# Posts by Reiny

Total # Posts: 38,075

**Mathematics**

unit digit ---- x tens digit --- y so the number is 10y + x 10y + x - 18 = 10x + y 9y - 9x = 18 y - x = 2 also: x+y=6 add those last two equation: 2y = 8 y = 4 so x = 2 the number is 42 check: is 42 - 18 = 24 ? YES

*October 15, 2016*

**math**

n/18m = (2^2x3^2x7)m/18 = 2x7m = 14m since m is a natural number, 14m is always a whole number. did you mean: n/(18m) ? make the necessary changes.

*October 15, 2016*

**Scince**

"A person is standing on 60m height per hour" - makes no sense to me

*October 15, 2016*

**Trigonometry**

I am sure you meant: (1+tan 200° tan 80°)/ (tan200°-tan 80°) --- those brackets are critical recall: tan(A-B) = (tanA - TanB)/( 1 + tanAtanB) = 1/[ (1+tanAtanB)/(tanA - tanB) ] tan(200-80) = tan 120 = - tan60° = -√3 = (tan 200 - tan80)/(1 + ...

*October 15, 2016*

**math**

number of ways without restriction: 9!/9 = 8! now let's put Sam between Ron and Ed RSE or ESR, so that's 2 ways let's consider RSE as one grouping, that means we still have 6 others to arrange number of ways = 2x7!/7 number of ways for the stated condition = 8! - 2...

*October 15, 2016*

**Pre-calculus**

Did you notice 16+29 = 45 ? so sin16° cos29° + cos16° sin29° = sin(16+29) = sin 45 = 1/√2 or √2/2

*October 15, 2016*

**math (Reiny please help)**

As Steve already pointed out to you, the question is not clearly stated. http://www.jiskha.com/display.cgi?id=1476444898 How many songs are on the album? The way you stated it , we could have 3 R, 4 C, and 1 H as an album, or 1R, 1H, or ... What about the order of the songs? ...

*October 15, 2016*

**Pre-calculus**

Steve's answer of 45° is correct, I didn't see the "acute" angle part, and 180-135 = 45°

*October 15, 2016*

**Pre-calculus**

You should know that the slope of a line is the same as the tangent of the angle that the line makes with the x-axis 2x-3y-6=0 , slope = 2/3, tanØ = 2/3, Ø = appr 33.69° with the x-axis same with x+5y-20=0 slope = -1/5 , line leans to the left. angle with x-...

*October 15, 2016*

**Pre-calculus**

sin(α+β+γ) , I will use sin(a+b+c) for easier typing = sin( (a+b) +c) = sin(a+b)cos c + cos(a+b)sin c = (sinacosb + cosasinb)(cosc) + (cosacosb - sinasinb)sinc = sinacosbcosc + cosacoscsinb + cosacosbsinc - sinasinbsinc now put back your α,β, and γ

*October 15, 2016*

**math (Reiny please help)**

No. You are simply choosing 4 of 15 things, and since the order of placing the order does not change, it is simply C(15,4) to order the pizza. Now for the size, you will choose 1 of the 5 sizes or C(5,1) = 5 so number of ways = C(15,4) x C(5,1) = (1365)(5) = 6825

*October 15, 2016*

**maths**

clean up your equations x/4 + y/5 = 1 --times 20 --> 5x + 4y = 20 2x/9 - y/9 = -2 -----> 2x - y = -18 y = 2x+18 using substitution, 5x + 4(2x+18) = 20 carry on

*October 15, 2016*

**Pre-calculus**

sin x=-3/5 and sec x>0 ---> sin x=-3/5 and cos x>0 so your angle must be in quadrants IV If you sketch your triangle , you will realize that you are dealing with the 3-4-5 right-angled triangle, and using the CAST rule sinx = -3/5 , cscx = -5/3 cosx = 4/5, secx = 5/4 ...

*October 15, 2016*

**Differentiation**

According to your suggested answer, I think your function was y = 2^x then taking the ln of both sides: lny = ln(2^x) = x ln2 now differentiate, y' / y = ln2 y' = y(ln 2) = ln2 (2^x) you cannot use log2 , it must be ln2

*October 15, 2016*

**Arithmetic progression**

let the four parts be a, a+d, a+2d, and a+3d a + a+d + a+2d + a+3d= 24 4a + 6d = 24 2a + 3d = 12 ----> d = (12-2a)/3 a^2 + (a+d)^2 + (a+2d)^2 + (a+3d)^2 = 164 4a^2 + 12ad + 14d^2 = 164 2a^2 + 6ad + 7d^2 = 82 2a^2 + 6a(12-2a)/3 + 7(12-2a)^2/9 = 82 times 9 18a^2 + 216a - 36a^...

*October 15, 2016*

**Math**

The area of the lawn is 15 m^2 The path has no effect on the area of the lawn

*October 15, 2016*

**Geometric progression**

You posted over 20 of these type of questions yesterday. Did you even look at some of the replies? Are you attempting to learn how to do these kind of problems? Show me how you started this one, and I will try to guide you along.

*October 14, 2016*

**Algebra**

current ages: billy ---- x Suzy --- x+10 next year: billy --- x+1 Suzy --- x+11 x+11 = 2(x+1) carry on

*October 13, 2016*

**Math (Reiny please help!)**

you are welcome

*October 13, 2016*

**Math (Reiny please help!)**

The actual steps will vary from person to person, and there is no single way to solve this. You sort of have to decide on the simplest equation as a starting point. In this case it is the last equation, it only has two variables. 2x + 2z = 4 , or x + z = 2 ---> x = 2-z I ...

*October 13, 2016*

**Algebra. NEED HELP ASAP PLEASE**

the way you typed it ... 4(t − 1) + 4/4t + 4 = 4t - 4 + 1/t + 4 = 4t + 1/t Something tells me you meant: 4/(t-1) + 4/(4t+4) = 4/(t-1) + 1/(t+1) , the LCD is (t-1)(t+1) = ( 4(t+1) + t-1)/((t-1)(t+1)) = (4t + 4 + t - 1)/(t^2 - 1) = (5t + 3)/(t^2 - 1) , t ≠ ± 1

*October 13, 2016*

**Algebra**

Follow the same steps as in the post when you were Lay.

*October 13, 2016*

**Algebra**

y = 2(x+5)(x-1) http://www.wolframalpha.com/input/?i=plot+y+%3D+2(x%2B5)(x-1)

*October 13, 2016*

**Algebra**

obvious first equation: x + y = 40 2nd equation deals with value of the nuts 6x + 4y = 4.75(40) 6x + 4y = 190 3x + 2y = 95 ** double the first one: 2x + 2y = 80 *** subtract *** from ** x = 15 in your head looking at x+y = 40 y = 25 check: 6(15) + 4(25) = 190 4.75(40) = 190

*October 13, 2016*

**algebra**

correct, now solve the equation

*October 13, 2016*

**Math**

For each of them , make a sketch In each case you will get a right-angled triangle You MUST know the basic trig ratios in terms of opposite, adjacent, and hypotenuse. e.g. tanØ = opposite/adjacent 1) so we have tanØ = 160/120 = 4/3 Make sure your calculator is ...

*October 13, 2016*

**math**

wx + zy = c zy = c - wx y = (c - wx)/z

*October 13, 2016*

**Math HELP!**

looks like for every increase of 1 in the x, the y decreases by 5 so the slope = change in y/change in x = -5 notice (0,-1) is the y-intercept, so y = -5x - 1

*October 13, 2016*

**Investment**

i = .04/4 = .01 n = 12 What is the question?

*October 13, 2016*

**math**

(7^-64)x(7^-150)/(7^-7)x(7^2)=7^t when multiplying powers with the same base, keep the base and add the exponents Left Side = 7^(-64 -150 -7 + 2) = 7^-209 so we have: 7^-209 = t^t clearly t = -209 If the text has an answer of +209, it is wrong. Do you perhaps have a typo, such...

*October 13, 2016*

**math**

a)no restrictions (my answer is 11C5) -- correct b)all boys (is this correct 5C5) -- correct c)all girls (my answer 6C5) -- correct d)more girls than boys (answer 6C4x5C1 +6C3x5C2)? ---- more girls than boys ---> 3G,2B - 4G,1B - 5G = C(6,3)xC(5,2) + C(6,4)xC(5,1) + C(6,5) e...

*October 13, 2016*

**math**

easier to see the letters this way: B I I I O E E E N N N G G R number of ways without restrictions = 14!/(3!3!3!2!) = 201,801,600 (do you know why I am dividing by 3!3!3!2! ? ) let's put the BO together, could also be OB let's treat that pair as one element number of ...

*October 13, 2016*

**math**

Perhaps you feel more comfortable with rectangular graphing r=2/1+cos theta r = 2/(1+ x/r) r + x = 2 √(x^2 + y^2) + x = 2 √(x^2 + y^2) = 2-x square both sides x^2 + y^2 = 4 - 4x + x^2 y^2 = 4 - 4x Steve meant to say, vertex is (1,0)

*October 13, 2016*

**algebra**

speed of slower car --- x mph speed of faster car ---- x+7 mph distance of slower car = 3x distance of faster car = 3(x+7) 3x + 3(x+7) = 273 carry on ...

*October 12, 2016*

**problem solving**

mike's age ---- x years Sandra's age --- x-8 years Six years ago: Mike was x - 6 Sandra was x-8-6 = x-14 x-6 = 3(x-14) x-6 = 3x - 42 36 = 2x x = 18 Mike is now 18 and Sandra is now 10 years old check: 6 years ago Mike was 12 and Sandra was 4 which is 3 times as old My ...

*October 12, 2016*

**math**

2^-3=1/x 2^3 = x x = 8, you are correct 7^y=1/49 7^y = 1/7^2 t^y = 7^-2, thus y = -2

*October 12, 2016*

**7th Math**

First of all , if you have a "hypotenuse", then you must have a right-angled triangle. If the sides are 10 cm each, then the area of one triangle = (1/2)(10)(10) = 50 cm^2 Assuming you have 16 of those, then the total area is 800 cm^2 btw, the hypotenuse would be &#...

*October 12, 2016*

**Quick math help**

Find the tenth term of the sequence: -6,1,8... Is it 57? YES For the sequence:2,4,8,16 the value of s4 is____. Is it 8? If s4 means the sum of four terms, why not just add them up, they are there in front of you, sum(4) = 30 Find the 7th term of the sequence: 1,2,4,... Is it ...

*October 12, 2016*

**Quick math help**

1. list the terms a(n) = 4n, start with n=1,2,.. terms are 4, 8,12, 16, 32 now add them up 2. I think you mean a(n+1) = 4a(n) + 18, where a(1) = 3 a(2) = 4a(1) + 18 = 4(3)+18 = 30 a(3) = 4a(2) + 18 = 4(30)+18 = 138 carry on to a(6) This is called a recursive sequence, where ...

*October 12, 2016*

**geometry**

why are you reposting this? Steve already did it for you http://www.jiskha.com/display.cgi?id=1476313817

*October 12, 2016*

**geometry**

Is there a question?

*October 12, 2016*

**maths**

confusing wording. I interpret that to say, d = -3 sum(15) = -120 sum(15) = (15/2)(2a + 14(-3) ) = -120 15( 2a - 42) = -240 2a - 42 = -16 2a = 26 a = 13 first term is 13 last term = term(15) = a+14d = 13 + 14(-3) = -29 check: sum(15) = (15/2)(first + last) = (15/2)(13 -29) = -120

*October 12, 2016*

**Geometry**

let the other endpoint be (x,y) I will find the x, then you find the y using the same method. for the x: (x+3)/2 = 5 x+3 = 10 x = 7 for the y: ......

*October 12, 2016*

**math**

speed of lorry ---- x km/h speed of car ----- x+20 km/h time for the car = 280/(x+20) time for lorry = 280/x 280/x - 280/(x+20) = 70/60 divide by 70 4/x - 4/(x+20) = 1/60 times 60x(x+20), the LCD 240(x+20) - 240x = x(x+20) 240x + 4800 - 240x = x^2 + 20x x^2 + 20x - 4800 = 0 (x...

*October 12, 2016*

**Maths**

so there are 15 boys and 16 girls prob(that both picked are girls) = C(16,2) / C(31,2) = 120/465 = 8/31 or prob(girl, girl) = (16/31)(15/30) = (16/31)(1/2) = 8/31

*October 12, 2016*

**Math**

I am sure that the work to be shown should look something like this: 17/2 = x/5 2x = 5(17) x = 85/2 or 42.5 2. 22/30 = 100/x 22x = 3000 x = 3000/22 or 1500/11 or 136 4/11 3. you said: 2/1 = 12/2 or 2 = 6 !!!! , surely that made no sense to you.

*October 12, 2016*

**Math Check Answers**

1. 1 7/8 + 1/9 = 15/8 + 1/9 , LCD = 72 = 135/72 + 8/72 = 143/72 none of the choices match 2. 8 8/9 - 5 1/11 = 80/9 + 56/11 = 880/99 + 448/99 = 1328/99 none of your choices match this. 3.3.) 7 2/3 x 3 7/9 = 23/3 x 34/9 = 782/27 not your choice. are you just guessing? show me ...

*October 12, 2016*

**geometry**

basic trig ratios .... cos60° = yz/12 yz = 12 cos 60° = ..

*October 12, 2016*

**maths**

I let a = 20° and tested your equation the way you typed it, it is not true did you mean: [(x+y)/(x-y)]^(2x)+y/2]^2=1 ? or [( (x+y)/(x-y)]^2 )x)+y/2]^2=1 ? or ....

*October 12, 2016*

**math**

make your sketch. let AB = BC = y let AC = x so 2y + x = 82 x = 82-2y given the information, that is as far as we can go

*October 12, 2016*

**math**

2(x-4) ≤ 17

*October 12, 2016*

**Plane and solid geometry**

you will have to "complete the square" 2x^2+4y^2-12x-64y-16=0 2(x^2 - 6x + ....) + 4(y^2 - 16y + ....) = 16 2(x^2 - 6x + 9) + 4(y^2 - 16y + 64) = 16 + 2(9) + 4(64) 2(x-3)^2 + 4(y-8)^2 = 290 divide each term by 290 2(x-3)^2 /290 + 4(y-8)^2 / 290 = 1 (x-3)^2 / 145 + (y...

*October 12, 2016*

**Math for Reiny**

you are correct at -1 I made an error, (shouldn't do stuff in my head) I think I was taking csc^2 (45°) , π/2 = 90°, not 45° my bad

*October 12, 2016*

**Math**

y = -1/(x+5) - 1 step #1 in finding the inverse is to interchange the variables, so x = -1/(y+5) - 1 now solve this for y x+1 = -1/(y+5) (x+1)(y+5) = -1 xy + 5x + y + 5 = -1 y(x+1) = -5x - 6 y = -(5x+6)/(x+1), x ≠ -1,-5

*October 12, 2016*

**Math**

Perfect setup, notice the coefficients of x are ±2, so nothing has to be done add 2nd and last ---> 2y + 4z = 2 , #4 add 1st and last ---> 5y + 6z = 5 , #5 #4 times 5 ----->10y + 8z = 10 #5 times 2 ----> 10y + 12z = 10 subtract those two equations: 4z = 0 z...

*October 12, 2016*

**math**

You couldn't have two different answers. There are 12 white or green marbles so prob(a white or green) = 12/ 17

*October 12, 2016*

**math**

Since you are drawing ONE marble, the prob( white AND green) = 0 That should have been obvious, how can you have a white and a green marble at the same time. My question to you... What is the probability if drawing a white OR a green ?

*October 12, 2016*

**Geometric progression**

first condition: 8/x = y/8 xy = 64 2nd condition: y-x = -8-y 2y + 8 = x in xy=64 (2y+8)(y) = 64 2y^2 + 8y - 64=0 y^2 + 4y - 32=0 (y+8)(y-4) = 0 y = -8 or y = 4 since xy= 64 if y = 4, x = 16 if y = -8 , x = -4

*October 12, 2016*

**Geometric progressio**

Again, use your definition: k/3 = 48/k k^2 = 144 k = ± 12

*October 12, 2016*

**Geometric progression**

its 5th term is 48 --- ar^4 = 48 The 7th term of a g.p. is 8 times of the 4th term ---> ar^6 = 8ar^3 ar^6 - 8ar^3 = 0 ar^3( r^3 - 8) = 0 ar^3 = 0 ---> not very likely or all terms are 0 r^3 = 8 r = 2 in ar^4 = 48 a(16) = 48 a = 3 state your conclusion

*October 12, 2016*

**Geometrc progression**

Follow the method I showed you in http://www.jiskha.com/display.cgi?id=1476257173

*October 12, 2016*

**Algebra**

let the exponential equation be y = a e^(kx) for (0,200) 200 = a e^0 a = 200 so you have y = 200 e^kx for (6,380) 380 = 200 e^(6k) 1.9 = e^(6k) take ln of both sides, and use rules of logs ln 1.9 = 6k lne, but lne = 1 6k = ln 1.9 k = ln 1.9/6 the exponential equation is y = ...

*October 12, 2016*

**Geometric progressio**

Use your definitions: the fifth term of a g.p. is 81 ---> ar^4 = 81 second term is 24 -----> ar = 24 divide them: (ar^4)/(ar) = 81/24 r^3 = 27/8 r = 3/2 then in ar=24 (3/2)a = 24 a = 16 the GP is 16, 24, 36, 54, 81, ...

*October 12, 2016*

**Math 201**

follow the same steps I just outlined in http://www.jiskha.com/display.cgi?id=1476258106 for 1985, let t = 0, so for 1997 , t = 12 so you have the two ordered pairs (0,100000) and (12, 160000)

*October 12, 2016*

**Algebra**

follow the same steps as in http://www.jiskha.com/display.cgi?id=1476258106

*October 12, 2016*

**Math**

amount of the $5 candy ------ x pounds 5x + 4(60) = 4.4(x+60) solve for x and your Christmas wishes are fulfilled.

*October 12, 2016*

**Algebra**

a.) P= 400×(0.43)^t decay factor: 0.43 <----- correct This means that the function decays by 57 % for each period the rest are the same

*October 12, 2016*

**Math**

Vivian's solution is correct

*October 11, 2016*

**Math**

your derivative is correct. now just plug in x = π/2 to get the slope remember that tan(π/2) is undefined, BUT cot (π/2) = cos(π/2) / sin(π/2) = 0/1 = 0 so slope = -csc^2 (π/2) = 2 equation of tangent: y-1 = 2(x- π/2) clean it up if needed. ...

*October 11, 2016*

**Math**

number of miles when it happens --- x 150 + .5m = 70 + .9m solve for m

*October 11, 2016*

**algebra homework help**

correct

*October 11, 2016*

**Math**

1. A rational number can be expressed by an exact fraction so it is 4/5 2. correct 3. C is correct, B is not but √25 = 5 = 5/1 , so rational 4. B is correct, C is not E is irrational 5. correct

*October 11, 2016*

**math**

let the smaller number be x let the next consecutive even number be x+2 x+2 = 2x - 6

*October 11, 2016*

**algebra homework help**

+-89 is the same as -89, so either way is good you are correct with n/-42 - 89 = -87

*October 11, 2016*

**math**

http://www.jiskha.com/display.cgi?id=1476234090

*October 11, 2016*

**Math**

If you want the specific order, RWB, then it is (3/10)(1/9)(6/8) = 1/40 If the order of the red, white and blue does not matter, the prob = 6(1/40 ) = 3/20

*October 11, 2016*

**algebra homework help**

x + x+1 = 285 2x = 284 x = 142 the two number are 142 and 143, which are consecutive and 142+143 = 285

*October 11, 2016*

**math**

I would say: 36° C

*October 11, 2016*

**Math**

militants ??? 121 L/min = 121000 ml / 60 seconds = (121000/60) ml/s = (6050/3) ml/s

*October 11, 2016*

**Algebra 2**

shortest side ---- x longest side ----- 2x middle side ---- y longest side is also x+y-3 2x = x+y-3 x = y-3 y = x+3 sum = x+2x + y = 19 x+2x+(x+3) = 16 4x=16 x = 4 shortest side = 4 longest side = 8 middle side = 7 check: they clearly add up to 19 is the longest side equal to ...

*October 11, 2016*

**Pre-calc**

You posted this yesterday http://www.jiskha.com/display.cgi?id=1476153606 Why did you post it again today?

*October 11, 2016*

**math**

straight-forward trig ... sin 57.8° = 600/length of wire length of wire = 600/sin 57.8° ft = ...

*October 11, 2016*

**math**

total area = (19)(9) + 14(9) ft^2 = 297 ft^2 number of cans needed = 297/400 = .7425 Assuming you are buying the paint only by the gallon, you will have to buy 1 gallon, so the cost will be $17.00 btw, time to update that textbook, paint at $17 a gallon ????

*October 11, 2016*

**Math**

ok, then according to their hint, 0 = -16t^2 + 400 16t^2 = 400 t^2= 400/16 = 25 t = √25 = 5 so it took 5 seconds How could it possible take 400 seconds or almost 7 minutes for a ball to fall from 400 ft ???

*October 11, 2016*

**Math**

Do it the same way, I showed you the previous one. 1 lb = 16 oz 1 gallon = 4 qt so 5 lb/gal = 5(16) oz / 4 qt = 5(16)/4 oz/qt = 20 oz/qt

*October 11, 2016*

**Math**

8 L/min = 8000 ml / 60 seconds = (8000/60) ml/s = 400/3 ml/s or appr 133.3 ml/s

*October 11, 2016*

**science**

check with your previous post of this

*October 11, 2016*

**physics**

Basic law of playground-math: the product of the distance and mass on both sides of the teeter-totter must be the same. so let the boys mass be b kg and that of the girls be g kg 1.2b = 1.5g 2.4b = 3g 1.8(b+14) = 3g 1.8b + 25.2 = 2.4b 25.2 = .6b b = 25.2/.6 = 42 sub into 1.2b...

*October 11, 2016*

**Maths**

Sounds like the instructions were not too clear. If it asks for the common factors, then I would list {2,3,4,6} as any of those is a common factor. Now the HIGHEST common factor of those is 6.

*October 11, 2016*

**math**

rate of flow = 50 gallons/5 min = 10 gallons/min

*October 11, 2016*

**MATH**

according to the order of operations 5/3x+1=2 times 3 5x + 3 = 6 5x = 3 x = 3/5 check: Left side = (5/3)(3/5) + 1 = 1+1 = 2 = Right side my answer is correct If you meant otherwise, you will have to insert brackets.

*October 10, 2016*

**Pre calc**

income = .11(s - 1800) + 575, where s is his sales solve : .11(s-1800) + 575 = 2200

*October 10, 2016*

**pre-calc**

mmhhh, what is 6-4 ?

*October 10, 2016*

**Math**

No idea what that means, or what you want to do with it.

*October 10, 2016*

**Math**

guessing you meant: 2/n = 15/(n^2- 1) then 2n^2 - 2 = 15n 2n^2 - 15n - 2 = 0 n = (15 ± √241)/4

*October 10, 2016*

**math**

checking: x + 10 + x − 20 + x + 25 = 180 3x = 165 x = 55 , you had that so the 3 angles are: 65°, 35° , and 80° You said "it is an acute angle", you must have meant " it is an acute-angled triangle"

*October 10, 2016*

**math**

Trey's rate = 1/40 Marcus rate = 1/20 combined rate = 1/40 + 1/20 = 3/40 time at combined rate = 1/(3/40) = 40/3 minutes

*October 10, 2016*

**Math**

I am sure you mean (x+2)/(x^2-49) + 3/(x+7) , those brackets are absolutely essential = (x+2)/( (x+7)(x-7) ) + 3/(x+7) so what do you think? hint: what would be the common denominator for 2/((3)(4) ) + 3/4 ?

*October 10, 2016*

**math**

Cabrina's distance --- x miles Dabney's distance = 690-x Cabrina's time = x/65 Dabneys time = (690-x)/50 x/65 + (690-x)/50 = 11.4 times 650 , the LCD 10x + 13(690-x) = 7410 10x + 8970 - 13x = 7410 -3x = -1560 x = 520 continue

*October 10, 2016*

**Quick math help**

#1, wrong 1+2+..+8+9+10 = (10/2)(first + last) = 55 #2. wrong a=-2 , d = 3, term(n) = 25 term(n) = a + (n-1)d 25 = -2 + 3(n-1) 27 = 3n - 3 30 = 3n n = 10 , so it is the 10th term #3. wrong a=2, d = 7, term(n) = 177 177 = 2 + 7(n-1) 175 = 7n - 7 182 = 7n n = 26 , so the 26th ...

*October 10, 2016*