Saturday

December 3, 2016
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*