a = 60 a = 30 the AP is 30 26 22 18 14 10 ...
July 3, 2016

Math- HELP!
inverse of y = 3x^2 - 2x -3 -----> x = 3y^2 - 2y - 3 take derivative ... 1 = 6y dy/dx - 2dy/dx 1 = dy/dx(6y - 2) dy/dx = 1/(6y-2) at (5,2) dy/dx = 1/(12-2) = 1/10
July 2, 2016

Mathematics
let f(x) = x^3 + 2x^2 - 11x - 12 try x = ±1, ±2, ±3, ±4 f(1) ≠ 0 f(-1) = -1 + 2 + 11-12 = 0 So x+1 is a factor, by synthetic division: x^3 + 2x^2 - 11x - 12 = (x+1)(x^2 + x - 12) = (x+1)(x+4)(x-3)
July 2, 2016

Algebra
I have no idea what that means.
July 2, 2016

maths
x-y = 69 x/y = 4 ---> x = 4y sub into the first: 4y - y = 69 3y = 69 y = 23 , then x = 4(23) = 92
July 2, 2016

math
smaller ---- x larger ------ x+6 7x = 6(x+6) 7x = 6x + 36 x = 36 State the conclusion
July 2, 2016

math
general term for the above: let term(n) = an^2 + bn + c for n = 1 4 = a+b+c ** for n = 2 9 = 4a + 2b + c *** for n = 3 20 = 9a + 3b + c **** subtract ** from *** 5 = 3a + b ## subtract *** from **** 11 = 5a + b ### subtract ## from ### 6 = 2a a = 3 into ## 5 = 9+b b = -4 into...
July 2, 2016

math
4, 9, x, 37 first difference: 5, x-9, 37-x 2nd difference x-14, 37-x - (x-9) x-14, 46-2x To be a quadratic sequence, the 2nd differences must all be the same, so x-14 = 46-2x 3x = 60 x = 20 so our terms are 4, 9, 20, 37
July 2, 2016

maths
make a Venn Diagram place 14 in the intersection. Leaving the 30-14 or 16 in the "only" math part of the diagram.
July 2, 2016

algebra
I looked it up and according to Hook's Law, the relation is linear. so you have two points (2,9) and (5,13.5) slope = (13.5-9)/(5-2) = 1.5 Using (2,9) my equation would be y-9 = 1.5(x-2) Using (5,13.5) would produce y-13.5 = 1.5(x-5) clearly the second one is wrong
July 1, 2016

Math
That would be 2^365 which is a number so huge that it is unimaginable. It has been estimated that the total number of atoms in the entire universe is 10^80 We can compare 10^80 with 2^365 by breaking down 2^365 into 2^300 x 2^65 = 2.037 x 10^90 x 3.6893 x 10^19 = 7.515 x 10^...
July 1, 2016

Maths
f(x) = 2x^3+b*x^2+3x-5 g(x) = x^3+x^2-4x+b f(2) = 16 + 4b + 6 - 5 = 4b + 17 g(2) = 8 + 4 - 8 + b = b + 4 "need the same divider when divided by x-2 " ----> I don't understand what that means. Are you saying they have the same remainder? If so, then 4b+17 = b+4...
July 1, 2016

math
A and B --- the two men W ----- the woman possible cases, there are only 6 ABW AWB BAW BWA WAB WBA I see 2 cases where the woman is on the left so prob(woman on left ) = 2/6 = 1/3 you do the other case.
July 1, 2016

math
I would have defined x as the number of 10cent coins. By defining the smallest quantity with your variables, usually fractions can be avoided. But, anyway.... number of 5 cent coins ---- x number of 10 cent coins ---x/3 value = 5x + 10x/3
July 1, 2016

Math
make a sketch of the triangle cotA = 3/4 ---> x=3, y=4 by Pythagoras r = 5 now we can find all possible trig ratios sinA = 4/5 cosA = 3/5 Once you establish the proper order of operation of your expression, just sub in the values e.g. is it 2sinA-3cosA ÷(2sinA - ...
July 1, 2016

Math
smaller --- x larger ---- x+10 x(x+10) = 56 x^2 + 10x = 56 x^2 + 10x + 25 = 56 + 25 (x+5)^2 = 81 x+5 = 9 x=4 one is 4, the other is 14
July 1, 2016

ALGEBRA
-5x-9y=-21 -- times 7 ---> -35x - 63y = -147 7x + 5y = -1 -- times 5 ---> 35x + 25y = -5 add them: -38x = -152 x = 4 sub into the original 2nd to get y
June 30, 2016

math
According to your garbled wording the number is 333
June 30, 2016

Maths
I read it differently. First we have to choose (combination) 3 of the 8 cities, which is C(8,3) or 8C3 = 56 (where did you get 12 cities ?) now for each of those choices, he can schedule the order of visit (permutation). Each choice can be arranged in 3! or 6 ways. number of ...
June 30, 2016

math equation
"If the side of a square are extended to form a rectangle." ?? A sentence that begins with "If ..." must end with "then ...." let the new sides be x+5 and x+2 (x+5)(x+2) = 130 x^2 + 7x + 10 - 130 = 0 x^2 + 7x - 120 = 0 (x-8)(x+15) = 0 x = 8 or x ...
June 30, 2016

Math
Set up a proportion equation: m = kw, where m is the amount of medicine, and w is the body weight, k is a constant for m = 205, w = 164 205 = k(164) k = 205/164 = 5/4 m = (5/4)w when m = 173.75, 173.75 = (5/4)w w = 139 or just use a simple ratio: w/164 = 173.75/205 w = 164(173...
June 30, 2016

Math
(x+73+60+86)/4 = 72 solve for x
June 30, 2016

Math
Are you studying vectors? the resulting velocity vector is (4,0) + (0,3) = (4,3) magnitude of vector = √(4^2+3^2) = √25 = 5 time to go 1 km at 5 km/h = 1/5 hours or 12 minutes angle between the resultant an normal: tanØ = 3/4 Ø = 36.87° for ...
June 30, 2016

Math(HELP PLEASE )
Is your table supposed to be a partial solution set to the given equation? If so, then only (-1,13) satisfies the equation , the other two points do not. Just rewrite the equation to the form y = -4x + 9 now pick any x you feel like, sub it in and you have another entry for ...
June 30, 2016

Math
There are an infinite number of solution pairs to your equation. From your post all of them are missing. One of them is (0,1) another is (3.8 , -7.55)
June 29, 2016

Math
This is a classic Distance-Rate-Time problem let the speed of slower train be x mph then speed of faster train is x+12 mph 2x + 2(x+12) = 400 solve for x
June 29, 2016

Math
quarterly rate = .10/4 = .025 = i number of payments = 4(5) = 20 = n amount = 70( 1.025^20 - 1)/.025 = ...
June 29, 2016

Maths
cost = 370 because of the 2.5% loss due to wastage, they only sold 97.5% of the fertilizer return = .975(1000)(.61) = 584.75 profit = 224.75 Percentage profit = 224.75/370 = appr 60.7 %
June 29, 2016

Math
amount sold by Susan ---- x L amount sold by William ---- (x+6.84) L amount sold by Tim ------ (x+18.3) L a) solve x+6.84 = 21 b) add them up and sub in your solution for x
June 29, 2016

algebra
Use your formulas. a+d = 24 a+4d = 3 subtract them: 3c = -21 d = -7 in a+d=24 a=7=24 a = 31 first term is 31, common difference is -7
June 29, 2016

Math
a+3d = 24 a+11d = 56 subtract them: 8d = 32 d = 4 sub into one of the above equations to find a
June 29, 2016

math
Look up "how many yards in a km" (After all, you are on a computer to post this ) btw, I did this on Moday http://www.jiskha.com/display.cgi?id=1467023818
June 29, 2016

Math
done http://www.jiskha.com/display.cgi?id=1467199616 why are you switching names?
June 29, 2016

Maths
height ---- h shadow length ----- √3 tanØ = h/√3h = 1/√3 Ø = ?? you should be familiar with the angle whose tangent is 1/√3 btw, I suspect a typo in 1√3, since we normally would not put that 1 in front of a radical. was it 1/√3...
June 29, 2016

math
really ?
June 29, 2016

math
Since in a code, the order matters, it would be 4x3x2 or 24
June 29, 2016

Differential Calculus
let the width of the rectangle be x m let the base of the rectangle be 2y m, making the radius of the semicircle equal to y m (my semicircle sits on the y ) 2x + 2y + (1/2)(2πy) = 10 2x + 2y + πy = 10 y(2 + π) = 10 - 2x y = (10-2x)/(2+π) area = 2x(2y) + (1/...
June 28, 2016

math
I assume she only needs fencing along 3 sides of the rectangle, plus a semicircle on the longer side. perimeter = 30 + 2(12) + (1/2)(2π(15)) = 54 + 15π or appr 101.12 m
June 28, 2016

math
yes
June 28, 2016

math
solve: 2x + 3x + 100 = 180 then find 2x and 3x
June 28, 2016

Algebra
smaller ---- x larger ------ x+3 4(x+3)/x = 2 4x + 12 = 2x carry on
June 28, 2016

math
8P5 ----> found on your calcualtor = P(8,5) ----> found on some Calculators = = 8!/3! = 6720
June 27, 2016

math
number of such numbers = 7x6x5x4 = 7!/3! = P(7,3) = 210 , as Steve stated
June 27, 2016

calculus
rectangle open on one side ?? Poor wording, I will assume that this is the "classic" problem where you have perimeter on only 3 sides, such as the rectangle is against a building. b = 40 - 2h A = bh = h(40-2h) = -2h^2 + 40h dA/dh = -4h + 40 = 0 for a max of A 4h=40 h...
June 27, 2016

Math
x^2+y^2-12x-10y = -12 x^2 - 12x + 36 + y^2 - 10y + 25 = -12+36+25 (x-6)^2 + (y-5)^2) = 49 new circle needs a radius of 5, so (x-6)^2 + (y-5)^2 = 25 Please tell me what you did to work on this "all day" .
June 27, 2016

Math
number of units ---- x cost = 950x + 60,000 we want 1700x ≥ 950x + 60000 750x ≥ 60000 x ≥ 80 At 80 units they break even, at more than 80 they make a profit
June 27, 2016

math
Steve took a guess at what you meant http://www.jiskha.com/display.cgi?id=1466985460 you ignored his reply and just reposted. what is "sim 17" supposed to be ??
June 27, 2016

math
traditional method: a+d = 24 a+4d = 3 subtract them: 3d = -21 d = -7 sub into a+d = 24 a - 7 = 24 a = 31 first term is 31, commond difference is -7
June 27, 2016

math
9,000,024 km = 9,000,024(100,000) cm = 9,000,024(100,000)/2.54 inches = 9,000,024(100,000)/(2.54(36)) yards = ... you do the button pushing
June 27, 2016

Please help immediately! Math
I see 6 rectangles + 2 hexagons area of one hexagon = 6(1/2)(9)(7.8) = ... take over
June 27, 2016

Urgent help here! Math
270kg of corn would feed 42 horses for 21 days 270kg of corn would feed 21 horses for 42 days 1 kg of corn would feed 21 horses for 42/270 days 360 kg of corn would feed 21 horses for (42/270)(360) days 360 kg of corn would feed 21 horses for 56 days
June 27, 2016

Math
translate from English to Math "If the 16th term of an arithmetic sequence is three times the fourth term" --->a+15d = 3(a+3d) a+15d = 3a+3d 12d = 2a a = 6d term 23 = a+22d = 6d+22d = 28d term 3 = a + 2d = 6d + 2d = 8d term23 : term3 = 28d : 8d = 28 : 8 = 7 : 2
June 27, 2016

Maths
slope is the same for all line segments = 3 so y = 3x + b plug in one of the points, I will use (1,4) 4 = 3(1) + b b = 1 rule, or the equation is y = 3x + 1
June 26, 2016

Math
let the number be x (28/5)x = -6/7 196x = -30 x = -30/196 = -15/98
June 26, 2016

math
let the angle be x its complement is 90-x its supplement is 180-x 7(90-x) = 3(180-x) - 10 solve for x
June 26, 2016

Maths
In a ||gram, opposite angles are equal, so we have 2x + 25+25 = 360 2x = 310 x = 155 Also not that adjacent angles would be supplementary. Check: 25° + 155° = 180°
June 26, 2016

Algebra
wind speed ---- x mph speed going with the wind = 160+x speed going against the wind = 160-x 800/(160-x) - 800(160+x) = 3 times (160-x)(160+x) 800(160+x) - 800(160-x) = 3(160+x)(160-x) 800x + 800x = 76800 - 3x^2 3x^2 + 1600x - 76800 = 0 x = (-1600 ± √3481600)/6 x...
June 25, 2016

Math
2x^2 = 6x 2x^2 - 6x = 0 2x(x - 3) = 0 x = 0 or x = 3 check: if x = 3 2(3)^2 = 18 6(3) = 18 , YUP! if x = 0 2(0) = 0 6(0) = 0 , YUP!
June 25, 2016

geometry
I would find the length of the lines PQ, PR, and QR then find the lengths of the sides of the other triangle. They should be the same values
June 25, 2016

math
I just googled "prime numbers" and there are about 18 million results. I am sure you can find the ones in your range.
June 25, 2016

Math HELPPPPP
x/7+y/11=1 multiply each term by 77, the LCD 11x + 7y = 77 7y = -11x + 77 y = (-11/7)x + 11 the gradient or slope is -11/7 (in your answer you included the variable) b) y+ 5/3x=7/3 , or y = (-5/3)x + 7/3 the slope is -5/3 , so Y=mx+c ----> Y = (-5/3)x + c if (2,3) lies on ...
June 25, 2016

Math
Two things: --- sin 37° ≠ 6/10 --- there are no "following"
June 25, 2016

Math
20 hundreds ---> 20(100) or 2000 3 x 10^2 = 300 so what is the difference between 2000 and 300 ?
June 25, 2016

Math
evaluate: 245612 - (18912 + 45608)
June 25, 2016

Math
I am a number between 1000000 and 2000000 ---> 1 ??? ??? my hundred thousands, thousands, and ones digits are the same ---> 1 x?x ??x ---> 1 xax bcx My ones digit is the sum of my tens and hundreds digits ---> x = b+c also the sum of my millions and ten thousands ...
June 25, 2016

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