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Posts by Reiny

Total # Posts: 38,653

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)

input output math
input 4 and output 25 ---> , x=4, y=25 input 5 and output 32 ---> , x=5, y=32 hard to tell with such little data : one could be y = 7x - 3 , if your relation is linear

Trigonometry
For any given angle, there are 6 trig ratios. They gave you one of them. sin Ø = -3/5 --- (you have a typo there) you should know that sinØ = y/r, and r is always positive. so you have y = -3, r = 5 by Pythagoras, x^2 + y^2 = r^2 x^2 + 9 = 25 x^2 = 16 x = ±...

algebra
since (1/2)bh = 40 bh = 80 b = 80/h cm

Math
Hope you got (-3, 1/2)

Math
Here is a thought: list the dates he does push-ups, 3 6 9 12 ... list the dates he does sit-ups, 4 8 12 ... well guess what? Here is another thought: What is the LCM of 3 and 4 ? On which days in January will this happen again?

algebra
Katy' weight --- x David ------ x+20 Jonathan --- 3x - 120 3x-120 = x+20 2x = 140 x = 70 sub back into my definitions for their weights Tell me how you got 42 ??

Math
surface area = base + 4 sides = 40(25) + 2(40)(6) + 2(25)(6) m^2 = ..... Once you have the total surface area, multiply that by your cost of 135 per square metre.

Math
So basically all we need is the area of the triangle plus the area of the circle. area = (1/2)(10)(8) + ?(4)^2 = 40 + 16? = ...... you do the arithmetic

Maths
first of the numbers ---- x the next odd number ---- x+2 x(x+2) = 195 x^2 + 2x - 195 = 0 (x+15)(x-13) = 0 carry on

Algebra
Assuming that your "new math" follows the traditional order of operation, just do it. a ? b = 2a ? 3b then: (1 ? 2) ? 7 = (2 - 6) ? 7 = -4 ? 7 = -8 - 21 = -29

Maths
let the sides be 3x, 4x, and 5x solve for x and sub into my definitions 3x+4x+5x = 12 you should be able to do it in your head. Did you notice that your triangle is also right-angled?

Math
Just make the changes to my solution I gave you before you found the typo http://www.jiskha.com/display.cgi?id=1485954263

Maths
length of base = 50-10 = 40 cm width of box = 40-10 = 30 cm height of box = 5 cm volume = length x width x height = ...... cm^3

Kevin ? - Math
The first part I already answered in your previous post. If the gradiant is 34, the diameter is quite steep. Lets find its equation: y = 34x + b but (1,2) lies on it, so 2 = 34(1) + b b = -32 y = 34b - 32 the equation of the circle I described in the earlier post is (x-1)^2...

math
nope .... amount = 500 (1.25)^m , where is the number of minutes (an increase of 25% results in what you started with plus the increase or 1 + .25 = 1.25 e.g. suppose an article costs $100 a 25% increase would be $25 so the cost is $125 that is: 100(1.25) = 125 )

Math
The line AB would be the horizontal diameter of a circle with centre (1,2) and radius 5 So just go 5 units to the left and to the right of (1,2) A could be (-4,2) and B could be (6,2) or B(-4,2) and A(6,2) notice AB = ?(6+4)^2 + 0^2) = 10

Math
what is (26.5+31)/2 ?

Math
Follow the same steps I just showed you here http://www.jiskha.com/display.cgi?id=1485922261

Math
Follow the same steps as I just showed you when you were Bobby

Math
f'(x) = lim (f(x+h)?f(x))/h , as h ---> 0 =lim (4hx?1h+5h^2)/h , as h ---> 0 = Lim (4x - 1 + 5h) , as h ---> 0 = 4x - 1

Math
4 inches ---> 6 ft 1 inch -----> 6/4 ft or 1.5 ft

maths
"4th term is 7" ---> a+3d = 7 "7th term is 13" ---> a+6d = 13 subtract them: 3d = 6 d = 2 sub back into my first equation to find a, then use the Sum of Terms formula to find sum(20)

math
The previous one is (2n-2) the next one after 2n is (2n+2

Math
8 bananas at 50 g each is 400 g what is 400/1000 times $6.50 ?

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