Sunday
February 26, 2017

Posts by Reiny

Total # Posts: 37,803

Algebra
x=3, so Alysia is 3 and Adam is 33 3+33 = 36
February 10, 2017

Algebra
Ms. Sue meant to say: x + 30+x = 36
February 10, 2017

Algebra 1
Yes, except since this is money in dollars you would round it to the nearest cent. $500,637.91
February 10, 2017

Algebra 1
What is 20000(1.05)^66 ?
February 10, 2017

Math
rate of first ---- x rate of 2nd ---- y 1500(3)x - 1500(3)y = 13.50 x-y = .003 the difference is .3%
February 10, 2017

polynomial
I don't understand how looking at the graph of y=2x³+x²+x+8 , which does not have a "nice" rational solution, will help you in solving y = 2x^3 + x^2 - x + 5. The latter also has an irrational solution. http://www.wolframalpha.com/input/?i=y%3D2x%C2%B3%...
February 10, 2017

Maths
you are solving, 6750(1.05)^t = 8000 1.05^t = 1.185185.. take log of both sides, and use log rules t = log 1.185185.../log 1.05 = 3.482239 so that is 3 years and .482239 years multiply the decimal part by 12 to get 3 years, 5.7868.. months so 3 years, 5 months and .7868 months...
February 10, 2017

maths
graphing utility?? why? 6sinx + 3cosx = 0 divide by cosx 6sinx/cosx + 3 = 0 6tanx = -3 tanx = -1/2 we know that the tangent is negative in II or IV and we know tan (.4636) = +.5 x = ?-.4636 = appr 2.678 or x = 2? - .4636 = appr 5.820 If you insist: http://www.wolframalpha.com/...
February 9, 2017

Math
12.5 litres takes the car 168.75 km then 1 L takes the car 168.75/12.5 km then 15 L will take the car .....
February 9, 2017

Math
Why do you think this question might deal with the concept of a Lowest Common Multiple ?
February 9, 2017

Math
How many square cm are there in 1 square metre? - then how many in 1/2 square metre ?
February 9, 2017

Math
simplify and re-arrange ... y-5 = (2/7)(x-11)
February 9, 2017

Math
of course it isn't right x = 3 would be a vertical line. A quick sketch will show you that your 2 points do not lie along a vertical line slope = m = (-8-8)/(5-3) = -16/2 = -8 equation: y-8 = -8(x-3) re-arrange to whatever form you learned.
February 9, 2017

Slopes
slope = m = (7-4)/(-5-0) = ... once you find m, replace it in the equation y-4 = m(x+6) arrange into the form that you are familiar with.
February 9, 2017

Algebra II
Don't understand your question. Don't understand your answer.
February 9, 2017

Math
p5^y + 5^-y = 5 p5^y + 1/5^y = 5 now replace px + 1/x = 5 times x px^2 + 1 = 5x px^2 - 5x + 1 = 0 which is what we want
February 9, 2017

calculus
V= (4/3)? r^3 dV/dt = 4? r^2 dr/dt when V = 64 64 = (4/3)? r^3 48/? = r^3 r = (48/?)^(1/3) = appr 2.4814 ---> I stored the 10 decimal answer in dV/dt = 4? r^2 dr/dt 20 = 4?(2.4814..)^2 dr/dt dr/dt = appr .2585 inches/min
February 9, 2017

Math
You must know the binomial expansion and the general term of the expansion!! 5th term = C(9,4) (4^4)(-x/5)^5 = 126 (256)(-x^5)/3125 = -32256/3125 x^5 oops, just did in descending powers, so C(9,5) 4^5 (-x/5)^4 = 126(1024)(x^4/625) = 129024/625 x^4 , in ascending order
February 9, 2017

Maths
distance at original speed = (1/4)(60 km = 15 km time at reduced speed = 15/36 hours = 5/12 hr = 25 minutes
February 9, 2017

Geometry
clearly the largest circle will have a diameter of 4 ft, or a radius of 2 ft area = ?(2^2) = 4? ft^2 = ...... In this time of calculators, using 3.14 for ? and then rounding off that rounded constant is rather silly. Most calculators have a special key for ?, use it.
February 9, 2017

Maths
correct your spelling and incomprehensible gibberish
February 9, 2017

Math
Yes, could have been easily checked by taking 20% of it.
February 9, 2017

Math
regular price ---- x it said the 20% discount came to $15 well, .2x = 15 x = 15/.2 = ......
February 9, 2017

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
February 9, 2017

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...
February 9, 2017

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...
February 9, 2017

algebra
Compare this question to your previous one. What is your answer ?
February 8, 2017

algebra
The product of 5 and 6 = 30 the product of 7 and 8 = 56 the product of 31 and g = 31g
February 8, 2017

Math
Your post makes absolutely no sense to me.
February 8, 2017

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 ...
February 8, 2017

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)
February 8, 2017

Math
(w^-2 j^-4) ^-3 (f^7 f^3) = (w^6)(j^12)(f^10)
February 8, 2017

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
February 8, 2017

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...
February 8, 2017

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
February 8, 2017

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
February 8, 2017

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
February 8, 2017

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...
February 8, 2017

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...
February 8, 2017

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...
February 8, 2017

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
February 8, 2017

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...
February 8, 2017

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
February 8, 2017

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
February 8, 2017

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)
February 7, 2017

math
father's age ----- x Mark's age ---- x-32 x + x-32 = 72 easy to solve for x
February 7, 2017

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
February 7, 2017

Math
sum of interior angles of a hexagon = 180(6-2) = 720 , from 180(n-2) 5x + 155 = 720 5x = 564 x = 113°
February 7, 2017

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
February 7, 2017

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
February 7, 2017

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
February 7, 2017

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
February 7, 2017

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 ...
February 7, 2017

Algebra
3b = a(B + b) 3b = aB + ab 3b - ab = aB (3b - ab)/a = B
February 6, 2017

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%...
February 6, 2017

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 ...
February 6, 2017

Precalculus
(f o f)(x) = (x^2 + 18)^2 + 18 expand if needed.
February 6, 2017

@ 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.
February 6, 2017

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 ...
February 6, 2017

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...
February 6, 2017

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 ...
February 6, 2017

Further maths
a+7d = 18 a+11d = 26 subtract them: 4d = 8 d = 2 in a+7d = 18 2+7d = 18 carry on
February 6, 2017

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 ...
February 6, 2017

Further maths
Can't get any easier! a = 3 a+7d = 31 replace a with 3 and solve for d
February 6, 2017

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
February 6, 2017

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 ...
February 6, 2017

Math
P(A) = 1/6 P(not A) = 5/6 odds if favour of A = 1/6 : 5/6 = 1 : 5
February 6, 2017

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 ...
February 6, 2017

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.
February 6, 2017

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 ...
February 6, 2017

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°
February 6, 2017

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°
February 6, 2017

Mathematics
scale is 31.5 km : 3 cm = 31.5(1000)(100)cm : 3 cm = 3,150,000 : 3 = 1,050,000 : 1
February 6, 2017

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
February 6, 2017

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 ???)
February 6, 2017

MAth
total number ---- x 106/x = 11/227 11x = 240062 x = 2187.45.. there are appr 2187 fish in the lake
February 6, 2017

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...
February 6, 2017

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
February 5, 2017

math
amount invested at 3% --- x amount invested at 4% --- 6000-x .03x + .04(6000-x) = 214 continue...
February 5, 2017

Math
multiply every term by 6, the LCM 4x + 6 = 3 <--- the "equivalent" equation asked for 4x = -3 x = -3/4
February 5, 2017

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))
February 5, 2017

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
February 5, 2017

maths
just replace n with 20 and go for it
February 5, 2017

maths
?(x+a)=b square both sides x+a = b^2 x = b^2 - a , a ? -x
February 5, 2017

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 ...
February 5, 2017

Math
Just did it, look below to your previous post
February 5, 2017

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 ...
February 5, 2017

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...
February 5, 2017

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 ...
February 5, 2017

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
February 5, 2017

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...
February 5, 2017

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 ....
February 4, 2017

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 ...
February 4, 2017

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 ...
February 4, 2017

Calculus
Take the first derivative, set it equal to zero, and solve for x That is your x
February 3, 2017

Calculus
Proofread you question before posting it. Not familiar with the different modes of transportation of functions if you meant commute.
February 3, 2017

Calculus
Show me that you know the formula. Show me that you can do the substitution and we can go from there
February 3, 2017

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...
February 3, 2017

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.
February 3, 2017

math
This looks just like a good-ol' fashioned arithmetic sequence with a = 14 and d = x use your formula for term(11)
February 3, 2017

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