Wednesday
December 7, 2016

Posts by Reiny

Total # Posts: 36,897

Math (Confused)
Not confusing at all, simply replace wherever you see an x with the given value, C(x) = .75x + 5 C(0) = .75(0) + 5 = 5 that rules out a), b), and e) C(50) = .75(50) + 5 = 42.5 so far, only c) works simply check by finding C(100)
October 17, 2016

Ratio
Just like in your previous question , I looked up "duplicate ratio" http://www.math-only-math.com/types-of-ratios.html and again, just follow the definition ( Where and in what course are they teaching this?)
October 17, 2016

Ratio
I actually had to look this up, had never heard of it. Subduplicate ratio: The sub duplicate ratio m : n is the ratio √m : √n. So, the sub duplicate ratio of the ratio m22 : n22 is the ratio m : n. For example: The sub duplicate ratio of 25 : 81 = √25 : &#...
October 17, 2016

Math115
done, check back to your last post of this
October 17, 2016

Differentiation
use x^2 to show "x squared" etc I would expand it first, just like in my previous reply , then take the derivative. check your answer by doing it both ways, like I showed you
October 17, 2016

Differentiation
did you mean y = (x^2 - 5x+6)(x-3) ? For this one, I would have actually expanded it. y = x^3 - 3x^2 - 5x^2 + 15x + 6x - 18 = x^3 - 8x^2 + 21x - 18 dy/dx = 3x^2 - 16x + 21 or .... by the product rule: dy/dx = (x^2 - 5x + 6)(1) + (2x - 5)(x-3) = x^2 - 5x + 6 + 2x^2 - 6x - 5x + ...
October 17, 2016

Arithemetic progression
use your formula a = 5, d = 2 , n = ? , sum(n) = 480 (n/2)(10 + 2(n-1)) = 480 n(8 + 2n) = 960 8n + 2n^2 = 960 n^2 + 4n - 480 = 0 (n+24)(n-20) = 0 n = -24 or n = 20 , but n must be a whole number the sum of 20 terms would be 480 check: sum(20) = (20/2)(10 + 2(19)) = 480
October 17, 2016

correction - Arithmetic progression
First of all we need all the even number, which are 2,4,6,..., 98 there are 49 of them, so sum(49 evens) = (49/2)(4 + 2(48)) = 2450 Now this includes all multiples of 5 that end it 0, but not those that end in 5 so we have to add 5,15,25,35,45,55,65,75,85, and 95 they add up ...
October 17, 2016

Math115
looks like you considered 1968 as t = 0 , that's fine so you would two ordered pairs (0,20000) and (25,100000) I agree with your linear equation, but you should state it as p(t) = 20000 + 3200t, where t is the number of years after 1968 for the exponential: let p(t) = ...
October 17, 2016

Maths
let the amount be x x(1.06)^2 - x(1 + 2(.06)) = 92 x(1.1236) - x(1.12) = 92 .0036x = 92 x =25,555.56
October 17, 2016

algebra
Danielle's age ---- x Travis' age ------ x+19 14 years from now: Danielle ------- x + 14 Travis ---------- x+19 + 14 = x+33 x+33 = 2(x+14) take over, it is easy from there.
October 16, 2016

6th grade algebra
What does the weight of the flag have to do with the width of the stripes?
October 16, 2016

Math
starting amount ---- x spent $5, amount left = x-5 after spending half of that on jogging shoes, amount left = (1/)(x-5) after spending $2 for lunch, amount left = (1/2)(x-5) - 2 spent half of that on a DVD, amount left = (1/2)[(1/2)(x-5) - 2] which equals 10 (1/2)(x-5) - 2 = ...
October 16, 2016

Math
I am going to rephrase your question, without fancy symbols cos(7E) + cos(3E) = cos(5E) , where 0 ≤ E ≤ 360° Correction on the formula you are using: should say: cosA + cosB = 2cos((A+B)/2)cos((A-B)/2) so cos(7E) + cos(3E) = 2cos(5E)cos(2E) but cos(7E) + cos(2E...
October 16, 2016

Maths
I will assume your "using while numbers" should say "using whole numbers" so 36 = 1 x 36 = 2 x 18 = 3 x 12 = 4 x 9 = 6 x 6
October 16, 2016

value
x^2 - 13x = 30 x^2 - 13x - 30 = 0 (x-15)(x+2) = 0 can you take over ?
October 16, 2016

math trig
Find an old mathbook with trig tables, go to the sine column, find the nearest value of the angle so that sinØ = .6 The nearest angle you will find is 37°
October 16, 2016

Calculus
a) let y = f(x) * g(x) then y' = f(x)* g '(x) + g(x) * f '(x) given: f(4) = 3 f '(4) = -2 g(4) = 6 g '(4) = -4 so y' = 3(-4) + 6(-2) = -24 how did you get -27 ? do the others the same way
October 15, 2016

Calculus
Treat it as two ordered pairs, (11,27000) and (10,34000) and then find the equation of the line like you did in grade 9 slope = (34000-27000)/(10-11) = -7000 y = mx + b y = -7000x + b using (10,34000) 34000 = 10(-7000) + b b = 104000 y = -7000x + 104000 , y ≤68000 so at ...
October 15, 2016

Math
Make a sketch. Draw a radius to the base of the isosceles triangle. let the base of the isosceles triangle be 2x, and let its height be h+12 area = (1/2)(2x)(h+12) = x(h+12) but x^2 + h^2 = 12^2 x^2 = 144 - h^2 x = (144 - h^2)^(1/2) area = (144 - h^2)^(1/2)(h+12) d(area)/dt...
October 15, 2016

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

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