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Posts by Reiny

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math
now: daughter ---- x years Mary -------- 3x years 4 years ago: daughter : x-4 Mary : 3x-4 (x-4)(3x-4) = 40 3x^2 -16x + 16 = 40 3x^2 - 16x - 24 = 0 I was expecting it to factor, hoping for whole number solution, but .... x = (16 ± ?544)/6 = 6.55 or a negative check: if ...

Math
let the two numbers be 9x and 3x then 9x + 3x = 72 .. x = 6 sub into my definition to get the numbers.

Math
Find the midpoint of AB, then use your "distance between two points" formula to get CM .

Maths
let the numbers be x and x+1 solve: x + x+1 = 39

math
your first equation should have been 4x +5 = 37 instead of 4x(5) = 37 but then you miraculously switched it to the right one as you solved it. The answer is correct

Further mathematics
x^2 + y^2 = 5xy complet the square: x^2 + 2xy + y^2 = 7xy (x+y)^2 = 7xy take log of both sides 2log(x+y) = log 7 + logx + logy 2log(x+y) - log7 = logx + logy 2log(x+y) - 2log 7^(1/2) = logx + logy 2[ log(x+y) - log ?7] = logx + logy 2 log( (x+y)/?7 ) = logx + logx as required ...

algebra~help me
18^(4-4y)=54(?2)^(3y-2) take log of both sides (4-4y)log18 = lof54 + (1/2)(3y-2)log2 4log18 - 4ylog18 = log54 + (3y/2)log2 - log2 4log18 - log54 + log2 = y( (3/2)log2 + 4log18) 3.58972... = (5.4726...) y y = .655941

Calculus
so considering t = 0 to correspond with 2016 1000 = A 3^0 , but 3^0 = 1 A = 1000 b) y(5) = 1000 3^(4/3) = .... Use your calculator c) 100000 = 1000 3^(t/4) 1000 = 3^(t/4 take log of both sides log 1000 = log 3^(t/4) 3 = (t/4)log 3 t/4 = 3/log3 t = 12/log3 = appr 25.15 years iv...

math
Assuming the farm is a rectangle ... length --- x width = 39 2x + 2(39) = 187.2 find x once you have x, take x/39

algebra
How about you showing me some of your steps, now that I have done two very similar to this one for you ?

algebra
breath (width) ---- x length -----------x+12 2x + 2(x+12) = 144 carry on

algebra
smaller --- x larger --- y Now just translate into Math. 3(y - x) = y+3 3y - 3x = y+3 3x - 2y = -3 ** 3(y+x) = 8x + 2 3y + 3x = 8x + 2 5x - 3y = 2 *** solve ** and *** You should get two whole numbers.

Differential calculus
If expanded you would get a standard cubic Its x-intercept are (2,0), (-1,0) and (-3,0) http://www.wolframalpha.com/input/?i=plot+y%3D(x-2)(x%2B1)(x%2B3)

maths
let the two numbers be 5x and 7x "it's lam is 210" , I have no clue what that means.

maths
I will assume you meant the ninetieth term. If a and d are the first term and common difference respectively, then term(90) = 30 a + 89d = 30 a = 30-89d sum(17) = (17/2)(2a + 16d) = (17/2)(2(30-89d) + 16d) = (17/2)(60 - 162d)

Math
Did you make a sketch? 1) sin30° = h/15 h = 15sin30 = 15(1/2) = 7.5 m Very unsafe way to place a ladder, the angle should be > 76° at the ground 2) in reference to the 60° angle, the 13 m is the "adjacent" and you want the "opposite" side ...

Statistics
numer of ways = 15 x 14 x 12 = .... (assuming the order matters, and you have specified positions)

Math
correct (the jet stream does not just flow over the US )

I dont know
they can be any (x,y) such that x^2 + y^2 = 64 e.g. (2 , ?60), (?39 , 5) , (8,0), (8,0), (4?2 , 4?2) etc

Algebra2
but log8 2 = 1/3 so log8 (a/2) = log8 a - 1/3

math
equilateral ---> all sides are equal, so 3x+2 = 2y-x 4x + 2 = 2y 2x + 1 = y also 3x+2 = y + 3 3x+2 = 2x+1 + 3 x = 2 then y = 5 so each side is 3x+2 = 8 and the perimeter is 24

Math
9/(2x) = 15/12 "cross-multiply" 30x = 108 x = 108/30 = 18/5 or 3.6

Math
amount of peaches --- x lbs amount of melons ---- y lbs amount of apples ----- 100 - x - y lbs (assume both x and y are whole numbers) 10x + 3.5y + .5(100-x-y) = 100 double every term 20x + 7y + 100 - x - y = 200 19x + 6y = 100 x = (100 - 6y)/19 , clearly 0 < y < 6 by ...

10th Grade Math
To have a triangle, the sum of any two sides must be greater than the third side. look at C 5+10< 18 all the others form a triangle

maths
The volume of 2 similar objects is proportional to the cube of its linear sides 320/x = 8^3/6^3 512x = 69120 x = 69120/512 = 135 or the side ratio is 6/8 = 3/4 old volume = 8(l)(w) = 320 lw = 40 new volume = 6(3l/4)(3w/4) = 54/16 lw = (54/16)(40) = 135

maths
surface area of smaller = 4? r^2 surface area of larger = 4?(3r)^2 = 36?r^2 which is 9 times as great or the area of similar objects is proportional to the square of their linear dimension, so 1^2 : 3^2 = 1 : 9

Algerbra
so it will differ only in the constant let the equation be y = -4x + b but (-8,-4) lies on it, so -8 = -4(-8) + b solve for b and write the equation.

Trigonometry
tanØ = 4/1 = 4 Ø = 75.96 The angle should be 76° by ratio: 4/1 = 16/x x = 4

Math
number of adult tickets sold = 3x number of children tickets sold = 5x 5x = 3x + 180 take over.

math
LCD is 5b a/5 +4/b = ab/5b + 20/5b = (ab + 20)/(5b)

Algebra
slope of main street = (33-17)/(-22+2) = -4/5 so slope of Grimes Blvd = +5/4 y - 9 = (5/4)(x-80) y = (5/4)x - 100+ 9 y = (5/4)x - 91

Math
Follow the same steps I just showed you in your previous problem.

Math
number of girls ---- 7x number of boys ---- 5x "there are 8 more girls 10 boys" makes no sense are you saying, "there are 8 more girls than boys" ? which translated into math would be 7x = 5x+8 take it from here

maths
done, see below

algebra
number of nickels ---- x number of dimes ----- x+10 number of quarters = 37-(x + x+10) = 27 - 2x value of coins = 5x + 10(x+10) + 25(27-2x) = 5x + 10x + 100 + 675 - 50x = 775 - 35 x

Math
I don't know, you did not state the rate of interest.

maths
volume of wooden rod = ?(2^2)(6) = 24? volume which is submerged = 12? So the volume in the cylinder will change by that amount ?(4^2)h = 12? 16h = 12 h = 12/16 cm = 3/4 cm new depth = 4+3/4 cm = 19/4 cm or 4.75 cm

maths
" ... is placed in the tin or floats exactly half 2.what is the New depth of water " Retype in proper English so I can understand it.

maths
OK, even though have always been told that we can't add apples and oranges, ..... let the amount of apples be x lbs amount of oranges ----- (52 - x) lbs 5.25x + 3.8(52-x) = 4.25(52) 5.25x + 197.6 - 3.8x = 221 1.45x = 23.4 x = 16.1 lbs of apples and 35.9 lbs of oranges appr...

math
cost = 7.2(12) = 86.4 18 eggs = 1.5 dozen so you sold 10.5 dozen at 7.5 return = 10.5(7.5) = 78.75 loss = 86.4 - 78.75 = 7.65

Maths
Four times as much, or 32 kg Can you show me why that is so?

maths
volume of ball = (4/3)?(4.5)^3 So that is the change in volume in the cylinder once removed ?(6^2) h = (4/3)?(9/2)^3 36h = (4/3)(729/8) = 243/2 h = 243/72 = 27/8 the water will fall 27/8 cm or 3.375 cm check my arithmetic.

Algebra 1
The boat will be .15 miles from Ellen coming and going away. So 1 - 70t = .15 OR -1 + 70t = .15 t = .01214... hrs or t = .01642.. hrs t = .01214(3600) sec or t = .01642(3600) sec t = 43.7 sec OR t = 59.1 sec

check - Math
ok, the cat's were adopted, that means the count was reduced by 120, not increased. I read the question incorrectly number of cats after adoption = 2x - 120 make the simple change in the equation and solve

Math
number of cats ---- 2x number of dogs ----3x after adoption: number of cats = 2x + 120 (2x+120) : 3x = 3 : 7 (2x+120)/(3x) = 3/7 14x + 840 = 9x 5x = -840 x is a negative, which is not possible. notice 2:3 = .66.. and 3:7 = .42 , which is < 2/3 How can the ratio of cats : ...

maths
Area of a triangle = (1/2)(ab)sinØ where a and b are sides with Ø as the angle between them. Your data is perfectly suited for that formula

found my error - Go with Steve - maths need help
The second equation had addition, I read it as another subtraction.

maths need help
Log (a+3) (base 9) - log b(base 9)= c + (1/2) log9 (a+3) - log9 b = c+1/2 log9 ((a+3)/b) = c+1/2 ---> 9^(c+1/2) = (a+3)/b 3^(2c+1) = (a+3)/b ** log (a-3) (base 3) + log b (base 3)=c - 1 log3 (a-3)+ log3 b = c-1 log3 ( (a-3)/b )= c-1 --> 3^(c-1) = (a-3)/b *** divide ** by...

Math
let the roots of ax^2+bx+c=0 be m and n then m:n = r:1 m/n =r/1 m = rn sum of roots = m+n = rn + n = n(r+1) = -b/a ** product of roots = mn = n^2 r = c/a *** divide ** by *** (r+1)/nr = (-b/a) / (c/a) = -b/c rc + c = -bnr rc + bnr = -c r(c + bn) = -c r = -c/(c+bn) For acr^2+(...

math
A standard rotation is 2?. So whatever angle you have either adding or subracting multiples of 2? will yield a coterminal angle. e.g 8?/3 -----> think 480° 8?/2 - 2? = 2?/3 -----> think 120° 8?/3 + 2? = 14?/3 -----> think 840° 8?/3 - 4? = -4?/3 -----> ...

calculus
c(x)=3x^3 - 12x^2 +9000x c ' (x) = 9x^2 - 24x + 9000 = 0 for a max/min of c(x) 9x^2 - 24x + 9000 = 0 This equation has no real solution. c(0) = 0, for all values of x > 0, c(x) increases so our minimum cost is when we don't produce anything, (that actually makes ...

Math
If you are referring to your previous post, look at my reply to it.

Math
For any number to be divisible by 6, it must be divisible by both 2 and 3 To be divisible by 2, the unit digit must be even or zero, so that eliminates A - 5. To be divisible by 3, the sum of the digits must be a multiple of 3 (divisible by 3) Since we have a sum of 8 for the ...

Algegra
So let's just change Ax + By = C to the form y = mx + b Ax + By = C By = -Ax + C divide each term by B y = (-A/B)x + C/B So compare that to y = mx + b m = -A/B so I have just developed a quick way to find the slope of any equation in general form e.g. 7x + 9y = 17 has slpe...

Math
so with her new test, there will be 6 tests (sum of what you have so far + x)/6 = 69 solve for x

maths
original fraction --- x/y first new fraction: (x+1)/(y+1) = 2/3 3x + 3 = 2y + 2 3x - 2y = -1 ** second new fraction: (x-2)/(y-2) = 3/5 5x - 10 = 3y - 6 5x - 3y = 4 *** solve the two equations ** and ***

mathematical methods for economics
Did you try Venn diagrams? Start filling in from the intersection of all three circles. Put 50 in that intersection, then work your way outwards from there.

Math, Surds
let the length of each side be s s^2 = 60 s = ?60 = ?4*?15 = 2?15 each side is 2?15 m perimeter = 8?15 m

Mathss
If you have a right-angled triangle, the area is (1/2) base x height You have the base and height, clearly 65 will not be used since it is the hypotenuse. So go for it. For the second, if you have two sides and the contained angle, then the area is (1/2)(a)(b)sinØ, ...

maths
The first two triangles are clearly right-angled. Is the third one ? is 65^2 = 33^2 + 56^2 ??, YES So make sketches of each one. for a) I labeled by triangle ABC, where a = 30 angle A = 90, and angle B = 30° sin35° = 30/b bsin35 = 30 b = 30/sin35 = appr 52.30 tan35 = ...

MATHS
All of the trig ratios shown are based on "standard" angles. We used to have math kits that contained a compass, a protractor and two triangles. One had angles 45-45-90°, the other had 30-60-90° The ratio of sides of the 30-60-90 were 1 : ?3 : 2 and for the ...

Math probability
prob(big winner) = 1/C(68,5) = 1 / 10,424,128 = appr .000,000,1

algebra
first number ---- x second number --- x+9 third number ----- 82 - x - x - 9 = 72 -2x all three numbers are expressed in terms of one variable: x , x+9, and 72-2x

algebra 1
just subtract them: 10y = -10 y = -1 plug that into the first: -4x + 7(-1) = -3 -4x = -3+7 = 4 x = -1 x = -1, and y = -1

Math
There are no "points in the table below"

Math
y+x =10 y - x = 20 add them: 2y = 30 y = 15 15+x = 10 x = -5 x = -5, y = 15

Life Science Math
acceleration --- a then v = at + c at the start, t = 0, and v=0 0 = 0 + c ---> c = 0 so v = at when t = 3 sec = 3/3600 hrs or 1/1200, v = 60 60 = a(1/1200) a = 72000 ------> v = 72000t if s is the distance travelled , s = 36000t^2 + k when t = 0 , s = 0, so k = 0 s = ...

f math
I will assume that by t ta you mean Ø so sin(90 - 5Ø) = cos(180 - Ø) but sin(90 - 5Ø) = cos Ø just like sin(90 - 30) = cos30 so we have cos(5Ø) = cos(180-Ø) take arccos of both sides 5Ø = 180-Ø 6Ø = 180 &...

f math
What is "t ta" ?? Where does "d" enter the picture?

Math
agree with C I did not answer the question that was asked My 4 slices would represent 1/2 of an 8 slice pizza.

Math
If each pizza is cut into 8 slices, then in the 7 pizzas there are 56 slices So each of the 14 student would get 56/14 or 4 slices. You did not post any "answer choices", so I hope 4 is in there.

Math
let one number be x let the other be x+7 x + x+7 = 63 solve for x, and all that is unknown shall be revealed.

Math
Done the way you typed it: |1-15x/5| < 3 1 - 15x/5 < 3 AND -1 + 15x/5 < 3 -3x < 2 AND 3x < 4 x > -2/3 AND x < 4/3 What you probably meant: | (1-15x)/5 | < 3 (1 - 15x)/5 < 3 AND (-1 + 15x)/5 < 3 1 - 15x < 15 AND -1 + 15x < 15 -15x < 14 AND...

Math Quadratic Equations . URGENT!!!!
look back when you posted this earlier

Trig
Did you make a sketch? I followed your labels and let the base of the building be B in triangle DAB, tan30 = DB/30 DB = 30tan30° = ... in triangle CAB, tan 60 = CB/30 CB = 30tan60 = ... CD = CB - DB = ....

Math
correct, ***80 is the only one divisible by 4

Math
A number is divisible by 4 if its last two digits are divisible by 4, or the last two digits are zeros. I see only one such case

Math, Quadratic equations
this was answered when you were Rachel.

Math, Quadratic equaitons
your data does not match the equation , so I don't know which is the correct one I will go with the equation: h = -4t^2 + 8.1t + 3 , (according to your data it would be 8.2t) when h = 6 6 = -4t^2 + 8.1t + 3 4t^2 - 8.1t + 3 = 0 using the formula: t = (8.1 ± ?17.61)/8...

College Math
You are partly on the right track. The C(13,7) is the number of to choose 7 of the 13 marbles. you want the case of 3 reds plus 4 non-reds prob(your stated event) = C(3,3)*C(10,4)/C(13,7) = 1*210/1716 = 35/286

f math
1 - cos^2 x = 0 , for 0 ? x ? 270° cos^2 x = 1 cos x = ± 1 now look at the cosine curve. Where is the y equal to either +1 or -1 within your domain ?

Calculus
y = ln(sint) dy/dt = (1/sint)(cost) = cost/sint for x= cos^2 t = (cost)^2 dx/dt = 2cost(-sint) (dy/dt) / (dx/dt) = (cost/sint) / (-2sintcost) dy/dx = -1/(2 sin^2 t) = (-1/2)(sint)^-2 d(dy/dx) / dx = (-2)(-1/2)(sint)^-3 (cost) = cost / sin^3 t sub in t = ?/4 d(dy/dx) / dx = (?2...

Maths
remember that sinx = cos(90-x) - property of complementary angles, "co-sine" vs sine Your statement is only true if (cos40-sin30)/(sin60-cos50) =tan50 , but not the way you typed it. cos40 = sin50 and sin60 = cos30 so LS = (sin50 - sin30)/(cos30 - cos50) remember ...

Math
let the obtuse angle be A and its opposite diagonal be x. By the cosine law: x^2 = 45^2+28^2-2(48)(28)cosA similarly... y^2 = 45^2+28^2-2(48)(28)cosB but A+B = 180 B=180-A and cosØ = -cos(180-Ø) by the CAST rule e.g. cos 60 = - cos120 then cos B = -cosA x^2+y^2...

math
original fraction: x/y case1 (x+5)/(y+5) = 1/2 2x + 10 = y+5 2x - y = -5 ** case2 (x-1)/(y-1) = 1/5 5x - 5 = y - 1 5x - y = 4 *** subtract ** from *** 3x = 9 x = 3, then from ** 6 - y = -5 , y = 11 the original fraction was 3/11 check: (3+5)/(11+5) = 8/16 = 1/2, check! (3-1)/(...

Math Quadratic Functions
A squaring of the input value is involved. A rather vague question.

math
just like in 5/6 - 3/7 you will need a common denominator. In my example, it would be 42? How did I get 42 ? Next step 35/42 - 18/42 ---> how did I get those fractions = 17/42 Now to your problem 5/(x-2) - 4(x-3) LCD = (x-2)(x-3) ---> same step as above e.g = 5(x-3)/((x-...

Calculus
I will assume you are saying $1 per square foot let the base be x ft by x ft, let the height be y area of top and 4 sides = x^2 + 4xy cost of top and 4 sides = 1(x^2 + 4x) = x^2 + 4xy area of base = x^2 cost for the base = 2x^2 total cost = 3x^2 + 4xy = 114 y = (114 - 3x^2)/4x...

Math (Calculus) (mean value theorem emergency)
your secant equation is correct checking the other parts: f '(x) = 2x - 1 ---> you had that setting that equal to 1, since the slope of our secant is 1 2x-1 = 1 2x = 2 x = 1 so all you have to do is sub that back into the original f(1) = 1 - 1 - 12 = -12 So the point ...

algebra
yes

algebra
no Why do you think it is C or are you just guessing?

algebra
no , B does not have the necessary brackets

algebra
if the point is (a,b) and the slope is m then the equation is y - b = m(x - a) now which one of the given answers follows that pattern?

Math help pls. !!
(2x-3)(5x+2)=0 This is only possible if one or more of the given factors equal zero. But we don't know which one, so 2x-3 = 0 OR 5x+2=0 2x = 3 OR 5x = -2 x = 3/2 or x = -2/5

Math
(1/2)x^2 - 2x = 6 times 2 x^2 - 4x = 12 x^2 - 4x - 12 = 0 it factors: (x - 6)(x + 2) = 0 now follow the steps I showed you here http://www.jiskha.com/display.cgi?id=1479598571

math
number of digits = 3x2x1 = 6 , we could actually list them 137 173 317 371 713 731 Here is a list of primes: http://primos.mat.br/indexen.html you will find that all are prime except 371, 713 and 731 731 =17 x 43 713 = 23 x 31 371 = 7 x 53

math algebra
I did this when you were rita http://www.jiskha.com/display.cgi?id=1479589996

FUNCTIONS HELPPPPP????
After seeing how you responded to Steve when he helped you with this question .... http://www.jiskha.com/display.cgi?id=1479505703

Math
Volume of cylinder = ?(r^2)(h) plug in your values.

math algebra
rate of gandola in still water --- x mph speed of current ---- y mph time to go 2.8 miles with the current = 2.8/(x+y) time to go 2 miles against the current = 2/(x-y) they are the same! 2.8/(x+y) = 2/(x-y) 2.8x - 2.8y = 2x+2y .8x = 4.8y 8x = 48y x = 6y or y = (1/6)x All we ...

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