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Posts by Reiny

Total # Posts: 38,634

Math
number of children --- 3x number of adults ----- 2x , notice 3x : 2x = 3:2 3x+2x = 500 x = 100 so we would have 300 children and 200 adults price of adult ticket ---- x 300(2) + 200x = 1600 solve for x

math
#1 checking for the given roots P(1) = 1 - 8 + 23 - 28 + 12 = 0 yup, x-1 is a factor P(2) = 16 - 64 + 92 - 56 + 12 = 0 yup, x-2 is a factor now divided x^4-8x^3+23x^2-28x+12 by (x-1) to get a cubic, then divide that cubic by (x-2), leaving you with a quadratic expression set ...

math
A:B:C = 1:2:3 = 12x : 24x : 36x for A: acid:water = 1:5 = (1/6)12x : (5/6)12x = 2x : 10x for B: acid:water = 3:5 = (3/8)24x : (5/8)24x = 9x : 15x for C: acid:water = 5:7 = (5/12)36x : (7/12)36x = 15x : 21x now pouring this into one container in 1:2:3 from A we are getting 2x ...

math
we don't know the rate, let it be r A will get only 1/2 years interest = (1/2)(r)(5000) = 2500r B will get a full year on his 10,000 = 10000r C will get 7500r + (1/2)(r)(5000) = 10000r 2500r + 10000r + 10000r = 9000 22500r = 9000 r = .4 so C will get 10,000(.4) = 4000 40% ...

Algebra2
The primary solutions are .71 and ?-.71 or .71 and 2.43 so I would state it as .71 + 2?n and 2.43 + 2?n , which is a variation of B so you are correct, but I find their choice puzzling (notice -3.85 + 2? = 2.43)

8th gr algebra
your first card could be 52 different ones, leaving 51 different ones to draw for you second, then 50 for the third and 49 for the fourth, and finally 48 for the last. so what is 52(51)(50)(49)(48) = ...

Algebra II
for the y-intercept, let x = 0 f(0) = e^(0-0+20) - 1 = e^20 - 1 that is really big, appr 485,165,194 for the x-intercept, let y = 0 e^(x^2-9x+20)-1 = 0 e^(x^2-9x+20) = 1 e^(x^2-9x+20) = e^0 so x^2 - 9x + 20 = 0 (x-5)(x-4) = 0 x = 5 or x = 4

Math
I agree with Scott time for first leg = d/10 time for return leg = d/8 total time = d/10 + d/8 = 9d/40 avg rate = total distance/total time = 2d/(9d/40) = 2d(40/9d) = 80/9 mph distance = (27/60)(80/9) = 4 miles So she ran 4 miles in total. check: 2 miles at 10 mph = 2/10 hrs 2...

math help pleaseee
If x=-4 is one of the solutions, then x+4 must be a factor of x^3 - 28x - 48 so do a long division. You must get a quadratic with no remainder. solve that quadratic = 0 to get the other two zeros. hint: the remaining quadratic factors to give 2 more integer solutions.

math
I will do a) you do b) in the same way f(g(x)) = f(x/2 + 4) = 2(x/2 + 4) - 8 = x , mmhhhh - interesting!

Algebra 1
y = .4x + 7 creates ordered pairs of the type (x,y) so at the y-intercept, it would be (0,7) and what does (0,7) stand for ? or since x is the number of days since it was cut, what would be x right after you cut the grass??

Math
a = ln2 ---> 2 = e^a b = ln11 ---> 11 = e^b ln(3?22) = ln3 + (1/2)ln22 = ln3 + (1/2)(ln11 + ln2) = ln3 + (b+a)/2 are you sure you typed it correctly? I suspect we were asked for ln (2?22)

MATH
You could just leave it like that, or x^2 y + y^3 = 3x or y(x^2 + y^2) = 3x just curious. Did they actually have tanx in the polar form and then asked for the cartesian form? I would have expected something like r^2 = 3/tanØ If it actually was r^2 = 3/tanx then it would...

Algebra 2 help please.
arc length = rØ, where r is the radius and Ø is the central angle in radians. 255° = (255/180)? radians = 17?/12 17?/12 r = 52 r = 52(12)/(17?) = 624/(17?) m = 11.6838... m using my calculator value of ? or even more simple: 2?r/360 = 52/255 2?r = (52/255)(...

Algebra 2 help please.
if f(t)=2150?(1.04)t then the 2150 is the value of f(t) when t = 0 that is, 2150 is the initial value you can tell your answer is incorrect by subbing in t = 2 f(2) = 2150(1.04)^2 = appr 2325 ? 2150

Maths
Steve did this same question here: http://www.jiskha.com/display.cgi?id=1493739139

Maths
Ms Sue wins the reply of the day reward.

Calculus I
Steve got the same answer in 2 different ways. I must have made an error in my arithmetic, too lazy to find it

Calculus I
let the position on the x-axis be (x,0) and the position on the y-axis by (0,y) the article is moving to the right on the x-axis at 2 units/s ---> dx/dt = 2 the article is moving DOWN the y-axis at 3 units/s ---- dy/dt = -3 according to my diagram, at any moment of t ...

Maths
Finally, even after you changed your name 3 times first subtract them: -2x -4y + 4=0 x + 2y + 2 =0 x = -2-2y sub into the first: (-2-2y)^2 + y^2 - 10(-2-2y) - 8y +18=0 4 + 8y + 4y^2 + y^2 + 20 + 20y - 8y + 18 = 0 5y^2 + 20y + 38=0 y = (-20 + ?-360)/10 , which is not a real ...

MATH
number of kid's tickets --- x number of adults ------- 2x 10x + 25(2x) = 1800 solve for x, sub into my definitions

precalculus
we know the amplitude, we know the vertical shift but we don't know the frequency. Not enough information to write a specific equation.

Maths
Sounds like a repeat of this without correcting the error. http://www.jiskha.com/display.cgi?id=1493740391

MMATH08
If you call it an angle bisector, then it will bisect.

maths
check your typing, the second circle contains two y terms and no constant. Is that correct ?

Math geometry
#1. I agree with your first answer of .3535 #2. at least 1 of the 4 marbles drawn is white ---> what you don't want is all non-white. prob(none are white) = (9/12)(8/11)(7/10)(6/9) = 14/55 prob(at least one white) = 1 - 14/55 = 41/55 = .7455 correct to 4 decimals I have...

Math
why would your text write 2 2/4 instead of 2 1/2 ? divide 2 1/2 by 1/4 get rid of those useless mixed fractions .... 5/2 ÷ 1/4 = (5/2)(4/1) = ... or in decimals: 2.5 ÷ (.25) = ...

Math
Got me stumped too, since I don't know what you are talking about. Not familiar with a unit called idk

7th grade math
total surface area would be 2 squares + 4 rectangles = 12x12 + 4(4x12) m^2 = .... Why would you ice the bottom of the cake ?

math power series(please helpassessment tomorrow)
for e^1 sum(1) = 1 sum(2) = 1 + 1 = 2 sum(3) = 2 + 1/2! = 1/2 = 2.5 sum(4) = 2.5 + 1/3! = 2.5 + 1/6 = 8/3 = 2.666.. sum(5) = 8/3 + 1/4! = 8/3 + 1/24 = 65/24 = 2.70833.. sum(6) = 65/24+1/5! = 65/24+1/120 = 163/60=2.71666.. sum(7) = 163/60+1/6! =163/60+1/720 =1951/720=2.7180555...

Algebra2
in y = a cos (kØ) a is the amplitude, and the period is 2?/k so evaluate the period and state the amplitude of your equation.

Algebra2
correct if your domain for the intersection is 0? Ø ? 2? you should also include ?, 4?/3, 5?/3, and 2?

Math
I must have been thinking about those new type of hexagons that have five sides, duhhh!!

Math
So you need the perimeter. What is 5(52) cm? How many metres is that? (the beauty of the metric system shows up here) multiply number of metres by $4.10

Algebra Help please
same question from Bobby/Jules/Alice

Algebra Help ASAP Please
answered when you were Jules

math
to be divisible by both 2 and 3, it must be divisible by 6 So the first number past 40 divisible by 6 is 42. Now just add multiples of 6 to 42 that is: 42, 48, 54, ...

STATISTICS
each toss is an independent event, so Prob(99 consecutive heads) = (1/2)^99 or appr 1.5777 x 10^-30 rather slim, I would say

Math
Make a sketch and you will see that you can use Pythagoras x^2 + 1.5^2 = 6^2 carry on

Maths
Tanya ---- x Tshepo ---- 2x+5 jake = 3(2x+5) solve: 3(2x+5) = 45 then sub the value of x into my definitions. What did you get?

discrete math
a) amount at end of 1st year = 8000 + 1600 - 2500 = 7100 amount at end of 2nd year = 7100+1420-2500=6020 amount at end of 3rd year = 6020+1240-2500=4724 amount at end of 4th year = 4724+944.8-2500=3168.80 amount at end of 5th year = 3168.8 +633.76-2500= 1302.56 , which is less...

Math
original number: let the unit digit be x then the tens digit is x+1 since the sum of all 3 digits is 14 the hundreds digit must be 14 - x - (x+1) = 13 - 2x now the actual number, using place holder value, is 100(13-2x) + 10(x+1) + x = 1300 - 200x + 10x + 10 + x = -189x + 1310 ...

math
close, 2 errors! 5% = .05, not .5 why do you set the total to 1200, didn't it say 860 ? make the change, now solve that equation.

math
makes no sense, I think you just wrote something down because I asked you for an equation. you have 3 variables in your first equation, so you will need 3 different equations to solve if a, b, and c are you different investments, then a+b+c = 860 , not 1000. Where did it say ...

math
What is your equation ?

Math
no, you are just writing stuff down. based on what it said: number of nickels --- x number of dimes---- 2x+1 number of quarters = 25-(x + 2x+1) = 24 - 3x now form a "value" equation: 5x + 10(2x+1) + 25(24-3x) = 410

Math
Ok, your turn. For the first two, I have given you the equation What have you done for these last two? Show me your preliminary steps.

Math
solve 7500+15x = 10000 + 12.5x

Math
let amount invested at 7% be x solve .07x + .1(x-2000) = 820

Elementary Statistics
10 different horses could come in first, that leaves 9 to come in second, and 8 to come in third, so what is 10x9x8 ??

advanced functions
Again, watch those needed brackets, assuming you meant: 4/(2x-3) < 1/(x+4) I see critical values at x = 3/2 and x = -4 try a value x between -4 and 3/2, say x = 0 is 4/(0-3) < 1/(0+4) is -4/3 < 1/4, YES, so -4 < x < 3/2 try a value x < -4 , say x = -5 is 4/(-...

Advanced functions
Assuming you meant: f(x)= -1/(x^2-7x+6) = -1/((x-6)(x-1)) vertical asymptotes are caused by the denominator being zero, so x-6 = 0 ----> x = 6 or x-1 = 0 ---> x = 1

Calc
r = 5cscØ r = 5/sinØ we know that y/r = sinØ or r = y/sinØ then y/sinØ = 5/sinØ y = 5 , a horizontal line check: http://www.wolframalpha.com/input/?i=polar+plot+r%3D5cscx

Advanced Functions grade 12
More information is needed, such as a point which satisfies the function equation.

Advanced Functions
if (x-4)(x+2)<=0 then x ? -2 and x ? 4 or -2 ? x ? 4

Grade 12 Advanced Functions
bob's equation should have been l^3 - 5l^2 - 500 = 0 (l-10)(l^2 - 5l + 50) = 0 l = 10 , since the quadratic has complex roots the box is 10 by 10 by 5

math
sin130° = sin 50° tan60° = ?3 cos540° = cos180 = -1 tan230° = tan50 sin400= sin40 sin130.tan60 ÷cos540.tan230.sin400 = (sin50°)(?3)/(-1) (tan50)(sin40) = -?3sin50 (sin50/cos50)(sin40) = -?3 sin40° sin^2 50° / cos50° I see nothing ...

Math
I don't understand the question. Is the 1232 km distance measured along a "great circle" of the earth, thus the arc length ? if so, then just use a simple ratio. Circumference of earth = 40075 km Ø/360 = 1232/40075 Ø = appr 11.1°

math
A regular hexagon can be divided into 6 equal equilateral triangles. So each one has an area of 64?3 let's look at one of those. Area of a triangle = (1/2)absinØ, where a and b are sides with Ø as their contained angle. If each side is x, then (1/2)x^2 sin60&...

math
Of the 40 marbles you have, 30 of them are blue, so Prob(blue) = 30/40 = 3/4 or .75

Math fp1
clearly the roots of the given equation must be complex numbers, thus they must be conjugates of each other let w = a+bi then w* is a - bi sum of roots = a+bi + a-bi = 2a product or roots = (a+bi)(a-bi) = a^2 + b^2 but from the given equation: sum of roots = -4-i-qi product of...

math
time for first leg = 24/18 hrs resting = 1/2 hour last leg = 6/20 hrs add up the three times

Physics
h = -16t^2 + 32t + 300 , from your data v = dh/dt = -32t + 32 so when t = 1 v = -32 + 32 = 0

math
L = km/h when L = 40, m=175, h = 286 , (skipping the units) 40 = k(175)/286 k = 286(40)/175 = 2288/35 L = (2288/35)m/h , plug in h=50 and m=250

Precalculus
check for intersection x^2 - 5x + 3 = -x^2 + 5x - 5 2x^2 - 10x + 8 = 0 x^2 - 5x + 4 = 0 (x-1)(x-4) = 0 x = 1 or x = 4 but we need the area for 0 ? x ? 4 , so we have two sections, because there is a cross-over at x = 1 Area = ?(x^2 ? 5x + 3 + x^2 - 5x + 5)dx from 0 to 1 + ?(-x...

Math
let the numerator be x then the denominator is x+7 3 is added to the numerator, so the new numerator is ...... 1 is subtracted from x+7 , so the new denominator is ...... the new fraction is ???/???? ???/???? = 4/5 solve for x show me your steps, so I can check it

Precalculus -- Systems of Equations
or, the distance from (0,0) to x-2y - 8 = 0 is |0 - 0 - 8|/?(2^2 + 1^2) = 8/?5 so yes, r = 8/?5

Math
missing information: number of purple marbles

Geometry
You should of course know that the sum of the 3 angles is 180° how about angle Y = x then angle X = (5/8)x and angle Z = (1/4)x so 5x/8 + x/4 + x = 180 I suggest you multiply each term by 8, the LCD and it is a piece of cake after that.

math
originally there were 25 odds and 25 evens, the 5 numbers already drawn are all odd, so there remains: 25 evens and only 20 odds so for the next draw: prob(odd) = 20/45 prob(even) = 25/45 so what do you think?

math
1. So, don't you just need two equal widths for your rectangle ??? x + x + 9 = 25 Can't get any easier. 4. I can't follow your description. My rectangle has two width of 12 ft, and some length x x + 12 + 12 = 44 x = 20 , so it overlaps the existing 12 ft fence.

Math
#1, I would include the spinner part as well. Since the spinner has no memory , whatever happened on the first spin, has no effect on the second #2 correct

co-ordinate geometry need help steve reiny
There are several ways to do this: 1. There is an actual formula to do this, Google "distance from a point to a line" and study it 2. rigorous method. There is a great video form the KhanAcademy webpage that explains in great detail . Your line is y = 2x , (easier ...

co-ordinate geometry need help steve reiny
Your wording is incorrect. Did you mean : find the distance from the point to the given line?

Math
Looks like they want you to cut the circle into "many" equal isosceles triangles, finding the base of one of them , then multiplying by the number of such triangles e.g. in your case , visualize 360 isosceles triangles each with equal sides of 5 and a vertex angle of...

algebra
length ---- x width = 2x/3 x - 2x/3 = 7 once you have the width and length, perimeter = 2widths + 2lengths

Math
Depends what information you are given. I would prefer if you didn't concentrate on a "formula" but rather analyze the problem. Here is a nice short video where they find the slant height as part of another problem. https://www.youtube.com/watch?v=r5EQCSW_rLQ

Math
Of course being a day late with your joke makes it fall flat. Yesterday, 26 April 2017 could have been written as "today"

Math
let Dad start with x belt: x/2 + 50 amount left = x - (x/2 + 50) = x/2 - 50 sandals: (1/2)(x/2 - 50) + 30 = x/4 + 5 amount left = x/2 - 50 - (x/4 + 5) = x/4 - 55 T-shirt: (1/5)(x/4 - 55) + 20 = x/20 + 9 x/4 - 55 - (x/20 + 9) = 15 x/4 - 55 - x/20 - 9 = 15 x/5 = 79 x = 395 pesos

Math
How is it compounded? monthly? , quarterly? daily?, continuously ? ????

math
cotØ = 11/12 tanØ = 12/11 r^2 = 11^2 + 12^2 = 265 r = ?265 since tanØ is positive, Ø would be in I or III in I, tanØ = 12/11 , sinØ = 12/?265 in III tanØ = 12/11, sinØ = -12/?265

Math-Please Help
nope, show your steps so I can see where you went wrong.

Mathematics
I always taught that 0/0 was indeterminate and did not fall into the "undefined" category. Such as in limits that result in 0/0 situations, e.g. lim (x^2 - 4)/(x-2) , as x ---> 2 you would get 0/0 = lim (x-2)(x+2)/(x-2) as x ---> 2 = limi x+2 , as x --->2 = ...

Mathematics
here is another explanation: if multiplication is repeated addition, e.g. 3x4 = 3+3+3+3 = 12 and division is repeated subtraction: e.g. 20 ÷ 4 20-4 = 16 16-4 = 12 12-4 = 8 8-4 = 4 4-4 = 0 I subtracted the 4 five times to get to zero so 20÷4 = 5 so how about 20 &...

Mathematics
Look at these cases: 12/3 = 4 because 3x4 = 12 20/10 = 2 because 2x10 = 20 5/0 = ?? because ?? x 0 = 5 , but that is a contradiction, since anything times zero is zero. or 5/.1 = 50 5/.01 = 500 5/.001 = 5000 5/.000000000001 = 5000000000000 notice I am dividing by a smaller and...

science
let the distance be x km time for first bus = x/54 time for 2nd bus = x/36 total time = x/54 + x/36 = 5x/108 total distance = 2x avg speed = total distance / total time = 2x / (5x/108) km/h = 108/5 km/h = 21.6 km/h

Maths
number of fivers --- x number of twos ---- 3x 5x + 2(3x) = 77 solve for x and state conclusion

Math
let the total be x students so x/3 + x/4 + x/6 + 18 = x multiply by 12 4x + 3x + 2x + 216 = 12x finish it up

maths
I would use substitution. from x-2y = 0 ---> x = 2y sub that into the 2nd: 3(2y)+ 4y = 20 continue to find y, then replace in x = 2y

Math
The algorithm I use sets it up this way: D = -3(3-0) - 2(0 - (-3)) - 3(0 - (-3)) = -9 -6 - 9 = -24 KhanAcademy shows 2 basic methods https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-determinants-and-inverses-of-large-matrices/v/finding-the-determinant-of-a-3x3-...

math
(5/8) ÷ (y/9) = 9/8 5/8 = (9/8)(y/9) 5/8 = y/8 y = 5

math
yes

math
vertical asymptotes have slopes which are undefined. An answer of "undefined" is caused by division of zero. So what is your conclusion?

Final Maths
For half-life questions, it is usual to use a base of 1/2 or .5 amount = 12 (1/2)^(t/5700) , where t is the number of years if the amount = 10 10 = 12 (.5)^(t/5700) .8333... = .5^(t/5700) take logs of both sides and use log rules log .8333... = (t/5700) log .5 t/5700 = log ....

Math - probability
out of the 224, the expected number of A+ i = .357(224) = 79.968 or 80 cases out of the 224, the expected number of AB- = .006(224) = .... carry on

Math
2. multiply the probability you found in 1. by 60

Calculus - Fundamental thm of Calc
To fully understand what Steve did, watch these two KhanAcademy clips https://www.khanacademy.org/math/ap-calculus-ab/fundamental-theorem-of-calculus-ab/fundamental-theorem-of-calculus-tut-ab/v/fundamental-theorem-of-calculus and https://www.khanacademy.org/math/ap-calculus-ab...

Math
let the angles in the interior of the triangle be x, y, and z Extend the base at the z angle let the exterior angle be k we know x+y+z = 180° we know that the z + k = 180 , (angles forming a straight line) so x+y+z = z + k x + y = k state your conclusion

fgh
Not being familiar with the game of cricket, I find this sentence confusing: "A team of 11 players must have at least 5 batmen, 4 bowlers and 1 wicket-keeper" Assuming that you would want 11 players, that could mean: 6 batmen, 4 bowlers, 1 wicket-keeper; 5 batmen, 5 ...

math
Really? How can you claim that it is negative, after having it shown that it is positive. Look at the calculation.

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