# 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.