# Posts by Reiny

Total # Posts: 38,372

**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 ...

**math algebra**

Gray's rate = 1/15 Anna' rate = 1/20 Job done by Gray = 6(1/15) = 2/5 leaving 3/5 of the job left to be done by Anna time for Anna to complete = (3/5) / (1/20) = 12 It will take her 12 days to finish the roof

**Math**

6 1/7 - 1 5/21 = 43/7 - 26/21 = 129/7 - 26/21 = 103/21

**math algebra**

assuming that you meant: f(x) = (x+1)/(x^2-9) and g(x) = x/(x-3) The domain for both f(x) and g(x) are all values of x except those that make the denominator zero domain of f(x): all x's except x = ±3 domain of g(x): all x/s except x = 3 (f+g)(x) = (x+1)/(x^2 - 9...

**math - business**

Steve is probably off line now, so I will answer. For any quadratic function of the form y = ax^2 + bx + c the x of the vertex is -b/(2a), once you have the x you just sub that back into the equation to get the y of the vertex. In your case: P = -.005x^2 + 4x - 200 a = -.005 b...

**GEOMETRY**

You have similar triangles. Since XA = AY AY : XY = 1 : 2 triangle XYZ is similar to triangle AYB XZ/XY = AB/AY 8.4/2 = AB/1 AB = 8.4/2 = 4.2

**Algebra**

3n^2+5n-100=? If this is a quadratic equation, the your ? is 0 If you are dealing with the corresponding quadratic function you would normally find it as y = 3n^2 + 5n - 100 , where y is the dependent variable, and n is the independent variable What about it ?

**Pre-calculus**

Watch those brackets, you must have meant: (sin(x+y)+sin(x-y))/(cos(x+y)+cos(x-y))=tanx LS = (sinxcosy + cosxsiny + sinxcosy - sinxcosy)/(cosxcosy - sinxsiny + cosxcosy + sinxsiny) = 2sinxcosy/(2cosxcosy) = (sinx/cosx)(cosy/cosy) = tanx = RS

**Pre-calculus**

I checked with my calculator and actually found the angles. It works !!!

**Pre-calculus**

If siny = -2/?13 , and coty ?0, then y is in quad III so cosy = -3/?13 then sin 2y = 2sinycosy = 2(-2/?13)(-3/?13) = 12/13 cos 2y = cos^2 y - sin^2 y = 9/13 - 4/13 = 5/13 so sin 2y = 12/13 and cos 2y = 5/13 if sin 2x = 7/25 remember cos^2 (2x) = 1 - sin^2 (2x) = 1 - 49/625 = ...

**Probability Help**

at least one boy ----> exclude the case of all 5 girls, which is (1/2)^5 = 1/32 prob(at least one boy in 5) = 1 - 1/32 = 31/32

**Math**

A:B:C = 5:5:7 or 5x : 5x : 7x Cindy ate 30 Skittles less than Ann and Ben together -----> 7x = 5x + 5x - 30 -3x = -30 x = 10 5x = 50 7x = 70 They ate 50+50+70 = 170 of them

**Calculus**

g(x) = sinxcosx g ' (x) = sinx(-sinx) + cosxcosx = cos^2 x - sin^2 x = cos 2x at x = ?/3 g '(x) = cos (2?/3) = -.5 equation: y - ?3/4 = (-1/2)(x - ?/3) So I agree with your answer. for a max/min of g(x) , g '(x) = 0 cos 2x = 0 2x = ?/2 or 2x = 3?/2 x = ?/4 or x = 3...

**Calculus**

with the information given, you should be able to form the equation h = -16t^2 + 68t + 6 dh/dt = -32t + 68 = 0 for a max of h 32t = 68 t = 2.125 evaluate h when t = 2.125

**argghh - Calc**

forgot to change the units from km/h to m/s go with Damon's answers

**Calc**

if we have acceleration of a, then v = at + c case1: when t=0, v=25 25 = 0+c ---> v = at + 25 so when t = 13, v = 90 90 = 13a + 25 a = 65/13 = 5 m/s^2 -----> v = 5t + 25 distance = (5/2)t^2 + 25t + k when t=0 , distance = 0 , so k = 0 distance = (5/2)t^2 + 25t when t = ...

**Math**

I agree with all of them

**Math**

amount taken out as loan = 25 - .2(25) = 20 or just take .8(25) = 20 amount owing after 8 years = 20(1.025)^8 = 24.368 gh cedis

**Math**

1 7/10 = 17/10 "as many" suggests multiplication e.g. bill eats 3 times as many donuts as Bob if Bob eats 4 donuts, then Bill would eat 3*4 or 12 donuts so Elizabeth has (17/10) as many as Rosalie. let Rosalie's number of plants be x then: (17/10)x = 51 ----> ...

**Math**

time for first trip = d/x time for return = d/y total time = (d/x + d/y) = (dy + dx)/(xy) = d(x+y)/(xy) total distance = 2d average speed = 2d/( d(x+y)/(xy) ) = 2xy/(x+y) = 50 xy/(x+y) = 25 xy = 25x + 25y 25y - xy = 25x y(25 - x) = -25x y = 25x/(x-25) e.g. let x = 50, then y...

**math**

horizontal path = 15(2.5) = 37.5 units^2 vertical path = 9(2.5) = 22.5 units^2 total = 60 units^2 BUT, we counted the intersection of the paths twice, so we have to subtract 2.5(2.5) or 6.25 units^2 leaving us with 63.75 units^2

**Geometry**

So what is (3/2)(4.8) ? Just add up your 4 sides, remember they come in equal pairs.

**Order MATH!**

I suggest you change them all to decimals, and then it is easy to see.

**Pre-calculus**

correction for #1, should say: (1+cosx)/(1-cosx) = (secx + 1)/(secx - 1) RS = (1/cosx + 1)/(1/cosx - 1) = (1/cosx + 1)/(1/cosx - 1) * cosx/cox = (1+ cosx)/(1 - cosx) = LS Well, that was easy. #2, hint: change everything to sines and cosines expand and simplify the LS #3, use ...

**Maths**

So in 60 minutes he can type 3200 words. How many words can he type in 1 minute? Then how many in 15 minutes ?

**additional maths (maths)**

so you just want the max of d(t) find the derivative, set it equal to zero, and solve that for t Once you have the value of t which gives you the maximum, plug it back into d(t) to actually find that distance. Very straight-forward.

**Maths**

The missing angle ? = 45° by the sine law: a/sin35 = 40/sin100 a = 40sin35/sin100 = appr 23.3 c/sin45 = 40/sin100 c = 40sin45/sin100 = appr 28.7 area = (1/2)(ab)sin45 = appr 329.5 units^2

**maths**

so he gave away 60%, leaving him with 40% .4x = 9600 solve for x

**Math (Differentials)**

our f(x) = x^(1/3) , and f ' (x) = (1/3)x^(-2/3) = 1/(3(x)^(2/3) ) I will go with your x = 27 , dx = -2 f(x + dx) is appr = f(x) + f ' (x) (dx) f(25) = f(27) + (1/3)(27)^(-2/3) = 3 + (1/27)(-2) = 3 - .0741 = 2.926 you simply added the part at the end instead of ...

**algebra 2**

Your calculations are correct (sum of roots = 2+3i + 2-3i = 4 product of roots = (2+3i)(2-3i) = 4-(-9) = 13 ) It said to write the quadratic equation, which is x^2 - 4x + 13 = 0 you had y = x^2 - 4x + 13 , which is the quadratic function.

**Math**

I will place the parabola as opening to the right, with its vertex at (0,0) so the equation is y^2 = 4px, where (p,0) is the focus but (6,16) lies on it 16^2 = 4p(6) p = 256/24 = 32/3 So it should be placed at (32/3 , 0)

**Geometry**

original area = base x height = bh new area = .7b x 1.2h = .84bh so there is a 16% decrease in the area

**Calculus: Centers of Mass**

A quick calculation shows that the line intersects the parabola at (2,2) in the first quadrant lots of work ahead of us: first you must find the area of the region, it has to be done in two parts: from x=0 to x=2 under the curve, then from x=2 to x=4 under the straight line ...

**correction - Difficult Math**

I misread "Thirty of the cards from his cousin are National League players" as one third of the cards from his cousin are NL players

**Difficult Math**

total collection ---- x from dad --- x/4 from uncle --- x/5 ---> (.2)x = (2/10)x = x/5 from brother --- x/2 leaving : x -x/4 - x/5 - x/2 = x/20 so from cousin = x/20 so (1/3)(x/20) = 30 x = 1800 Steve has 1800 cards check: from dad = 1800/4 = 450 from uncle = .2(1800) = 360...

**Math**

999,999,999,999 = appr 1,000,000,000,000 = 10^12 ( you would be off by $1 on 1 Trillion dollars) 100,000,000,000,000 = 10^14 so 100,000,000,000,000 times 999,999,999,999 = 10^12 * 10^14 = 10^26 that would be 100 septillion.

**Math**

In arithmetic "of" means multiplication, so 1/10 of 2(10)+4(1)+6(1/10)+7(1/100)+8(1/1000) = (1/10)(20) + 4 + .6 + .07 + .008 = 2+4+.6+.07+.008 = 6.678 http://www.wolframalpha.com/input/?i=evaluate+1%2F10+*+2(10)%2B4(1)%2B6(1%2F10)%2B7(1%2F100)%2B8(1%2F1000) if you ...

**Algebra**

Help with what? You have given us two different circles. What do you want to do? They do intersect. Here is a picture of your problem http://www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2%2B6y%2B5%3D0+,+x%5E2%2By%5E2-2x-8%3D0

**Maths**

no XYYYY , where X is the vowel, Y can be anything else number of ways = (2)(4!) = 48 e.g. E(BGIN) - one of the 24 ways to arrange BGIN I(GBEN) - one of the 24 ways to arrange GBEN

**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...

**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...

**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

**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...

**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. ...

**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.

**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...

**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 ...

**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

**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 = ...

**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

**Algebra**

x e^.06t = 70000 x = 70000/e^(.06(19)) = 22,387.33

**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

**Math**

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

**Math**

Did you mean, find cos t ? if so, cos t = 5/?29

**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

**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

**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/(...

**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 ...

**TRIANGLE MATH HELP!!!**

Obviously.

**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

**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