# Posts by Reiny

Total # Posts: 38,771

**precalculus**

#1 term(5) = C(8,4) (2x)^4 (-4)^4 = 70(16x^4)(256) = 286720 x^4 <-------- B general term of (a+b)^n: term (k+1) = C(n,k) * (a)^(k-1) * b^k #2, correct

**math**

4/9 b^6 = (2/3 b^3)^2

**calc**

x/8 - (2/9)y dy/dx = 0 dy/dx = (x/8) / (2y/9) = 9x/(16y) at (4?2,3), dy/dx = 36?2/(48) = 3?2/4 equation: y - 3 = (3?2/4)(x - 4?2) clean it up to whatever form is needed. Proof: http://www.wolframalpha.com/input/?i=plot+(x%5E2%2F16)-(y%5E2%2F9)%3D1+,+y+-+3+%3D+(3%E2%88%9A2%2F4...

**Physics- Car moving with speed of 22 m/s...**

acceleration --- (-a) velocity = -at + c when t = 0, v = 22 22= 0+c ---> c = 0 v = -at + 22 when t = 6.5, v = 0 0 = -6.5a + 22 a = 22/6.5 = 44/13 distance = d = (-1/2)a t^2 + 22t + k d = (-22/13)t^2 + 22t + k when t = 0, d = 0, so k = 0 when t = 0 , d = 0 when t = 6.5, d...

**algebra**

(4.2*10^2)(4.2*10^5) = 17.64 x 10^7 = 1.764 x 10^8

**algerbra**

h(t) = -16t^2 + 96t 144 = -16t^2 + 96t t^2 - 6t + 9 = 0 (t-3)(t-3) = 0 t = 3

**math**

After giving .3x of the flowers to her sister Fariza has .7x of them left over giving (4/7) to her brother leaves her with (3/7)(.7x) (3/7)(.7x) = 45 .3x = 45 x = 150 she kept 45/150 or 30% of them for herself She had 150 of them the sister got (.3)(150) or 45 the brother got...

**math**

What Ms Sue is saying is .... y = 3x + 3

**Calculus**

Ok, so the second derivative is negative and you know that if the 2nd derivative is negative the function is concave downwards. Of course you should recognize that we are dealing with a quadratic function, a parabola, which opens downwards for all values of x

**MATH HELP PLEASE**

For any number to be divisible by 9, the sum of its digits must be divisible by 9 So far we have a sum of 16, so we need a 2 21258 is divisible by 9 Surely you know how to do the other two questions.

**Zee school , math subject.**

What is the area of the original sheet ? What is the area of one of the squares to be cut out? How many of those cut-out squares are there? What is left over after we cut them out? ... etc. I'll wait for your reply and check your answers.

**Math grade 6, ratio**

number of oranges --- x after give-away number of oranges = x-10 number of pears = 24 and he had twice as many pears as oranges 24 = 2(x-1) 2x - 2 = 24 x = 13 ratio of oranges : pears = 13 : 24

**Math grade 6, ratio**

current count: boys --- 4x girls ---- 3x 4x = 3x + 6 x = 6 there were 24 boys and 18 girls after 2 girls are added, new ratio is 24 : 20 = 6 : 5

**math**

let the 3 numbers be x, x+1, and x+2 2(x+2) + x = 4(x+1) - 15 solve for x, then sub into my definitions

**Math grade 6, ratio**

Number of stamps for david -- 4 x number of stamps for Tim = 3x after give-away, Tim has 1.5x David has 5.5x ratio of Tim : David = 1.5x : 5.5x = 1.5 : 5.5 = 15 : 55 = 3 : 11

**Math**

Don't repost the same question without looking at your previous one http://www.jiskha.com/display.cgi?id=1481770968

**Pre-calculus**

Cannot make out your typing what does "cos \theta" mean ? is it r = -5( 2cosØ + sinØ) ??? if so, here is the graph: http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+-5(+2cos%C3%98+%2B+sin%C3%98) certainly not a line

**Math**

3x^4 + 4x^3 =0 x^3(3x+4) = 0 x = 0 or x = -4/3 looks like two x-intercepts f ' (x) = 12x^3 + 12x^2 = 0 for a max/min of f(x) 12x^3 + 12x^2 = 0 x^2(12x + 12) = 0 x = 0 , f(0) = 0 x = -1, f(-1) = 3 + 4(-1) = -1 looks like (-1, -1) is a minimum , and we will consider (0,0) ...

**The Value of an Annuity**

You do these kind of questions, you MUST know the basic formulas. I used Amount = payment( (1+i)^n - 1)/i I you don't know this, how can you possibly handle this topic of annuities?

**The Value of an Annuity**

i = .067/4 = .01675 n = 140 P(1.01675^140 - 1)/.01675 = 800,000 p = ..... b) multiply p by 140 c) subtract 800,000 - answer to b)

**Math**

let the sides by 17x by 2x ( ---> ratio is 17x : 2x = 17 : 2 ) 34x^2 = 136 x^2 = 136/34 = 4 x = 2 sides are 17(2) by 2(2) or 34 by 4

**math**

18x^2=420-6x You now have a quadratic equation 18x^2 + 6x - 420 = 0 3x^2 + x - 70 = 0 (x + 5)(3x - 14) = 0 x = -5 or x = 14/3 since x> 0, x = 14/3 so the sides are 6(14/3) or 28 and 3(14/3) or 14 so the perimeter is 2(28+14) = 84 ft check: 18x^2 = 18(14/3)^2 = 392 420 - 6x...

**precalculus**

see your previous post under anonymous

**precalculus**

see reply when you were "anonymous"

**Algebra**

9x^2+ 25y^2 =225 divide each term by 225 x^2/25 + y^2/9 = 1 ellipse, with a = 5 and b = 3 domain: -5 ? x ? 5 range: -3 ? y ? 3

**can you check my answers precalculus**

Please give yourself a "nickname" and stick with it. That way I can check for your previous posts. I recall just answering that one.

**Math**

thord te ????? "The eleventh term of an A.P.with positive terms is four times its third term" ---> a+11d = 4(a+2d) a+11d = 4a + 6d 5d = 3a d = 3a/5 "the product of thord te and eleventh term is 256" I will read that as third term (a+2d)(a+11d) = 256 a^2...

**precalculus**

Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) P(k+1) = Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) + (6(k+1) + 1 = Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) + (6k + 7) "What is the first step when writing a proof using mathematical induction? " Test to see ...

**Math | Algebra**

amount of brand A needed --- x lb amount of brand B needed ---- 20-x lb .25x + .2(20-x) = .23(20) .25x + 4 - .2x = 4.6 .05x = .6 x = 12 State your conclusion

**math**

What's the question? If you want the maximum height: the vertex will tell you how high it went and how long it took to reach that height. the t of the vertex is -64/(-32) = 2 seconds h(2) = -64 + 128 + 192 = 256 ft above the ground (the vertex was (2, 256) when will it hit...

**algebra**

5,100,000 = 5.1 x 10^6 (notice I moved the decimal 6 places)

**precalculus**

I think this link nicely fits with your problem, carefully study the 3 steps I used to do an induction problem. The problem is the same as your #4 http://www.jiskha.com/display.cgi?id=1481512314 #1. I don't like your notation, did you mean P(k+1) and P(k) ? or Pk+1 and Pk ...

**Math**

no, why would you divide by 3? you correctly converted the square feet to square yards by dividing by 9, and your cost was in square yards. your cost is $610.50

**precalculus**

http://www.jiskha.com/display.cgi?id=1481565350

**algebra**

well, first lets get rid of those nasty fractions ... multiply the first by 10 6x = 5y + 110 or 6x - 5y = 110 ** 3x + 8y = 13 <--- I assume yours was a typo double the 2nd: 6x + 16y = 26 *** subtract *** from ** -21y = 84 y = -4 sub back into 3x+8y=13 to find x

**Math - Algebra (Percents and Ratios)**

number of people in stands --- x number who were parents = (3/4)x) of those 4/7 were moms total moms = (3/4)(4/7)x = (3/7)x percentage of moms = (3/7)x / x = 3/7 = appr 43%

**algebra**

I will show you the first one .... ?50 = ?25*?2 = 5?2 general method: Factor your number so that one or more factors are perfect squares. e.g. ?720 = ?9*?16*?5 = 3*4*?5 = 12?5 Show me what you did for the 2nd question

**pure math**

Did you mean (1 - x/2)^(1/5) ? Are you studying the binomial theorem?

**math**

You are welcome

**math**

Yes, it would be because of the repeated multiplication by .88 suppose we show a few steps after 1 km : Pr = 1013(.88) after 2 km : Pr = 1013(.88)(.88) = 1013 (.88)^2 after 3 km : Pr = 1013(.88)^2 (.88) = 1013 (.88)^3 etc , for after x km : Pr = 1013 (.88)^x

**One step inequalities**

x - 9 ? 27

**precalculus**

Steve had done the above steps for you, see the first of the Related Questions for you. First, it might help if you looked at the graph http://www.wolframalpha.com/input/?i=polar+plot+r%3D8cos(3%C3%98) Steve told you: |cos 3Ø| ? 1 so |8cos 3Ø| ? 8 | r | ? 8 , so ...

**Math**

Take a small rectangular piece of paper, such as a business card, hold a finger on the end of the longer side and rotate the card. What do you notice ?

**Probability**

first of all listing the choices of digits 444 --- can be arranged in 1 way 442--- can be arranged in 3 ways 443--- can be arranged in 3 ways 422--- can be arranged in 3 ways 433--- can be arranged in 3 ways 423--- can be arranged in 6 ways 222--- can be arranged in 1 way 223...

**Math**

weight of empty basket --- x weight of 1 pear ---------- y x + 30y = 11.2 x + 18y = 7 subtract them: 12y = 4.2 y = .35 sub back: x + 18(3.5) = 7 x = 4.2 Each pear weighs 350 g and the basket ways 4.2 kg so basket with 7 pears = .......

**maths**

total expenses = 2030+4900+3150 = .... so 2x + 3x + 4x = total above find x, sub back into 2x, 3x, and 4x

**Algebra**

Athena's age is expressed as a function of the cousin's age, so it is usually easier to define the domain Four years ago: let the cousin's age be x then Athena was 2x-5 present: cousin ---- x+4 Athena ----- 2x-5 + 4 or 2x - 1 x+4 = 3(2x-1) - 18 x+4 = 6x - 3 - 18 25...

**maths**

done http://www.jiskha.com/display.cgi?id=1481713097

**Math**

Prob(a 6) = 1/6 , prob(not a 6) = 5/6 so in 5 tosses you want that 3 times Prob(of your event) = C(5,3) (1/6)^3 (5/6)^2 = 10(1/216)(25/36) = 125/3888 or appr .03215

**precalculus**

Steve said: http://www.jiskha.com/display.cgi?id=1481636669 and this: http://www.jiskha.com/display.cgi?id=1481653351 Make use of it please

**business**

amount = 2000 ( 1.05^40 - 1)/.05 = ....

**math**

hina gets ---- x rina gets ----- 3x - 100 x + 3x-100 = 300 4x = 400 x = 100 Hina would get 100 and rina would get 3(100) - 100 or 200

**precalculus**

umhh, what part of the solution I gave you yesterday did you not like? http://www.jiskha.com/display.cgi?id=1481597953

**I THINK I FIGURED IT OUT!**

Another simple way to look at it: 24 ----> 6 , so it was reduced by a factor of 1/4 what is (1/4) of 18 ????

**I THINK I FIGURED IT OUT!**

NOPE, look at my last reply to your previous post

**a.p.**

ok, your turn use your definitions

**a.p.**

terms are a, a+d, a+2d, a+3d 4a + 6d = 4 2a + 3d = 2 ---> a = (2-3d)/2 a(a+3d) + (a+d)(a+2d) = -38 a^2 + 3ad + a^2 + 3ad + 2d^2 = 38 2a^2 + 6ad + 2d^2 = -38 2(4 - 12d + 9d^2)/4 + 6d(2-3d)/2 + 2d^2 = -38 (4 - 12d + 9d^2)/2 + 6d(2-3d)/2 + 2d^2 = -38 times 2 4 - 12d + 9d^2 + ...

**a.p.**

sides must be a, a+d, and a+2d a^2 + (a+d)^2 = (a+2d)^2 a^2 + a^2 + 2ad + d^2 = a^2 + 4ad + 4d^2 a^2 - 2ad - 3d^2 = 0 (a - 3d)(a+d) = 0 a = 3d or a = -d case 1: a = 3d let d = 1 then a = 3 , and the sides are 3, 4, and 5 let d = 2 then a = 6, and the sides are 6, 8, and 10 ...

**math**

what is 7x8x4 ?

**Algebra PLEASE HELP ME**

BC = 11 - (-2) = 13 what is the difference between a height of 8 and a height of 20 ?? Did you look at your diagram?

**Algebra PLEASE HELP ME**

slope of BC = (8-8)/(11=2) = 0 so BC is a horizontal line Thus the line through A must be a vertical line All vertical lines have the form x = something Look at the given point A, what is its x value ? so the equation of your required line is x = 3 Make a sketch. The base BC ...

**Math lovely Math**

prob(elephant) = 7/20 prob(tiger) = 6/20 continue ... add them up to make sure they add up to 1, they will! If they don't you messed up

**Math**

arc = rØ, where Ø is in radians 25 = 7Ø Ø = 25/7 radians

**Math**

cost per hour = 175/5 = 35 (not bad for babysitting, but then again I haven't needed a babysitter in 70 years) cost = 35t , where t is the number of hours slope is 35 y-intercept is 0 It is a proportion, and it is a function

**h.p.**

The base of your powers is an arithmetic sequence sum(1) = 1 sum(2 ) = 1+ 4^2 = 17 sum(3) = 17 + 7^2 = 66 sum(4) = 66 + 10^2 = 166 sum(5) = 166 + 13^2 = 335 sum(6) = 335 + 16^2 = 591 ... with the third difference column of 18, we know it must be in the form of a cubic we could...

**math**

32/9 = 3 5/9 you will have to guess at the 5/9, since your numberline probably has divided the unit in tenths, not ninths so between 3 and 4 , just a bit more than half way between 3 and 4

**Pre-Calculus**

I don't see "the following function"

**precalculus**

form y = (3/2)x b:a = 3/2, but a = 3 b/3 = 3/2 2b = 9 b = 9/2 hyperbola: x^2 /9 - y^2/(81/4) = 1 or x^2/9 - 4y^2/81 = 1 or 9x^2 - 4y^2 = 81 whichever form your text considers standard form

**Calculus**

first number --- x 2nd number ----y 3rd number ---- 40-x-y x + 3y + 4(40-x-y) = 80 x + 3y + 160 - 4x - 4y = 80 -3x- y = -80 3x + y = 80 y = 80-3x product = x(y)(80-x-y) = 80xy - x^2 y - x y^2 = 80x(80-3x) -x^2(80-3x) - x(6400 - 480x + 9x^2) = .... = 160x^2 - 6x^3 d(product)/dx...

**Math Help**

First of all you don't have an equation, so "cross-multiplication" is a meaningless term. You did not match up the corresponding numbers, which was my whole point, and objection to this question your equation should have been: 24/6 = 18/x or 6/24 = x/18 <--- I...

**Math Help**

Show me the steps that gave you 72, as I said, I got 4.5 x : 18 = 6 : 24 <-- following corresponding pattern x/18 = 6/24 24x = 108 x = 108/24 = 4.5

**Math Help**

It is not a matter of choosing an answer. You must determine the answer with some solution. Why did you "choose" that answer? I would assume that the sides are listed in the corresponding order. In that case none of the answers given are correct. I got x = 4.5

**Calculus**

Since (1-2x-3x^2)/(1+x) = (1+x)(1-3x)/(1+x) = 1 - 3x, x ? - 1 what do you think you should use

**Algebra**

I divided the 2nd equation by 2 to get the x terms to be both 5x Are you not familiar with the method of elimination? Just like we can multiply each term of an equation by some number, we can also divide each term by some number without changing the value of the equation. (...

**math**

?x - 6 = x^(1/4) let ?x = t then we have t - 6 = ?t square both sides t^2 - 12t + 36 = t t^2 - 13t + 36 = 0 (t-9)(t-3) = 0 t = 9 or t = 3 if t = 9, then x = 81 if t = 3, then x = 9 since we squared our equation, all answers must be verifies if x = 81 LS = ?81 - 6 = 9-6 = 3 RS...

**Algebra**

1000 e^(kt) = 1274 e^(5k) = 1.274 take ln of both sides 5k = ln 1.274 k = ln 1.274/5 = .048323... = 4.83 % rounded to the nearest hundreth

**Math**

y = 1500 (1.071)^t , where t is in hours

**Math**

As Steve already did this for you, I don't know why you are repeating it. ... Anyway, prob(of your event) = (3/10)(5/10) = 15/100 = 3/20 , which is what Steve had told you.

**Math**

number for Mr Jones ---- x number for Mr Smith ---- x-500 .03x = .05(x-500 .03x = .05x - 25 -.02x = -25 x = 1250 Mr. Jones sold 1250 widgets and Mr. Smith sold 750 check: .03(1250) = 37.5 .05(750) = 37.5

**precaculus**

no, tanØ = -1 , not Ø = -1 since (2,-2) is in quadrant IV, Ø = 315° or 7?/4 so one answer is (2?2 , 7?/4) another would be (-2?2, 3?/4)

**Algebra**

by definition, |anything| ? 0 so |1-4k| must surely be ? -11 for anything inside the absolute value sign

**pre-calculus**

length --- l width ----w 2l+2w=36 l+w = 18 l = 18-w area = lw = w(18-w) = 18w - w^2 d(area)/dw = 18-2w = 0 for a max of area 2w = 18 w = 9 then l = 18-w = 9 so the area of the base of the box must be a square, 9 by 9 as you probably expected.

**pre-calculus**

let the length be l let the width be w so 2l + 2w = 36 l + w = 18 l = 18-w area = wl = w(18-w) = 18w - w^2

**precalculus**

x^2 - 16 = 4y^2 or (x+4)(x-4) = 4y^2 let x = t then t^2 - 16 = 4y^2 y^2 = (t^2 - 16)/4 y = ± ?(t^2 - 16)/2 , -4 ? t ? 4

**Calculus**

http://www.jiskha.com/display.cgi?id=1481558182

**Algebra**

Surely you can follow the method I just showed you in your previous question almost identical to this one. Did you even look at my answer ?

**algebra**

double the 2nd: 5x + 6y = 24 now sub the first one into that 5x + (-5x + 24) = 24 5x - 5x + 24 = 24 0 = 0 , which is a true statement, thus you have an infinite number of solutions.

**Calculus**

Consider it as the points (1,-4), (2,-4), (3,-3) etc let the function be ax^2 + bx + c = y for: (1,-4) ---> a + b + c = -4 * (2,-4) ---> 4a + 2b + c = -4 ** (3,-3) ---> 9a + 3b + c = -3 *** subtract * from ** 3a + b = 0 # subtract ** from *** 5a + b = 1 ## subtract # ...

**Calculus**

Just do it. I am sure you can subtract.

**precalculus**

I would leave the y value in exact form y = r sinØ = -14(?3/2) = -7?3 you also missed the negative sign in your y value exact point (-7, -7?3)

**pre calculus**

correct: http://www.wolframalpha.com/input/?i=parametric+plot+x%3Dt+,+y%3Dt%5E2%2B10 http://www.wolframalpha.com/input/?i=parametric+plot+x%3Dt%5E3,++y%3Dt%5E6%2B10

**Calculus**

intersection of y = 12 and y = e^x e^x = 12 x = ln 12 area = ?(12 - e^x)dx from 0 to ln12 = [12x - e^x] from 0 to ln12 = 12ln12 - e^(ln12) - (0 - e^0) = 12ln12 - 12 - 0 + 1 = 12ln12 - 11 http://www.wolframalpha.com/input/?i=area+between+y+%3D+e%5Ex,++y+%3D+12+from+0+to+ln12

**precalculus**

I think they want you to use a separate graph for each of the values of n to show what happens to the graph as n changes. Wolfram might be of help here: Just change the values in front of the 2nd term to see how it affects the graph. I have shown the graph for n = 3 http://www...

**quick question regarding math**

If your equation has the solution of all real numbers, then your equation is an "identity". here are the different cases for linear equations: case 1: one unique solution 3x -4 = 2x + 1 3x-2x = 1+4 x = 5 case 2: no solution 3x - 4 = 3x - 5 3x-3x = -5+4 0 = -1 , which...

**Math**

Not familiar with the notation A^BC for an angle The usual notation is angle ABC, where B would be the vertex of the angle and the containing sides would be AB and BC Explain your notation.

**Math.**

14x?1/2(4x+6)=3(x?4)?18 14x - 2x - 3 = 3x - 12 - 18 I am sure you can take it from here.

**math**

200000000 or 200,000,000 would be "two hundred million"

**Math**

The areas of similar objects are proportional to the square of their corresponding sides. so 28 : x = ?8 : ?25 28/x = 2?2/5 2?2x = 140 x = 70/?2 or 35?2

**Mathematics**

5 women 7 men, choose 4 a) number of ways with no restriction = C(12, 4) = 495 b) must be 3 men and 1 woman = C(7,3) x C(5,1) = 35 x 5 = 175 c) at least 3 women ---> 3 women or 4 women = C(5,3) x C(7,1) + C(5,4) x C(7,0) = 10x7 + 5x1 = 75

**math**

let the sides be 3x, 4x, and 5x 3x+4x+5x = 24 12x = 24 x = 2 sub back into my definitions of the sides so the sides are 6, 8, and 10