Wednesday
February 22, 2017

Posts by Reiny

Total # Posts: 37,761

pre calculus
250 pounds at 45° ---> (250cos45, 250sin45) 130 pounds at -60° ---> (130cos(-60), 130sin(-60) ) Resultant = (250cos45, 250sin45)+(130cos(-60), 130sin(-60) ) = (125?2, 125?2) + (65 , -65?3) = ( 125?2 + 65 , 125?2 - 65?3) = appr (241.7767 , 64.1934) maginitude...
November 26, 2016

Discrete Math
if you meant: x^1 + x^2 + x^3 + 2x^4 + x^5 = 68 there are none http://www.wolframalpha.com/input/?i=solve+x+%2B+x%5E2+%2B+x%5E3+%2B+2x%5E4+%2B+x%5E5+%3D+68
November 26, 2016

pre calculus
checking for right-angled triangle: is 100^2 = 55^2 + 85^2 ? NO so let's find the smallest angle by the cosine law: 55^2 = 100^2 + 85^2 - 2(100)(85)cosØ cosØ = 14200/17000 = .83529.. Ø = 33.35..° , (I stored it for accuracy on my calculator So area...
November 26, 2016

pre calculus
u=<0,-4>, v=<-2,-8> a) 2v+u = <-4,-16) + <0,-4) = <-4, -20> b) 5u - v = <0,-20> - <-2,-8) = <2, -12> c) do this one the same way
November 26, 2016

Mathmatics help please
clearly 25 and 15
November 26, 2016

Maths help asap please
3c-7 > 5c+4 3c - 5c > 4+7 -2c > 11 c < -11/2 or c < -5.5 so the smallest integer that is a solution is c = -6 check: if c = -6, -18 - 7 > -30+4 -25 > -36 , true! if c = -5 -15-7> -25+4 -22 > -21 , false
November 26, 2016

Math
subtract 2 from each part, and you are done -3<x+2<3 -3-2 < x+2-2 < 3-2 -5 < x < 1 ---> ( x lies between -5 and 1 )
November 26, 2016

Math
nothing wrong with that you could just use the trig-vector notation resultant = (10cos60,10sin60) + (20cos120,20sin120) + (30cos180,30sin180) + (40cos270,sin270) = (5, 5?3) + (-10, 10?3) + (-30, 0) + (0, -40) = ( -35, 5?3-40 )) your sketch will confirm that
November 26, 2016

Trigonometry
Both Steve and I both told you what was wrong with the wording of the question. http://www.jiskha.com/display.cgi?id=1480115359 Did you even look at the responses?
November 25, 2016

Math
(2 x 3)>2 - 5>2 is a false statement. you are basically saying: 6 > 2-5 > 2 6 > -3 > 2 the part 6 > -3 is true, but -3 > 2 is nonsense To ask "evaluate" the expression makes no sense Hey, wait a minute! Did you mean (2 x 3)^2 - 5^2 ?? then you...
November 25, 2016

math
You can't just drop the variable. 5(2x + 7) = 10x + 35 Now you can see that we can't add the 10 and 35 since they are "unlike" terms
November 25, 2016

Math
correct
November 25, 2016

math
The 14M, the 3M and the 1M are all expenses so what is 20 - (14+3+1) ?? I get 2 Million
November 25, 2016

Calculus AB
3y^3 + 2x^2 = 5 9y^2 dy/dx + 4x = 0 dy/dx = -4x/9y^2 when y = 1 , 3 + 2x^2 = 5 2x^2 = 2 x = ± 1 , but in quadrant 1, x = 1 dy/dx = -4(1)/9 = -4/9 equation of tangent: y-1 = (-4/9)(x-1) 9y-9 = -4x + 4 4x + 9y = 13 check: http://www.wolframalpha.com/input/?i=plot+3y%5E3+%...
November 25, 2016

Trigonometry
y = cos(3?/4 - x) already is a single function of x, namely the cosine function. I don't understand what else you want to do with it. We know: using cos(A-B) = cosAcosB + sinAsinB cos(3?/4 - x) = cos 3?/4 cosx + sin 3?/4 sin x = -?2/2 cosx + ?2/2sinx = ?2/2 (sinx - cosx...
November 25, 2016

Math
In the original number let the unit place by x then the tens place is 2x, (obviously x < 5) then the number in terms of its value is 10(2x) + x and the number reversed is 10x + 2x the difference between these two is 36, just translate this into Math. 10(2x) + x - (10x + 2x...
November 25, 2016

Math
clearly the 5 has to go in the unit position for the number to be odd At the front, what would be bigger, something 6 hundred or something 8 hundred?
November 25, 2016

Mathematics
let his sales be x .06x + 6000 = 10200 solve for x
November 25, 2016

Maths
330/x - 330/(x+5) = 1/2 That's ok, we end up with a quadratic. Multiply each term by 2x(x+5) 660(x+5) - 660x = x(x+5) 660x + 3300 - 660x = x^2 + 5x x^2 + 5x - 3300 = 0 (x-55)(x+60) = 0 x = 55 or x = -60, we would reject the -60 So your inward speed is 55 km/h, the return ...
November 25, 2016

math
90 = 2x3x3x5 since each pair of equal factors produces a perfect square, we have 3x3, a perfect square. So all we need is another 2 and another 5 How about 2x2x3x3x5x5 = 900 900 = 30^2 , so it is a perfect square, and it is divisible by 90
November 24, 2016

math-factors and multiples
both 40 and 32 divide by 8 both a^3 and a^2 divide by a^2 The GCF is 8a^2
November 24, 2016

math
It is 30a^2
November 24, 2016

math
5 ? m/-3 + 18 add m/3 to both sides 5 + m/3 ? 18 m/3 ? 13 m ? 39 or 5 ? m/-3 + 18 -13 ? m/-3 times -3 39 ? m m ? 39 , same as above
November 24, 2016

math
the slope of the 2nd is -2/16 = -1/8 which is the negative reciprocal of the slope of the first. Thus, the lines are perpendicular.
November 24, 2016

math
I assume we are factoring 25m^6-121m^4 = (5m^3 - 11m^2)(5m^3 + 11m^2)
November 24, 2016

Calculus applications
let the height be 100 cm^3 ?r^2 h = 100 h = 100/(?r^2) S = 2 circles + the sleeve = 2?r^2 + 2?rh = 2?r^2 + 2?r(100/(?r^2)) = 2?r^2 + 200/r you typed it wrong, it should have been 2?r^2 + 200 r^-1 dS/dr = 4?r - 200/r^2 = 0 for a min of S 4?r = 200/r^2 r^3 = 200/(4?) = 25/? r...
November 24, 2016

Math
Now: Marcus ---- x John ------ x+10 5 years from now: John's age = x+15 5 years ago: Marcus = x-5 3(x+15) = x-5 that would give you the silly answer of x = -25 checking now Marcus is -25 John is -15 5 years from now, John is -10 and 5 years ago Marcus was -30 sure enough 3...
November 24, 2016

maths
Without any restrictions, number of committees = C(10,4) = 210 include at least one woman ---> exclude cases of all 4 being men number of ways = 210 - C(5,4) = 205
November 24, 2016

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 ...
November 24, 2016

Math
let the two numbers be 9x and 3x then 9x + 3x = 72 .. x = 6 sub into my definition to get the numbers.
November 24, 2016

Math
Find the midpoint of AB, then use your "distance between two points" formula to get CM .
November 24, 2016

Maths
let the numbers be x and x+1 solve: x + x+1 = 39
November 24, 2016

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
November 24, 2016

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 ...
November 23, 2016

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
November 23, 2016

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...
November 23, 2016

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
November 23, 2016

algebra
How about you showing me some of your steps, now that I have done two very similar to this one for you ?
November 23, 2016

algebra
breath (width) ---- x length -----------x+12 2x + 2(x+12) = 144 carry on
November 23, 2016

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.
November 23, 2016

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)
November 23, 2016

maths
let the two numbers be 5x and 7x "it's lam is 210" , I have no clue what that means.
November 23, 2016

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)
November 23, 2016

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 ...
November 22, 2016

Statistics
numer of ways = 15 x 14 x 12 = .... (assuming the order matters, and you have specified positions)
November 22, 2016

Math
correct (the jet stream does not just flow over the US )
November 22, 2016

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
November 22, 2016

Algebra2
but log8 2 = 1/3 so log8 (a/2) = log8 a - 1/3
November 22, 2016

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
November 22, 2016

Math
9/(2x) = 15/12 "cross-multiply" 30x = 108 x = 108/30 = 18/5 or 3.6
November 22, 2016

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 ...
November 22, 2016

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
November 22, 2016

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
November 22, 2016

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
November 22, 2016

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.
November 22, 2016

Trigonometry
tanØ = 4/1 = 4 Ø = 75.96 The angle should be 76° by ratio: 4/1 = 16/x x = 4
November 22, 2016

Math
number of adult tickets sold = 3x number of children tickets sold = 5x 5x = 3x + 180 take over.
November 22, 2016

math
LCD is 5b a/5 +4/b = ab/5b + 20/5b = (ab + 20)/(5b)
November 22, 2016

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
November 22, 2016

Math
Follow the same steps I just showed you in your previous problem.
November 22, 2016

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
November 22, 2016

maths
done, see below
November 22, 2016

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
November 22, 2016

Math
I don't know, you did not state the rate of interest.
November 22, 2016

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
November 22, 2016

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.
November 22, 2016

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...
November 22, 2016

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
November 22, 2016

Maths
Four times as much, or 32 kg Can you show me why that is so?
November 22, 2016

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.
November 22, 2016

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
November 22, 2016

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
November 22, 2016

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 : ...
November 22, 2016

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
November 22, 2016

found my error - Go with Steve - maths need help
The second equation had addition, I read it as another subtraction.
November 22, 2016

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...
November 22, 2016

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+(...
November 21, 2016

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 -----> ...
November 21, 2016

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 ...
November 21, 2016

Math
If you are referring to your previous post, look at my reply to it.
November 21, 2016

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 ...
November 21, 2016

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...
November 21, 2016

Math
so with her new test, there will be 6 tests (sum of what you have so far + x)/6 = 69 solve for x
November 21, 2016

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 ***
November 21, 2016

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.
November 21, 2016

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
November 21, 2016

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, ...
November 21, 2016

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 = ...
November 21, 2016

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 ...
November 21, 2016

Math probability
prob(big winner) = 1/C(68,5) = 1 / 10,424,128 = appr .000,000,1
November 20, 2016

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
November 20, 2016

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
November 20, 2016

Math
There are no "points in the table below"
November 20, 2016

Math
y+x =10 y - x = 20 add them: 2y = 30 y = 15 15+x = 10 x = -5 x = -5, y = 15
November 20, 2016

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 = ...
November 20, 2016

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 &...
November 20, 2016

f math
What is "t ta" ?? Where does "d" enter the picture?
November 20, 2016

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.
November 20, 2016

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.
November 20, 2016

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.
November 20, 2016

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