# Posts by Reiny

Total # Posts: 38,777

**Math**

regular price ---- x it said the 20% discount came to $15 well, .2x = 15 x = 15/.2 = ......

**Aice Math**

(5-x/2)^6 I assume you know how to expand using the binomial theorem. (5-x/2)^6 = 5^6 + 5^5(-x/2) + 5^4(-x/2)^2 + ... = 15625 - (3125/2)x + (625/4)x^2 + ... so matching up terms: -3125x/2 = px ----> p = -3125/2 (625/4)x^2 = qx^2 ----> q = 625/4

**Math**

Using the binomial expansion (x^2-b/x)^4 = (x^2)^4 + 4(x^2)^3 (-b/x) + 6(x^2)^2 (-b/x)^2 + 4(x^2) (-b/x)^3 + (-b/x)^4 = 4x^8 - 4x^6 (b/x) + 6x^4 b^2/x^2 - ... = 4x^8 - 4x^5 b + 6x^2 b^2 - ... so the term containing x^2 is 6x^2 b^2 , which is equal to 294 6v^2 = 294 b^2 = 49 b...

**Math**

I = PRT you told me I = 1/9P --> P = 9I you told me r = t, where r is a stated percent I = 9I(r/100)(r) 1 = (9/100)r^2 r^2 = 100/9 r = 10/3 = 3.3333.. the rate is 3 1/3% check: suppose we have $1000 for 10/3 years at 3 1/3 % I = 1000(10/3)(10/300) = 111.11 and 1/9 of 1000...

**algebra**

Compare this question to your previous one. What is your answer ?

**algebra**

The product of 5 and 6 = 30 the product of 7 and 8 = 56 the product of 31 and g = 31g

**Math**

Your post makes absolutely no sense to me.

**Maths**

equation: x^2 - bx + c roots: ?a and ?b sum of roots = ?a + ?b = b product or roots = ?a?b = c --> ab = c^2 ?a + ?b = b square both sides (?a + ?b)^2 = b^2 a + 2?(ab) + b = b^2 then a+b = b^2 - 2?(ab) = b^2 - 2c DONE a^2 + b^2 = (a+b)^2 - 2ab = (b^2 - 2c)^2 - 2c^2 treat ...

**correction - Algebra 1**

Eddie's answer is not correct after 8 months, x = 8 y = 3(2^8) = 3(256) = 768 or: 3 6 12 24 48 96 192 384 768 now: 3 after 1 month -- 6 ---> 3(2^1) after 2 months -- 12 --> 3(2^2) ... after 8 months -- 768 = 3(2^8)

**Math**

(w^-2 j^-4) ^-3 (f^7 f^3) = (w^6)(j^12)(f^10)

**Math**

3 apples + 2 oranges + 2 apples - 1 orange = 5 apples + 1 orange 3x + 2y + 2x - y = 5x + y 3?3 + 2?5 + 2?3 - ?5 = 5?3 + ?5

**Ms. Sue! Math**

You should know that linear functions can be written in the form y = mx + b , (the y-intercept form), except vertical lines which have the form x = c so let's pick any slope from -1 to 0. How about m = -1/4 Equations with such a slope are y = (-1/4)x + 7 or y = (-1/4)x + 3...

**Algebra**

Extraneous roots mostly occur after squaring an equation. Since you verified your solution by subbing it back into the original equation, there are no extraneous roots LS = x/(5x+4) = (-6/7) / (5(-6/7) + 4) = (-6/7) / (-2/7) = (-6/7)(-7/2) = 42/14 = 3 = RS

**maths equation too hard**

you mean Newton's "iterative" method sure, why not? x^3 = 3^x let y = x^3 - 3^x dy/dx = 3x^2 - ln3(3^x) newx= x - (x^3 - 3^x)/(3x^2 - ln3 (3^x) ) start with x = 2.9 newx = appr 3.0471... using that newx = appr 3.0081... using that newx = appr 3.00006996 , not bad

**maths equation too hard**

Steve did this for you earlier. What did you not like about his reply? http://www.jiskha.com/display.cgi?id=1486532823 You could graph: y = x^3 and y = 3^x and see where they cross

**Maths**

prob(defect) = .05 prob(no defect) = .95 a) I read that as exactly 10 out of the 100 = C(100,10) (.05)^10 (.95)^90 = appr .0167, according to my calculator b) unreasonable question, you would have to do prob(exactly 0 defective) + prob(1 effective) + ...+ prob(10 defective) If...

**Mathematics**

case 1: the circumference of the cylinder is 30, and the height is 18 2?r = 30 r = 15/? V = ?(15/?)^2 (18) = 4050/? case 2: the circumference is 18 and the height is 30 2?r = 18 r = 9/? V = ?(9/?)^2 (30) = 2430/? volume of case1 : volume of case2 = 4050/? : 2430/? = 5 : 3 Just...

**math**

I read that as area = -x^2 + 7x + 30 this has to be positive, so -x^2 + 7x + 30 > 0 x^2 - 7x - 30 < 0 (x - 10)(x+3) < 0 so you know that -3 < x < 10 that is, x must be between -3 and 10 Possible values : let x = 1, then area = -1 + 7 + 30 = 36 the rectangle is 1...

**Continuity Calculus Help**

limit ?( (x^2 - 64)/(x-8)) as x -->8 = lim ?( (x-8)x+8)/(x-8) , as x ---> 8 = lim ?(x+8) , as x---> 8 = ?16 = 4

**Math**

I used to illustrate this problem to my students by taking a cone-shaped drinking cup from a water dispenser and cutting it open to show just that kind of a sector. It was easy to see that the arc of that sector becomes the circular base of the cone, so .... since the angle is...

**Calculus-derivatives**

Bob forgot to find the derivative first dy/dx = 12x + 4 12x+4 = -2 12x = -8 x = -8/12 = -2/3 f(-2/3) = 6(4/9) + 4(-2/3) - 9 = -25/3 We have a parabola shown below with a tangent at (-2/3 , -25/3) having a slope of -2 http://www.wolframalpha.com/input/?i=plot+y%3D6x%5E2%2B4x-9

**Math interest**

So the interest on your $5000 should amount to $5000 5000(.05)t = 5000 t = 1/.05 = 20 or, interest for 1 year = 5000(.05)(1) = $250 Since that stays constant (simple interest), it would take 5000/250 or 20 years

**physics/calculus**

h = -16t^2 + 12t + 600 a) sub in t=6 b) set -16t^2 + 12t + 600 = 0 divide by -4 4t^2 - 3t - 150 = 0 use the formula to find t = .... (use the positive answer only) c) v = -32t + 12 plug in your answer from b)

**math**

father's age ----- x Mark's age ---- x-32 x + x-32 = 72 easy to solve for x

**Maths**

first term is 3+2a common difference = d = 3+4a - (3+2a) = 2a term(5) = first term +4d = 3+2a + 4(2a) = 73 10a = 70 a = 7 check: d = 14 terms are: 17, 31, 45, 59, 73 all looks good

**Math**

sum of interior angles of a hexagon = 180(6-2) = 720 , from 180(n-2) 5x + 155 = 720 5x = 564 x = 113°

**Maths**

taking differences 1 2 1 5 3 2 11 6 3 1 21 10 4 1 the third differences are constant, so we could represent it as a cubic function. Lots of work, so I went to Wolfram: http://www.wolframalpha.com/input/?i=pattern+%7B1,2,5,11,21,....%7D

**Algebra**

1st term --- a 15th term = a + 14d = 9a 14d = 8a d = 4a/7 sum(35) = (35/2)(2a + 34d) = (35/2)(2a + 34(4a/7) = (35/2)(150a/7) = 375a

**Algebra**

a=10 a+(n-1)d = 62 10 + nd - d = 62 nd-d=52 n=(52+d)/d or d = 52/(n-1) sum(n) = (n/2)(2a + (n-1)d) = (n/2)(20 + (n-1)(52)/(n-1)) = (n/2)(20 + 52) = (n/2)(72) = 36n sum(n) = 36n so sum(n) varies directly as the number of terms

**Math**

33750 = 50*25*27 = 2*3*3*3*5*5*5*5 So the question becomes: in how many ways can these digits be arranged We have 8 digits , of which 4 are the same and another 3 are the same number of arrangements = 8!/(3!4!) = 280 e.g. 23535355 would be one of them

**Math**

please use t^2 to show exponents. the * symbol is traditionally used for a multiplication sign h = -16t^2 + 40t + 3 , note the - sign! dh/dt = -32t + 40 = 0 for a max of h 32t = 40 t = 40/32 = 1.25 seconds when t = 1.25 h = -16(1.25)^2 + 40(1.25) + 3= 28 when it hits the ...

**Algebra**

3b = a(B + b) 3b = aB + ab 3b - ab = aB (3b - ab)/a = B

**Math**

Did you use the quotient rule? y' = (x(2)(x+1) - (x+1)^2)/x^2 = (2x^2 + 2x - x^2 - 2x -1)/x^2 = (x^2 - 1)/x^2 set this equal to zero (x^2 - 1)/x^2 = 0 x^2 - 1 = 0 x^2 = 1 x = ± 1 if x = 1, y = 4 if x = -1 , y = 0 check: http://www.wolframalpha.com/input/?i=y%3D+(x%...

**Precalculus**

(f o g)(x) = f(g(x)) = f(x^2+3) = 3(x^2 + 3) - 1 (f o g)(7) = 3(49+3) - 1 = 155 (g o f)(x) = g(f(x)) = g(f(x)) = g(3x-1) = (3x-1)^2 + 3 (g o f)(7) = (20)^2 + 3 = 403 we could have done these without finding the general function. I will do the 2nd one that way, you do the 1st ...

**Precalculus**

(f o f)(x) = (x^2 + 18)^2 + 18 expand if needed.

**@ Rocky**

I had answered this question for you http://www.jiskha.com/display.cgi?id=1486418506 Look at all these unnecessary posts that you caused by not checking back to your previous post of this problem.

**algebra I**

where did the k come from in line 2 ? -4k+4k = 0 , so your k's disappear -38=-4k-8+4k-28 -38 = -36 which is a false statement, so there is no solution If your variable disappears and you have - a true statement, there will be an infinite number of solutions - a false ...

**Math**

First of all looking at your choices, only 1. and 2. are logical, the other two would show an increase not a decrease, so .... let the rate be r 560000 = 1000000 r^10 .56 = r^10 take 10th root of both sides using your calculator .56^(1/10) = r r = .94367.. so y = 560000(.94)^t...

**Calculus :**

if dV/ft = -4t - 2 V = -2t^2 - 2t + c if March 1 ---> t = 0 , and when t=0 , V = 5 5 = 0-0 + c V = -2t^2 - 2t + 5 so we want to know when V = 3 3 = -2t^2 - 2t + 5 2t^2 + 2t - 2 = 0 t^2 + t - 1 = 0 t = (-1 ± ?5)/2 = .618 or a negative Bad news, the pond is only safe ...

**Further maths**

a+7d = 18 a+11d = 26 subtract them: 4d = 8 d = 2 in a+7d = 18 2+7d = 18 carry on

**Further maths**

Your question does not make sense "The 8th term of a linear sequence is 18th" = gobbledegoop! In any arithmetic (linear) sequence, the terms either increase or decrease. A term can never repeat itself if you meant: The 8th term of a linear sequence is 18 , we can do ...

**Further maths**

Can't get any easier! a = 3 a+7d = 31 replace a with 3 and solve for d

**Geometry**

Having seen this problem many many times, consider a top view with O the centre of the silo then OB = 28+53 = 81 ft and OA = 28 ft we have a right-angled triangle, since a tangent meets its radius at 90° BA^2 + 28^2 = 81^2 BA^2 = 5777 BA=76.007 or appr 76 ft

**Algebra 2**

If you are doing more of these dice-rolling problems it might be a good idea to have a matrix for 2 dice showing rows and columns from 1 to 6, and sums as the entries of the matrix you will see that there are 18 even sums and 18 odd sums. For a sum of less than 8 we have: 1,6 ...

**Math**

P(A) = 1/6 P(not A) = 5/6 odds if favour of A = 1/6 : 5/6 = 1 : 5

**Maths**

let the 3 GP numbers be a , ar, and ar^2 a+ar+ar^2 = 39 a(1+r+r^2) = 39 a = 39/(1+r+r^2) ar - a = 6 a(r-1) = 6 a = 6/(r-1) then 39/(1+r+r^2) = 6/(r-1) 6 + 6r + 6r^2 = 39r - 39 6r^2 - 33r + 45 = 0 2r^2 - 11r + 15 = 0 (r - 3)(2r - 5) = 0 r = 3 or r = 5/2 if r = 3 , a = 6/2 = 3 ...

**Algebra**

y = a(x+1)^2 (x-6) , where a is any non-zero real number. More information such as a point on the function has to be given to find a.

**Algebra**

No wonder you could not find the pattern, since the pattern is not linear, that is, there is no common equal slope between any of the ordered pairs. All the choices represent linear functions, so there is no match. No pattern can be established from just those 4 points. Is ...

**geometry**

Not trigonometry involved here. It is elementary geometry, based on the definition of an isosceles triangle, and the fact that the angles in any triangle add up to 180°

**geometry**

I made my sketch so that angle B = angle C = 50° So the bisected angles are 25° each and angle BPC = 180 - 25 - 25 = 130°

**Mathematics**

scale is 31.5 km : 3 cm = 31.5(1000)(100)cm : 3 cm = 3,150,000 : 3 = 1,050,000 : 1

**ives**

sketch two perpendicular diameters and form your square. let the side of the square be x x^2 = 1^1 + 1^1 = 2 area of our square is x^2, so the area is 2 units^2

**maths**

125 yards = 125(36) inches = 4500 inches = 2.54(4500) cm = 11430 cm = 114.3 m so each roll is 114.3m by 1.4m = 60.02 m^2 since you have 25 of those rolls ..... (why would anybody measure a fabric roll with yards in length and cm in width ???)

**MAth**

total number ---- x 106/x = 11/227 11x = 240062 x = 2187.45.. there are appr 2187 fish in the lake

**algebra 2**

You titled it absolute value, so I will assume you are using "[" for absolute value. I read your question as 9|9-8x| = 2x+3 then 9(9-8x) = 2x+3 OR 9(9-8x) = -2x-3 case1: 9(9-8x) = 2x+2 <--- Steve did that one case2: 9(9-8x) = -2x-3 81 - 72x = -2x - 3 -70x = -84 x...

**Algebra (Answer Check)**

way too many steps.... -5 > -5 - 3w add 5+3w to both sides, addition does nothing to the inequality sign 3w > 0 divide by +3, no change in inequality sign needed w > 0

**math**

amount invested at 3% --- x amount invested at 4% --- 6000-x .03x + .04(6000-x) = 214 continue...

**Math**

multiply every term by 6, the LCM 4x + 6 = 3 <--- the "equivalent" equation asked for 4x = -3 x = -3/4

**math (precalc)**

ok then f(a) = (a-1)/(3a) f(a+h) = (a+h - 1)/(3(a+h)) (f(a+h)-f(a) )/h = ( (a+h - 1)/(3(a+h)) - (a-1)/(3a) )/h = ( a(a+h - 1) - (a+h)(a-1) )/(3a(a+h)) * 1/h = (a^2 + ah - a - a^2 + a - ah + h)/(3a(a+h)) * 1/h = h/(3a(a+h)) * 1/h = 1/(3a(a+h))

**math (precalc)**

f(x) = x - 1/3x ?? I think there are some missing brackets here, such as f(x) = (x-1)/(3x) or some variation of that or else why didn't they just say f(x) = 2/3x ? come back with the correction and I'll what I can do

**maths**

just replace n with 20 and go for it

**maths**

?(x+a)=b square both sides x+a = b^2 x = b^2 - a , a ? -x

**Math**

Notice that if you sketch a reasonably accurate hexagon, you have opposite sides that are parallel. So you can construct a rectangle down the centre. On either side you will have an isosceles triangle with base angles of 30° and equal sides of 15 By simple trig, you can ...

**Math**

Just did it, look below to your previous post

**Math**

number of fruits equation: m + l + c = 100 cost of fruits equation: m/20 + l + 5c = 100 subtract them m/20-m + 4c = 0 -19m/20 = -4c 19m = 80c but all my variables have to be whole numbers, so the first solution to 19m = 80c is m = 80, c = 19 put this back into the first ...

**Math**

With such a variety of questions, this looks like a test or an assignment. We don't do those for you. I will do one, which I think might give you trouble, the others you should be able to do by checking with your notes where you did similar problems 3) x^2 : 27 = 9 : x^3 x...

**Mathematics**

Number of people in each of the red cars --- x , x ? 4 leaves 12-2x for all other people in blue cars. if x = 1, blue cars contain 10 people sums with a total of 10 with different numbers, none > 4 , none the same : ----- can't find any if x = 2, blue cars contain 8 ...

**math**

One roll covers a rectangle of (70? by 1.12) m^2 = 78.4? m^2 we have 250 rotations, so the area = 250(78.4?) = 19600? m^2

**math**

Make a reasonable accurate diagram. Complete the parallelogram and draw in the resultant, you should be familiar with that. The obtuse angle of the parallelogram is 105° and the acute angle is 75° By the cosine law: |r|^2 = 6^2 + 15^2 - 2(6)(15)cos75° |r| = 14.6428...

**math**

width ---- x length ---- x+8 height = x/2 + 4 framing consists of 4 lengths, 4 widths, and 4 heights (make a sketch to see) 4x + 4(x+8) + 4(x/2 + 4) = 108 4x + 4x + 32 + 2x + 16 = 108 10x = 60 x = 6 continue ....

**Math - Factoring Trinomials**

If you had expanded your answer, you would have seen that it was wrong. How could you possible end up with those negative terms in the original when everything you have is positive ??? 2y^2-2y-24 = 2(y^2 - y - 12) what are two numbers that when multiplied yield -12 and have a ...

**Algebra 2**

given: a + ar + ar^2 = 26/3 a(1 + r + r^2) = 26/3 a = 26/(3((1 + r + r^2) ) a/(1-r) = 9 a = 9(1-r) 26/(3((1 + r + r^2) ) = 9(1-r) 27(1-r)(1+r+r^2) = 26 27(1 + r + r^2 - r - r^2 - r^3) = 26 27(1 - r^3) = 26 27 - 27r^3 = 26 27r^3 = 1 3r = 1 r = 1/3 , well that went better than ...

**Calculus**

Take the first derivative, set it equal to zero, and solve for x That is your x

**Calculus**

Proofread you question before posting it. Not familiar with the different modes of transportation of functions if you meant commute.

**Calculus**

Show me that you know the formula. Show me that you can do the substitution and we can go from there

**Algebra2**

Did you sub in the value of 30 to see if you are correct? Following the order of operations, I get: left side = 243(?32)^3 + 3 = appr 43990.7 , certainly ? 27 3^5sqrt(x+2)^3+3=27 3^5sqrt(x+2)^3 = 24 243?(x+2)^3 = 24 ?(x+2)^3 = 8/81 (x+2)^(3/2) = 8/81 x+2 = (8/81)^(2/3) = appr...

**Math**

let the number of weeks be w so 2^(w/5) = 3 solve for w, I suggest logarithms. Let me know what you get.

**math**

This looks just like a good-ol' fashioned arithmetic sequence with a = 14 and d = x use your formula for term(11)

**Pre Cal**

I = 1 (.96)^m .20 = .96^m using logs m = log .2/log .96 = appr 39.4 it would take about 39.4 m

**Calculus**

1200(1.06)^(t/8) = 2000 1.06^(t/8) = 1.6666... take logs of both sides, and use log rules .... t/8 = log 1.6666../log 1.06 = 8.7667 t = appr 70.13 years

**Algebra**

To be divisible by 8, the last 2 digits must be divisible by 8, to be divisible by 9, the sum of the digits must be divisible by 9 so far they add up to 6, so let's add: 3 ---> no good for the 8 part 12 ---> no good for the 8 part 21 ---> no good for the 8 part 30...

**math**

1/a - 1/b = 2/13 (b-a)/(ab) = 2/13 13b - 13a = 2ab 13b - 2ab = 13a b(13 - 2a) = 13a b = 13a/(13-2a) suppose we let a = 6 then b = 13(6)/(13-12) = 78 the fractions could be 1/6 and 1/78 check: 1/6 - 1/78 = 2/13 suppose we let a = 4/5 then b = 13(4/5) / (13 - 8/5) = 52/57 the ...

**maths**

If I understand it correctly, we have a triangle with sides 150 and 120 with an angle of 135° between them. Clear case of the cosine law. x^2 = 120^2 + 150^2 - 2(120)(150)cos135° = ... tell me you got 249.7 km

**math**

After t more hours: Micah has walked 2 + 4t miles Luke ran 6t miles 6t = 4t + 2 2t=2 t = 1 So after one hour, they will have gone the same distance, each one has gone 6 miles.

**math**

a+16d = 9(a + a+d + a+2d) a+16d = 27a + 27d -11d = 26a a+8d = 3a - 6 8d+6 = 2a or a = 4d+3 <----- sub that into the first equation -11d = 26(4d+3) -11d = 104d + 78 -115d = 78 d = -78/115 a = 4(-78/115) + 3 = 33/115 the first 3 terms are : 33/115 , -9/23, -123/115 check: the...

**check my work..math grade 8...surface area**

SA for men's = 4?(12.15)^2 SA for women's = 4?(11.7)^2 ratio of men's to women's = 4?(12.15)^2 : 4?(11.7)^2 = (12.15)^2 : (11.7)^2 = 147.6225 : 136.89 = 1.078402... : 1 = appr 1.08 : 1 notice that (12.15/11.7)^2= 1.078...

**math**

It will take 20 teacher-hours to do the job So for 3 teachers, it will take 20/3 hours to do the job of marking the 60 papers 20/3 hrs = 6 2/3 hrs or 6 hours and 40 minutes

**Statistics Math**

Just use your definition of P(A|B) P(A|B) = P(A and B)/P(B) = (.2)(.3)/.3 = .2

**Math**

Since the slope of the given line is 1/3, the slope of the new line must be -3 new line: y-3 = -3(x+4) (since the old equation was given in that form, I will leave the new one in that same form)

**Math**

Well, why not just sketch a grid and do what each of the rats do ? I am sure you can follow the steps just as well as any of us. I suggest you make the origin your starting point. It easy to see that Riley ends up at (7,3) with the cake at (7,4) Do the same for the other rat

**Math**

The highest power term determines the rank of the function Since both f(x) and g(x) have x^2 as their highest power, that is, they both have 2 as the highest exponent, they are of the same order.

**calculus**

your function for the height is h = -16t^2 + 32t + 48 find the vertex of this quadratic function using whatever method you have learned. Since you titled your post "Calculus", find the derivative, set it equal to zero and solve for t. Finally, plug that t value back ...

**Math**

12:00 --- full 11:59 --- half-full <------ 11:58 --- 1/4 full

**math**

To mean " 29p for each" , they should have said so. I read it as 29p for the 3 oranges, the same for the drinks so, the total spent is 119p

**MATH**

"THE SUM OF THEIR AGES WILL BE ???" missing data

**math**

amount of white rice ---- x pounds amount of wild rice ------4-x pounds (no need for 2 variables) .75x + 2.25(4-x) = 1.8(4) .75x + 9 - 2.25x = 7.2 -1.5x = -1.8 x = 1.2 so we have 1.2 pounds of white rice and 2.8 pounds of wild rice check: 1.2(.75) + 2.8(2.25) = 7.2 4(1.8) = 7....

**Math**

Isn't that the same as being given the two points (0, -1) and (4,0) ?? You MUST know how to find the equation if you are given two points, or else you are in deep trouble with this topic.

**calculus**

I don't have "Excel Solver"

**math**

we know that tan 0 = 0 so x/3 = 0 x = 0 but we also know that more solutions can be obtained by adding the period of tan(x/3) to any answer. tan x/3 = tan ( (1/3)x ) 180/(1/3) = 540 so solutions are : 0°, ± 540°, ± 1080°, ... or simply 540k°, ...

**algebra**

I assume the first is plumber A Cost = 60t , where t is the number of hours plumber B: cost = 55t + 40 when are the costs the same? When 60t = 55t+40 solve and you got the value of t plug it back into one of the equations to get the cost (no system of equations needed here)