Saturday
December 3, 2016

Posts by Reiny

Total # Posts: 36,897

Pre Calculus
sum of sines: sinA + sinB = 2sin( (A+B)/2) cos( (A-B)/2) then: sin 150° + sin 30° = 2sin 90° cos 60° = 2(1)(1/2) = 1 Difference of sines: sinA - sinB = 2cos( (A+B)/2) sin( (A-B)/2) then: sin 4θ − sin 2θ = 2cos(3Ø)sin Ø
July 11, 2016

pre cal
let √x = y then: 2y^2 - 5y + 2 = 0 (2y -1)(y -2) = 0 y = 1/2 or y = 2 √x = 1/2 ----> x = 1/4 or √x = 2 ------> x = 4 or 2x+2 = 5√x square both sides: 4x^2 + 8x + 4 = 25x 4x^2 - 17x + 4 = 0 (x - 4)(4x - 1) =0 x = 4 or x = 1/4 btw, in both solutions...
July 11, 2016

Pre-Calculus 11
-3* cube root of 2 is a negative number, so your result has to stay negative. change it to - cuberoot(54)
July 10, 2016

math
just use for formulas for an AS term(n) = a + (n-1)d for yours a=22000 d=500 n=7 sum(n) = (n/2)(first + last) (you have the last term from above) or sum(n) = (n/2)(2a + (n-1)d )
July 10, 2016

Math
number of men --- m number of girls --- g m+g = 120 Tina danced with 7 men Reena danced with 8 men .... Raveena danced with 120-g men this is an arithmetic sequence with a=7, d=1 term(g) = m a + (g-1)d = m 7 + g-1 = m g - m = -6 also g+m = 120 add them 2g = 114 g = 57 m = 120-...
July 10, 2016

Math
construct your right-angled triangle. r^2 = x^2 + y^2 , (x is a side , not an angle) 2^2 = x^2 + 1^2 , since sinØ = opposite/hypoenuse or y/r x^2 = 3 x = √3 , we know the angle must be in Quad I sinx = 1/2 --- given cscx = 2 cosx = √3/2 secx = 2/√3 ...
July 10, 2016

Pre Calculus
5.4 radians coterminal with 5.4 - 2π = -.883.. radians, which is in the IV th or if you want to "think" in degrees 1 rad = 180/π ° 5.4 rad = 309.39.. ° ----> 4th
July 10, 2016

Pre Calculus
I did this yesterday http://www.jiskha.com/display.cgi?id=1468085862
July 10, 2016

mathematics
of the 40 oranges, 12 are unripe ----> 28 are ripe prob(ripe) = 28/40 = 7/10 so prob(unripe) = 1 - 7/10 = 3/10 you are correct
July 10, 2016

maths
nope , (x+y)^2=x^2+2xy+y^2
July 10, 2016

math
all the numbers that don't have a 5 in them: 8 x 9 = 72 , (they can start with 1,2,3,4,6,7,8,9 and they can end with 0,1,2,3,4,6,7,8,9 ) Those with a 5 are 100-72 = 28 prob(have a 5) = 28/100 = 7/25
July 10, 2016

math
smallest --- x middle one -- 2x largest ------ 3x x + 2x + 3x = 180 solve for x, sub back into my definitions
July 10, 2016

Pre-calculus
x = a(y-3)^2 + 0 but (4,9) lies on it, so 4 = a(9-3)^2 + 0 4 = 36a a = 1/9 x = (1/9)(y-3)^2 is your equation.
July 10, 2016

Pre-Calculus 11
is it (5/7)√(3/2) ? or 5/(7√(3/2) )?
July 9, 2016

math
3x-5y=16 -9x+15=48 notice that if you divide the 2nd by -3 , you get 3x - 5y = -16 clearly you will have two different parallel lines, thus no solution. or if we subtract: 3x-5y=16 3x-5y=-16 0 = 32 not very likely !!!! , so no solution
July 9, 2016

Mathematics
Memorize this relationship until you can state it in your sleep. π radians = 180° Use it to answer this, and your two previous questions.
July 9, 2016

Mathematics
repeatedly add 360° and note the results
July 9, 2016

Pre Calculus
You really really really MUST know that.
July 9, 2016

Mathematics
What is (2π - 11π/13) ? I get 15π/13 , which is not one of your choices. Do you have a typo?
July 9, 2016

Pre Calculus
same type of question as your last one
July 9, 2016

Pre Calculus
8π / 7= π + (1/7)π so just a bit more than π, so in quadrant III here is a "sneaky way" set your calculator to radians take sin 8π/7 to get a negative take cos 8π/7 to get a negative the only quadrant in which both sine and cosine are ...
July 9, 2016

Maths
Everybody studying trig should know the ratio of sides, and thus the trig ratios, of the 30-60-90° right angled triangles, as well as the 45 -45-90° triangle for the 30-60-90 the sides are 1 - √3 - 2 units respectively looking at your sketch of that triangle, ...
July 9, 2016

Spherical Trigonometry
h/100 = tan 38° solve for h
July 9, 2016

Calc.
I assume we are looking at vectors, then (6,2y) - (5x,10) = (6,-4) 6-5x = 6 , solve for x 2y - 10 = -4, solve for y
July 8, 2016

Calc.
⃗⃗u dot ⃗v =| ⃗⃗u| | ⃗v| cosØ, where Ø is the angle between them 2 + 20 + 2 = √21 √30 cosØ 24/(√630 =cosØ I get Ø = appr 17.02° check my arithmetic
July 8, 2016

Pre-Cal
I will do the 2nd one, which is the harder of the two. Follow my steps to do the first one. sinx = -5/13 ,and the angle x is in III recall that sinØ = y/r so y = -5, r = 13 sketch a right-angled triangle in III with hypotenuse 13 and y = -5 x^2 + y^2 = r^2 x^2 + 25 =169...
July 7, 2016

Raquel, check your answer - Algebra
Racquel, check your calculations. 2000(.08) + 8000(.09) = 880 , not 860 as needed.
July 7, 2016

Algebra
sue's rate = 1/60 (driveways/minute) Tom's rate = 1/35 (driveways/minute) combined rate = 1/60+1/35 = 19/420 (driveways/minute) time at combined rate = driveway/( (19/420) (driveways/minute) ) = 420/19 minutes = 22.1 minutes
July 7, 2016

pre cal
well, why don't you try expanding (x+s)^2 to see what comes out. btw, we use ^ to show exponents eg. x^2 is "x squared"
July 6, 2016

Math
Just translate the English using your definitions of a GS ar^3 = 30 ar^8 = 960 divide the 2nd by third, the a's will cancel r^5 = 32 r = 2 in ar^3 = 30 a(8) = 30 a = 15/4
July 6, 2016

pre cal
I will assume you meant: x^2/162 +x/18 + 1/9 = 0 the LCD is 162, so multiply each term by that x^2 + 9x + 18 = 0 (x+3)(x+6) = 0 x = -3 or x = -6
July 6, 2016

pre cal
number of twenties --- x number of tens ------- 3x 20x + 10(3x) = 1950 50x =1950 x = 39 so there are 39 twenties and 117 tens check: 39(20) + 117(10) = 1950
July 6, 2016

Pre Calculus
You really need help pushing buttons on your calculator???
July 6, 2016

Pre Calculus
form the half-life equation, amount = 69(1/2)^(t/12.4) , where t is in years plug in 75 for t show me your work and I will help you with the others.
July 6, 2016

lagdamat
What is "lagdamat" ?? width ----- x length ----- 2x+2 x(2x+2) = 24 2x^2 + 2x - 24 = - x^2 + x - 12 = 0 I will leave it up to you to solve this very simple quadratic. Hint1, it factors Hint2, reject the negative
July 6, 2016

math
What is (3/10)(2/7)(2905) ?
July 6, 2016

probability
I read that as a binomial distribution. so C(4,1) (1/2)^1 (1/2)^3 = 4(1/2)^4 = 1/4 or there are 2^4 or 16 cases your event could be HTTT THTT TTHT TTTH, or 4 possibilities prob(exactly one head) = 4/16 = 1/4
July 6, 2016

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

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