Sunday
December 4, 2016

Posts by Reiny

Total # Posts: 36,897

Maths
That result is like adding 3/10 + 14/20 + 24/30 = 41/60 Wow, just adding the numerators and the denominators ! Unfortunately Math doesn't work like that 3/10 + 14/20 + 24/30 = 18/60 + 42/60 + 48/60 = 108/60 for 3 tests so average = (108÷3)/60 = 36/60 = 60% By simply...
November 17, 2016

calc
no, for the 2xy term you have to use the product rule 2y dy/dx + (2x)(dy/dx) + 2y(1) - 3x^2 = 0 keep all the dy/dx terms on the left, everybody else goes to the right 2y dy/dx + 2x dy/dx = 3x^2 - 2y factor out the dy/dx dy/dx (2y + 2x) = (3x^2 - 2y) divide dy/dx = (3x^2 - 2y...
November 17, 2016

math
The best way to do this is to actually sketch it. I am sure it will make perfect sense to you after you draw it. Remember that y =-2 is a horizontal line 2 units below the x-axis
November 17, 2016

math
profit = revenue - cost = 12x - .01x^2 - 8^x - 7 d(profit)/dx = 12 - .02x - (8^x)(ln8) = 0 for a max of profit 12 - .02x = ln8 (8^x) if x = 0, LS = 12 , RS = ln8 or appr 2.08 if x = 1, LS = 11.98 , RS = appr 16 so there is a solution between 0 and 1 This question does not make...
November 17, 2016

Math
Strange wording. "What fraction" of what should the shorter side be increased? Since the sides are stated in a ratio, they could be 4 cm by 5 cm, 40 miles by 50 miles, 8 ft by 10 ft, etc In each case the shorter side would be increased by 1/4 of its original length. ...
November 17, 2016

math
you are simply solving the quadratic 187 = -16t^2 + 45t + 364 16t^2 - 45t - 177 = 0 solve by using the formula, one of the answers will probably be negative. Reject it.
November 17, 2016

Maths
I will assume the 2nd direction is 125° The angle between the two directions is 90° so AC = ?(120^2 + 200^2) = 233.238 km or Suppose we did not see that 90° ,we could simply use vectors AC = (120cos35,120sin35) + (200cos125,200sin125) = (98.298.., 68.829..) + (-114...
November 17, 2016

Maths
As an illustration of your problem, place 3 identical coins, e.g. 3 quarters in such a way that they are tangent to each other. Sketching a triangle around them results in an equilateral triangle, we want the perimeter of that triangle. Let's concentrate on one of these ...
November 17, 2016

Algebra
place the vertex at (0,0) and the focus at (8,0) The directrix will be x = -8 let P(x,y) be any point By definition: ?( (x-8)^2 + y^2) = x+8 square both sides x^2 - 16x + 64 + y^2 = x^2 + 16x + 64 y^2 = 32x so at the point where the dish is 10 ft wide, y = 5 25 = 32x x = 25/32
November 16, 2016

Math
10,000(1.04)^n = 15000 1.04^n = 1.5 take logs of both sides log 1.04^n = log 1.5 n log 1.04 = log 1.5 n = log 1.5/log1.04 = 10.338.. 10 years will not be enough , so she makes 15,000 or more in the 11 th year for the second question you have an arithmetic sequence with a = ...
November 16, 2016

6 grade math
no need for guessing, just reverse the steps: the first thing we did was multiply by 2, then subtract 27 to get 407 So everything done in reverse: ( 407+27) divide by 2 = 434 ÷ 2 = 217
November 16, 2016

Algebra
x e^.06t = 70000 x = 70000/e^(.06(19)) = 22,387.33
November 16, 2016

Statistics
prob(exactly one boy) = C(7,1)xC(5,4)/C(12,5) = 7(5)/792 = 35/792 prob(exactly 2 boys) = C(7,2)xC(5,3)/792 = 21(10)/792 = 35/132 at least one boy = 1 - prob(all girls) = 1 - 1/792 =791/792
November 16, 2016

Math
you second equation is x-2055 = .25y , what's with the G ? but y = x x-2055 = .25x .75x = 2055 x = 2740
November 16, 2016

Math
Did you mean, find cos t ? if so, cos t = 5/?29
November 16, 2016

mathematics
Did you mean x+y=1 x-y=3 ?? if so, add them to get 2x=4 x=2 now subtract them 2y = -2 y = -1
November 16, 2016

math
Just translate from English to Math larger number --- x smaller number --- y x-y = 15---> x = y + 15 3x = 8y 3(y+15) = 8y 3y + 45 = 8y 45 = 5y y = 9 , then x = 9+15 = 24 state your conclusion
November 16, 2016

math
speed of train ---- t km/h speed of car ----- c km/h 120/t + 480/c = 8 15/t + 60/c = 1 times tc tc = 15c + 60t 200/t + 400/c = 25/3 times tc (25/3)tc = 200c + 400t tc = (3/25)(200c + 400t) = 24c + 48t 24c + 48 = 15c + 60t 9c = 12t c = 4t/3 sub into 15/t + 60/c = 1 15/t + 60/(...
November 16, 2016

math
boys rate = 1/b men's rate = 1/m job done by 2 men and 5 boys in 4 days = 4(2/b + 5/m) = 8/b + 20/m job done by 4 men and 4 boys in 3 days = 3(4/m + 4/b) = 12/m + 12/b 8/b + 20/m = 12/m + 12/b 8/m = 4/b 8b = 4m m = 2b or b = m/2 The man's rate is twice the boy's ...
November 16, 2016

TRIANGLE MATH HELP!!!
Obviously.
November 16, 2016

TRIANGLE MATH HELP!!!
clearly 47:29:104 ? 46:30:104, but close and 4 : 6 : 8 ? 5.6 : 8 : 11 because: 5.6/4 = 1.4 8/6 = 1.333... 1.375 which answer matches my conclusion
November 16, 2016

Math Help!!!
6/202.5 = x/52.5 202.5x = 6(52.5) 202.5x = 315 x = 315/202.5 = 3150/2025 = 14/9 or 1 5/9 or 1.5555.... take your pick 1.555... rounded to one decimal is 1.6
November 16, 2016

Math Help!!!
set up a simple ratio and solve for x 6/202.5 = x/52.5
November 16, 2016

Calculus
hint: What is the derivative of secx ??
November 16, 2016

Ravindra bharathi school Maths
Did you mean 1 m , 23 cm? which is 123 cm adding 21 cm gives her 144 cm (tall 10 year old girl, did I mis-read your question?)
November 16, 2016

Algebra
Retype after correcting the English.
November 16, 2016

math
one number --- 2x , (avoiding fractions) the other ----- x + 5 (2x)^2- (x+5)^2 = 17 4x^2 - x^2 - 10x -25 - 17 = 0 3x^2 - 10x - 42 = 0 x = (10 ± ?604)/6 = (5 ± ?151)/3 2x = .... x+5 = ... it works, I checked on my calculator
November 16, 2016

Maths
If I read this correctly, we would get: 1, 4, 5, 10, 20, 40, 80, ... in effect, each term is twice its previous term from the 4th term on Where does the number 2016 come in? clearly not in this sequence. suppose my term start with 1, 2 , then we get 1,2, 3, 6, 12, 24, , again ...
November 16, 2016

Math
6n = 8p or n = 4p/3 n = p+3.5 4p/3 = p + 3.5 times 3 4p = 3p + 10.5 p = 10.5
November 16, 2016

Maths
new length = 1.2(50) or 60 m new area = 2340 new width = 2340/60 = 39 increase in width = 9 m
November 16, 2016

math
I did the previous one for you. Do be successful in this topic you simply MUST know how to do this type of trivial question. They don't come any easier than this one. Show me the steps you would take to solve this problem.
November 15, 2016

math
number of ways to get 3 tens and 2 kings = C(4,3) * C(4,2) = 24 prob(of your event) = 24/C(52,5) = 24/2598960 = 1/108290
November 15, 2016

math. PLEASE HELP.
Following your description I got sin 29° = opp/hyp = 4.6/c csin29 = 4.6 c = 4.6/sin29 = 9.48826.. or appr 9.5 I don't know how you got 2.5
November 15, 2016

disagree - math
Batting "order" implies that the order they play is important, so 13 P 9 = 13*12*11*10*9*8*7*6*5 = ....
November 15, 2016

Math
dividing by: 2's leaving one remainder: 3 5 7 9 11 13 15 ... odd numbers 3's leaving one remainder: 4 7 10 13 16 19 22 25 28 ... common difference 3 So far: 7 13 19 25 31 37 43 49 .... (common difference is 6) 4's leaving one remainder: 5 9 13 17 21 25 29 33 37 41 ...
November 15, 2016

Algebra
The only condition your equation states is that y = 3 That is, there is no condition on x, so the x can be anything. e.g. (4,3), (1,3), (506,3), (12.34, 3), (?,3), .... the result is a horizontal line 3 units above the x-axis, that is, the y = 3
November 15, 2016

Geometry
What makes you say it is (9,5) ???
November 15, 2016

Algebra2
correct
November 15, 2016

Pre-cal
sec x = 2csc x 1/cosx = 2/sinx sinx = 2cosx sinx/cosx = 2 tanx = 2 yes, I would use tan^-1 (2), but make sure your calculator is set to radians, (DRG key) Also remember that the tangent is positive in quads I and III tan^-1 (2) = appr 1.107 x = 1.107 or x = ?+1.107= appr 4.249
November 15, 2016

math
so in 7 years ? amount = 3000(1.05)^7 = ....
November 15, 2016

Algebra
2a = 4 a = 2 e = c/a c/2 = 3/2 c = 3 in a hyperbola: a^2 + b^2 = c^2 4 + b^2 = 9 b^2 = 5 a^2 = 4 centre is (-2,3) (x+2)^2 /4 - (y-3)^2 /5 = 1
November 15, 2016

Algebra
g(x) = x^2 - 2 g(-2) = (-2)^2 - 2 = 4-2 = 2
November 15, 2016

Maths
smaller angle --- x larger angle --- x+20 x + x+20 + 90 = 180 2x = 70 x = 35 the angles are 35° , 55° and 90°
November 15, 2016

Trigonometry
taking your data: y = (4/7)sin (x + 3?) + 1 when x = ?/2 y = (4/7)sin(?/2+3?) = 1 = (4/7)sin (7?/2) + 1 = (4/7)(-1) + 1 = 3/7
November 15, 2016

MATH 123
1((1/2)^(t/5730) = .55 (.5)^(t/5730 = .55 take log of both sides log (.5)^(t/5730 = log .55 (t/5730) log .5 = log .55 t/5730 = log .55/log .5 t = 5730(log .55/log .5) = appr 4942 years
November 15, 2016

math
x + y ? 20 9x + 12y ? 200 whatever graph they give you, there should be one with the region below x+y = 20 shaded in AND the region above 9x + 12y = 200 shaded in. It should look something like this: http://www.wolframalpha.com/input/?i=plot+x+%2B+y+%3D+20+,+9x+%2B+12y+%3D+200...
November 15, 2016

math
When you have a function such as P(x) = 2(x-3)(x-4) you could also write it as y = 2(x-3)(x-4) So when they speak of the zeros of the function, they are really describing the x's that make y = 0 that is: 2(x-3)(x-4) = 0 Now think about the answer of 0 after a ...
November 15, 2016

maths
fog = f(g(x)) = f(2x-3) = (2x-3)^2 + 3(2x-3) + 1 = 4x^2 - 12x + 9 + 6x - 9 + 1 = 4x^2 - 6x + 1 now do gog in the same way
November 15, 2016

Math
A : B = 5:11 = 10 : 22 = ... = 10x : 22x A : B : C = 2:3:15 = 10:15:75 = ... = 10x:15x:75x in solution X we have 10x/(22x) of A so amount of A in 400 L ofX is (10/22)(400) = appr 181.8 L in solution Y amount of C in 400 L = 75x/(100x)(400) = 300 L
November 15, 2016

maths
qD(9) = 8000/(81+1) = appr 97.56 qD(8.5) = 8000(72.25+1) = appr 109.22 So, what do you think?
November 15, 2016

algebra
just translate .... four times a number --- 4x fourteen times its reciprocal --- 17(1/x) or 17/x the sum of ---> + is 15 ----> = 15 so: 4x + 17/x = 15 How easy was that?
November 15, 2016

Algebra
woman's rate ---- 1/x man's rate ----- 1/(x-5) , where x > 5 combined rate = 1/x + 1/(x-5) = (x-5 +x)/(x(x-5)) = (2x-5)/(x^2 - 5x) (2x-5)/(x^2 - 5x) = 1/6 x^2 - 5x = 12x - 30 x^2 - 17x + 30 = 0 (x-15)(x-2) = 0 x = 15 or x =2 , but x > 5 x = 15 The woman can do ...
November 15, 2016

Math
1-(-2)^2*(-1)^3 = 1 - 4(-1) = 1 + 4 = 5
November 15, 2016

maths
Make your sketch. Method 1, complete the parallelogram and find the diagonal x^2 = 5^2 + 3^2 - 2(5)(3)cos 150° = 59.9807... x = appr 7.74 (exact value: x^2 = 34 + 30?3/2 = 34 + 15?3 x = ?(34 + 15?3) ) method 2 place vector P along the horizontal so vector P = (5,0) vector ...
November 15, 2016

Algebra
same thing e.g. (1/2)(12) = 6 12/2 = 6 as to your question, mom's age ---- x Rowena's age -- x/2 8 years ago: mom ---- x-8 Rowena -- x/2 - 8 x/2 - 8 = (1/3)(x-8) times 6, the LCD 3x - 48 = 2(x-8) 3x - 48 = 2x - 16 x = 32 Mom is 32, Rowena is 16 check: 8 years ago, the ...
November 15, 2016

math
Arggghhhh!
November 15, 2016

Maths
How about this approach? A:B = 2:3 or 6:9 B:C = 9:5 ---> notice the value of B is the same so A:B:C = 6:9:5 or 6x:9x:5x 6x+9x+5x = 400 20x = 400 x = 20 so A got 6(20) = 120 B got 9(20) = 180 C got 5(20) = 100
November 15, 2016

Math
I am going to assume you meant (2x-7)/4 - (x-6)/7 = 0 then (2x-7)/4 = (x-6)/7 multiply both sides by 28, the LCD 7(2x-7) = 4(x-6) 14x - 49 = 4x - 24 10x = 25 x = 25/10 = 5/2 or 2.5 or 2 1/2
November 14, 2016

Math
50x^4 / (12x) = 25x^3 /6 or (25/6)x^3
November 14, 2016

thomas middle such
it is less than 300 --> 1xx or 2xx the hundreds digit is 3 less than the ones digit ---1x4 or 2x5 the tens digit is 5 more than the hundreds digit ---> 164 or 274 the sum if the digits is 11 ----> 164
November 14, 2016

algebra
original: width --- x length --- 5x , (it said so) new dimensions: length = 5x - 3 width = x+10 perimeter = 2* width + 2*length = 2(x+10) + 2(5x-3) = 374 2x + 20 + 10x - 6 = 374 12x = 360 x = 30 So the original rectangle had a width of 30 m and a length of 150 m
November 14, 2016

algebra
4b/2 + 3 = 11 + b 2b + 3 = 11 + b, since 4/2 = 2 2b - b = 11-3 b = 8 or 4b/2 + 3 = 11 + b multiply every term by 2 4b + 6 = 22 + 2b 4b - 2b = 22 - 6 2b = 16 divide both sides by 2 b = 8
November 14, 2016

math
the effective distance: 16 km east and 8 km north ---> right-angled triangle hint: Pythagoras
November 14, 2016

math
Poorly worded question. Are we to assume that some questions were skipped, and no reward or penalty for skipped questions? I will assume that. rights ---- x wrongs --- y skipped -- 40-x-y) 5x - 3y + 0(40-x-y) = 70 5x - 3y = 72 y = (5x-70)/3 , clearly 14 ? x ? 40 , x+y ? 40 ...
November 14, 2016

Math
Now: Benny ---- x years Apple ---- 38-x 6 years ago: Benny ---- x-7 Apple ----- 38-x - 7 = 31-x 31-x = 3(x-7) solve for x, and sub into my definitions
November 14, 2016

Maths
let the perpendicular height be 4x let the slant height be 5x (4x)^2 + 6^2 = (5x^2 16x^2 + 36 = 25x^2 carry on, of course you would reject the negative value of x after taking the square root at the end.
November 14, 2016

Maths
Think of the 5 kids standing in a row, and in each row changing positions 1 ---> 3 2 ---> 5 3 ---> 1 4 ---> 2 5 ---> 4 At the start,,,: 1 2 3 4 5 ---> A B C D E after 1 round: 3 4 1 5 2 ---> C D A E B after 2 round: 1 5 3 2 4 ---> A E C B D after 3 ...
November 14, 2016

math
depends where you want the water spout to be. It would make sense to have the spout at the origin. Then the zeros of the function would be (0,0) and (8,0) and the vertex would be at (4,6) height = a(x - 4)^2 + 6 but (0,0) lies on it, thus: 0 = a(0-4)^2 + 6 16a = -6 a = -3/8 ...
November 14, 2016

Aljebra
original number in first box --- x original number in 2nd box --- 123-x after shift: first box ----- x-10 2nd box --- 123-x + 10 = 133-x 133-x = 2(x-10) solve for x
November 13, 2016

Math
3?(x - 1) + 6 when x = 26 = 3?25 + 6 = ....
November 13, 2016

pre algebra
adult tickets ---- x children tickets --- 2x + 15 solve for x: 12x + 5(2x+15) = 1920
November 13, 2016

pre algebra
follow the same method and steps I just showed you in your other posts. The two questions are of the same structure.
November 13, 2016

intermediate maths
granddaughter's age---- x James' age --------- 6x 2 years from now: granddaughter's age --- x+2 James' age ---------- 6x + 2 6x+2 = 5(x+2) solve for x
November 13, 2016

Algebra
speed of slower rider --- x km/h speed of faster rider ---- 2x km/h distance gone by slower = 3(x) = 3x distance gone by faster = 3(2x) = 6x 3x + 6x = 90 9x = 90 x = 10 rate of slower rider = 10 km/h rate of faster rider = 2(10) = 20 km/h
November 13, 2016

Calculus
let the point of contact be P(a,b) let A be (1,7) slope of AP = (b-7)/(a-1) the closest point would be where the tangent at P is perpendicular to AP 2y dy/dx = 1 dy/dx = 1/(2y) so at P, the slope of the tangent is 1/(2b) so (b-7)/(a-1) = -2b b-7 = -2ab + 2b -b = -2ab + 7 2ab...
November 13, 2016

math
In a parallelogram Abcd angle add ??? side an ???? e ????? x+y ???? wow!
November 13, 2016

Math
Just follow the definition: a*b means 3a^2+b 3*1 means 3(3^2) + 1 = .....
November 13, 2016

Math
number correct --- x , 0 ? x ? 20 number wrong ---- y number skipped ---- 20-x-y 5x - y + 0 = 72 y = 5x - 72 y ? 0 if x = 14, y = -2 , not possible if x = 15 , y = 3 , skipped = 2 if x = 16, y = 8 , not possible , x+y>20 so he got 16 right, 8 wrong, and skipped 2 check: 5(...
November 13, 2016

Math
not arithmetic nor geometric gave up and checked with Wolfram found: term(n) = (7(3^n) - 3)/6 http://www.wolframalpha.com/input/?i=pattern+%7B3,+10,+31,+94%7D quite obscure, perhaps more terms would have helped.
November 13, 2016

Math
mmmhhhh when x=1 , 3+2x = 3+2(1) = 5 when x=2, 3+2x = 3+2(2) = 7 when x = 3 ..... continue
November 13, 2016

Math
number of girls --- x number of boys --- (5/11)x x - (5/11)x = 114 (6/11)x = 114 x = 114(11/6) = .... take over
November 13, 2016

Math
1:2:1/2 = 2:4:1 -----> ratios usually are not expressed in fraction form let their shares be 2x, 4x, and x but x = 48 so 2x = 96 and 4x = 192 add them up
November 13, 2016

Calculus
You did not do exactly the same, your slope was -3/5, different from mine. (another example of why I prefer traditional class room instructions, where the learning of math is not just "answer based" )
November 13, 2016

Calculus
How did you get the slope to be -3/5 ?? let the x-intercept be A(a,0) and the y-intercept be B(0,b) label point (3,5) as P By ratios in similar triangles: (a-3)/5 = 3/(b-5) ab-5a-3b+5 = 15 b(a-3) = 5a b = 5a/(a-3) Area of triangle = (1/2)ab = (1/2)(a)(5a/(a-3) ) = 5a^2/(2a-6) ...
November 13, 2016

Math
right now: x + 7x = 976 x= 122 Aaron has 122 cards and Ben has 854. after the give-away of k cards: ben has 854-k Aaron has 122+k Aaron has 3 times as many as Ben 122+k = 3(854 - k) 122+k = 2562 - 3k 4k = 2440 k = 610 check: after the exchange Ben has 854-610 = 244 Aaron has ...
November 12, 2016

Maths
3^9 + 3^12 + 3^15 + 3^n = 3^9(1 + 3^3 + 3^6 + 3^(n-9) ) = 3^9(757 + 3^(n-9)) 3^9 is a perfect cube, so all we need is (757 + 3^(n-9)) to be a perfect cube, clearly n >9 perfect cubes past 757 with 3^(n-9) as the 2nd number: 1000 243 <---- well, that was lucky 1331 574...
November 12, 2016

Calculus
let the height be h then h^2 + b^2 = 20^2 h = (400-b^2)^(1/2) Area = (1/2)(bh) = (1/2)(b)(400 - b^2)^(1/2) d(Area)/dt = (b/2)(1/2)(400-b^2)^(-1/2) (-2b db/dt) + (1/2)(db/dt)(400 - b^2)^(1/2) = -b^2 (db/dt)/?(400-b^2) + (1/2)(db/dt)?(400-b^2) when b = 11 and db/dt = 4 d(Area)/...
November 12, 2016

math
number of ways to give the fruits = 5!/(3!2!) = 10 (you could list them) Bananas at least two days in a row: BABAB is the only case where two or more B could not be together. Look at your list from above prog(at least two B's in a row) = 9/10
November 12, 2016

maths
Susan's age now ---- x Mary's age now ------3x Three years ago: Susan ---- x-3 Mary ----- 3x-3 x-3 + 3x-3 = 22 continue
November 12, 2016

Algebra
good road ---- x km poor road ----- 48-x km time on good road = x/72 time on poor road = (48-x)/48 x/72 + (48-x)/48 = 3/4 times 144 , the LCD 2x + 3(48-x) = 108 carry on, easy from here
November 12, 2016

Maths
without a calculator... let a=20142014 then 20142015 = a+1 then 20152015 = a + 1 + 1000 = a+1001 then 20152014 = a+1000 20142015×20152014 – 20142014 ×20152015 = (a+1)(a+1000) - a(a+1001) = a^2 + 1001a + 1000 - a^2 - 1001a = 1000
November 12, 2016

Algebra
2x^3 - 5x^2 - 5x - 1 = 0 let f(x) = 2x^3 - 5x^2 - 5x - 1 try f(1) = 2 - 5 - 5 - 1 ? 0 try f(-1) = -2 - 5 + 5 - 1 ? 0 try f(1/2) = 1/4 - 5/4 - 5/2 - 1? 0 try f(-1/2) = -1/4 - 5/4 + 5/2 - 1 = 0 , yeahh! so (2x + 1) is a factor and x = -1/2 by long algebraic division, which I ...
November 11, 2016

Math -fractions word problems
total number of students ---- x number of boys ----- (3/7)x number of girls ------(4/7)x (4/7)x = (3/7)x + 4 times 7, the LCD 4x = 3x + 28 x = 28 boys: (3/7)(28) = 12 girls = 28-12 = 16
November 11, 2016

intergrated science
I will assume that Calculus is part of your integrated science course. a = 2 then v = 2t + c at the beginning of the observation, t = 0 , v = 24 so 24 = a(0) + c ----> c = 24 v = 2t + 24 when t = 8 v = 2(8) + 24 = 40 m/s or, simply .... for each of the 8 seconds the ...
November 11, 2016

calculus
your values of x = -2, 3 are the x-intercepts, and you don't need a derivative to find them dy/dx = (x-3)(2/3)(x+2)^(-1/3) + (x+2)^(2/3) = (1/3)(x+2)^(-1/3) [2(x-3) + 3(x+2)] = (1/3)(5x)(x+2)^(-1/3) = 0 for a max/min of y ----> 5x = 0 or (x+2)^(-1/3) = 0 ---> no way ...
November 11, 2016

math- Trigonometry
I agree with Scott. For the given date, the calculations are correct. In reality, the question is absurd. Using Pythagoras, the height of the lighthouse would have to be appr 8.9 km high. and, using our given angle of 65.91..° tan 65.91 = height/4 height = 4tan 65.91 = ...
November 11, 2016

Math
or 15 machines 15 minutes to make 500 raviolis 75 machines 15 minutes to make 2500 raviolis 75 machines 15(2.4) minutes to make 2500(2.4) raviolis 75 machines 36 minutes to make 6000 raviolis (the 2.4 comes from 6000/2500)
November 11, 2016

maths
I assume you are solving? from the 2nd: y = -2x-4 sub into the first 3x - 2(-2x - 4) = 1 3x + 4x + 8 = 1 7x = -7 x = -1 back into y = -2x - 4 y = -2(-1) - 4 = -2 x = -1 , y = -2
November 11, 2016

Math
Assuming that x is the length of the missing parallel side ... area of trapezoid = (x+15)(10)/2= 5x + 75 area of triangle = (1/2)(15)(10) = 75 5x + 75 < 2(75) 5x < 75 x < 15 but clearly x has to be positive 0 < x < 15 looks like a common sense type of question ...
November 11, 2016

finite math
mortgage after downpayment = 140,000 i = .09/12 = .0075 n = 30(12) = 360 payment = p p(1 - 1.0075^-360)/.0075 = 140000 p(124.2818657.) = 140000 p = $1126.47
November 11, 2016

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