Reiny

There is no function equation for the Fibonacci numbers, you have to use a Recursion formula. F(n) = F(n-1) + F(n-2) for n>2 and F(1)=1, F(2)=1 what is the equation for the fibonacci sequence

18 years ago

according to my interpretation of the question in October they would collect: the 10% of the August sales = .10($10,000) the 20% of the Sept sales = .20($20,000) and the 70% of the Oct sales = .70($30,000) Do the arithmetic and add them up A project has a...

18 years ago

Complimentary angles add up to 90º So translate the English into Math. if you let the unknown angle be x then "the measure of the compliment of the angle" -----> 90-x "10 degrees less than three times the measure of the angle" ----> 3x - 10 so....... 90-x...

18 years ago

<Thanks to computers, writing may soon become a lost art.> Leo, a similar prediction is often made about arithmetic since the invention of the calculator. in one of Isaac Asimov writings they discover a man who is actually able to perform an operation lik...

18 years ago

break it down into cases at most one day of rain in 3 days to me means we could have: norain norain norain ----> (1/3)^3 = 1/27 rain norain norain -------> 2/3(1/3^2 = 2/27 norain rain norain -------> same as above = 2/27 norain norain rain -------> same...

18 years ago

3(2+3-2(4-5)2-1)-3(2+4(4-2)-8+3(2-5)+1-2)1-3)+4-5 rather silly question, and some of it makes no sense eg look at the first part ......-2(4-5)<b>2</b>-1 does this end up -2(-1)(2) ? or did you forget an operator before the last 2? there is a similar discr...

18 years ago

I saw your reply re my late night solution to your pumpkin question http://www.jiskha.com/display.cgi?id=1224212047 I did indeed make two typing errors, which even though they do not change the actual answer, nevertheless would have caused confusion. I wi...

17 years ago

Even though you mean well, your last three responses have been either incomplete or incorrect. The one to http://www.jiskha.com/display.cgi?id=1258225501 is totally off the mark. Please make sure you are familiar with the topic before replying.

15 years ago

Happy Pi Day to all math "nerds" Even Google changed their log today. http://www.squidoo.com/PiDay

15 years ago

You now have 6 different posts going for the same "cake question" I am not going to keep going back to see which one you replied to. Stay with one posting please. I just notice one way down the list where you did part a) Calculate the area on top of the s...

15 years ago

Several student tonight have asked me how I create the √ symbol to create √ symbol on a PC, hold down the Alt key, and at the same time press 251 on the number pad, then release the Alt key on Mac, hold down the Option key, and press V, release the Option...

15 years ago

have been looking at your post ... http://www.jiskha.com/display.cgi?id=1357047578 interesting question... let the altitude of 12 hit base a let the altitude of 14 hit base b then (1/2)(12)a = (1/2)(14)b 6a = 7b a = 7b/6 let the third side be c and its al...

12 years ago

re http://www.jiskha.com/display.cgi?id=1368707176 I have a solution, but what a mess. Before I type it all out, let me know if you still need the solution. I certainly don't feel like typing it all out unless you will actually look at it.

12 years ago

Please settle on one name

12 years ago

take a look at this question http://www.jiskha.com/display.cgi?id=1446147947 Am I guilty of overkill or over-thinking this ? Surely there has to be an easier way.

9 years ago

Peter, I found your question interesting and have been messing with it for a while www.jiskha.com/questions/1789041/Ethel-went-to-the-farmers-market-to-buy-some-eggs-not-in-a-dozen-cartons-on-the I finally made up a short computer program using a silly ol...

6 years ago

Ms. Sue was a kind, gentle, and good person that I had the privilege of knowing through this webpage. I have been a tutor for about 12 years on here, and was always impressed by the patient and competent way she helped students. You will be missed Reiny

5 years ago

I didn't say it shouldn't be 1/5x I just wanted you to be aware of the difference between 1/5x and 1/(5x) for your second part of your question .... look at x = (y-2)/(5y-3) , so far ok ? or x/1 = (y-2)/(5y-3) the common denomator is 5y-3 , so multiply ea...

12 years ago

welcome

12 years ago

y = ³√(1/5x) +3 is good Just make sure when you type the bracket part (1/5x) , it is only 5 that is divided and not the 5 as well that is why I wrote it as (x/5) Your new problem: y = (x-2)/(5x-3) -----> x = (y-2)/(5y-3) as the inverse cross-multiply 5xy...

12 years ago

for your first one, the variable dropped out, but you ended up with a true statement, 0=0 If that happens you will have an infinite number of solutions. In effect , the two equations are really the same equation. look at the 2nd 3x + 9y = 12 , divide by 3...

12 years ago

What you are doing here is comparing the circumference , the distance which is rolled bottom of cup: radius = 5 cm, so the circumference is 2πr = 10π top of cup: radius = 7 cm, so the circumference is 14π or appr 43.96 cm

12 years ago

y = (3/2)(x+4) = (3/2)x + (3/2)(4) = (3/2)x + 6 showing that my answer is the same as theirs they simply factored it, there was no need to do that. If you ever get an answer which looks different from the text book answer, try using proper algebraic manip...

12 years ago

I could have picked any x I wanted, since it must be true for all values of x I simply picked x = 4, because it gave me a "nice" answer. Same reason I picked x=8 I could have picked x = 45.678 As to your second post is that a new equation?? did you mean:...

12 years ago

For half-life question, a good equation to use is amount = starting value (1/2)^(t/k) where k is the half-life so : .35 = 1(1/2)^(t/2000) , t in years .35 = (.5)^(t/2000 log .35 = log ( (.5)^(t/2000) log .35 = (t/2000) log .5 t/2000 = log .35/log .5 t = 2...

12 years ago

60 inches : 9 inches = 20:3 , is your ratio or your scale so just set up a simple proportion x/100 = 9/60 x = 100(9/60) = 15 it should be 15 inches long notice: 100/15 = 20/3 and 60/9 = 20/3

12 years ago

mmmh, why don't we expand their answer y = (3/2)(x+4) = ..... well, what do you know ?? Either answer is correct.

12 years ago

From 1/5x = (y-3)^3 , which is the inverse and correct, you now have to solve for y So, take the cube root of both sides (x/5)^(1/3) = y-3 <b>y = (x/5)^(1/3) + 3</b> check: in original let x = 4 y = 5(1)^3 = 5 now use x=5 in your inverse y = (5/5)^(1/3) +...

12 years ago

slope = (-2-6)/(-1-1) = -8/-2 = 4 then y-6 = 4(x-1) , using the point (1,6) y-6 = 4x - 4 y = 4x + 2 test using the point which was not used, (-1,-2) LS = y = -2 RS = 4x + 2 = 4(-1) + 2 = -2 = LS all looks good other forms, which can be found by just re-ar...

12 years ago

from the 1st ---> 4x-9 = y sub that into the 2nd 2x + 3(4x-9) = 12 2x + 12x - 27 = 12 14x = 39 x = 39/14 y = 4(39/14) - 9 = 15/7 check: 1st: LS = 4(39/14) - 15/7 = 156/14 - 30/14 = 126/14 = 9 = RS 2nd: LS = 2(39/14) + 3(15/7) = 39/7+ 45/7 = 84/7 = 12 = RS

12 years ago

They both drove for the same time of t hrs distance covered by Allison = 60t distance covered by Austin = 48t 60t - 48t = 54 12t = 54 t = 54/12 = 4.5 So they both drove for 4.5 hours and Allison went 270 miles (Austin went 4.5(48) or 216 miles, which is 5...

12 years ago

Here is the way I do these: y = (2/3)x - 4 to find the inverse, I follow these steps 1. to find the inverse equation, simply interchange the x and y variables So the inverse of y = (2/3)x - 4 is x = (2/3)y - 4 2. Now you want to probably solve this for y...

12 years ago

No, it's not that simple Time for first trip = x/10 time for second trip =x/8 distance of total trip = 2x rate = total distance/total time =2x/(x/10 +x/8) =.. =.. =8.88 mph

18 years ago

multiply your first equation by 12 to get 4(x+2)-3(y-1)=12 4x-3y=1 call this equation #1 take your orignal second equation, multiply it by 4 and take all terms to the left side 20x-16y=0 call this equation #2 #1 times 5 ---> 20x-15y=5 #2 ----------> 20x-1...

18 years ago

basically, you pick any variable you want, and let the equation calculate the corresponding second variable. e.g. pick y=2, (one of their answer points) then x+2(2)=4 x+4=4 so x=0, then when x=0,y=2, which is the point (0,2) (the x is always written first...

18 years ago

That is correct if your matrix is 5 2 -1 1 The way you wrote it I at first assumed 5 -1 was a row, but it must clearly be a column for the point to become (4,1)

18 years ago

The slope of a line paralle to the given line is indeed -1/9 You have correctly answered the question the way it was worded. There is nothing else that has to be done.

18 years ago

C=5/9(F-32) multiply by 9 9C = 5(F-32) 9C = 5F - 160 9C + 160 = 5F 5F = 9C + 160 F + (9/5)C + 32

18 years ago

The cube of snow has a volume of 8by8by8 = 512 cubic feet One cubic foot weighs 30 lbs, so 512 cu feet weigh 512 x 30 = 15360 lbs

18 years ago

by definition a "cube" has 6 equal square faces

18 years ago

-8X-12+29x-39+62-3=15x+2 -8x + 29x - 15x = 2+12+39-62+3 6x = -6 x=-1

18 years ago

you are correct. x = -3 ± √13 (You can obtain a √ sign on a PC by holding down the Alt key and at the same time presing 251 on the number pad, then releasing the Alt key)

17 years ago

no 3x-27/55÷x-9/15x = 3(x-9)/55 ÷ (x-9)/15x = 3(x-9)/55 * 15x/(x-9) = 9x/11 , x not equal to 9 I divided top and bottom by x-9 and 5

17 years ago

you are correct you can check you answer by expanding your result, obtaining the original expression

17 years ago

first equation : x + y = 38 second equation: 175000x + 200000y = 7200000 which reduces to 7x + 8y = 288 multiply the firs equation by 7 7x + 7y = 266 subtract that from the second equation 7x+8y = 288 7x+7y = 266 y = 22 sub back into the first equation x...

17 years ago

I don't know how you got your answer, nor what you mean by "removing factors of 1" but (q^2-64)/(q+8)^2 =(q+8)(q-8)/(q+8)^2 =(q-8)/(q+8) , q not equal to -8

17 years ago

how about (2x2)^2 - 2 ?

18 years ago

AC = 2/3 CB so AC:CB = 2:3 6----------X------------------21 A..........C...................B -----2----- ---------3--------- then (X-6)/2 = (21-X)/3 cross multiply ... ... X=12

18 years ago

did you mean (27a^6b^3)^(1/6) + 7a(81b^4)^(1/8) ?? then... = [(3^3)(a^6)(b^3)]^(1/6) + 7a[(3^4)(b^4)]^(1/8) =(3^(1/2)(a)(b)^(1/2) + 7a(3^(1/2))(b^(1/2)) = 8a√(3b)

18 years ago

from the first set of data, select two ordered pairs, e.g. (3,8) and (5,14) slope =(14-8)/(5-3) = 3 so the equation is y = 3x + b but (3,8) lies on this so 8=3(3)+b b=-1 and the equation is y=3x-1 so when x=25 y=3(25)-1 = 74 do the second one the same way

18 years ago

must be a trick question. The sum of 4 odd numbers is always even, so not possible.

18 years ago

you forgot the case where all 5 are of the same suit "at least 4 of the same suit" means it could be 4 of the same suit or it could be 5 of the same suit. which would be 4(13C5)/52C5 add that on to your answer

18 years ago

Let the sisters age be x then Sue is 3x x+1 + 3x+1 = 22 Solve

18 years ago

use grouping 4z+8w^2-wz-32w = 8w^ - 32w + 4z - wz = 8w(w-4) - z(-4+w) = 8w(w-4) - z(w-4) = (w-4)(8w-z)

17 years ago

rewrite each with a common denominator of 16 5/8 = 10/16 3/4 = 12/16 9/16 = 9/16 7/8 = 14/16 Can you tell now? or change each fraction to a decimal by dividing top by bottom.

17 years ago

Point A (x,y) 90 degrees clockwise ----> A'(y,-x) reflection around the y-axis ----> A''(-y,-x) for point (-4,-3) 90 degrees clockwise ----> (-3,4) reflection around the y-axis ----> (3,4) Is that what you are after?

17 years ago

#1 I would isolate the x in the second equation, that is, x = 10-7y then substitute into the first equation. #2 an infinite number of solutions, since the first equation is simply 3 times the second.

18 years ago

Your equation is NOT a function. If you rearrange it to read : x^2 - y^2 = 1 you should recognize that it is a hyperbola. Where did you get the idea a relation cannot be an equation? All relations are equations. All functions are relations, but only some...

18 years ago

Hello Bob, love your analogy about mom's apple pie recipe. Allow me to enter the NM debate at this point. Do you happen to have a good explanation re the origin of the k in knots for "nautical miles per hour"?

18 years ago

That makes sense. BTW, interesting thread.

18 years ago

log(2^(6x-1))=log9, (assuming your exponent is 6x-1) (6x-1)log2=log9 6x-1=log9/log2 etc Unless you use some kind of interpolation, using logs along with a calculator will give you the most accurate answer. (I got x=.6949875)

18 years ago

According to your original line you are correct, but... are you sure that the second bracket wasn't (6x^2+42xy) ? Then I would have worked out better and the answer would have been 1/(6x^2)

18 years ago

Michele's answer is not correct x^=-9 has no solution in the set of real numbers (x=-3 is a real number solution) You will have to use imaginary or complex numbers x^2 = -9 x = ±√-9 x = ± 3i where i = √-1

18 years ago

I like doing these questions the following way: keeping the time constant: 1.5 teens eats 1.5 pizzas in 1.5 hours 3 teens eats 3 pizzas in 1.5 hours 9 teens eats 9 pizzas in 1.5 hours now keep the teens constant: 9 teens eats 9 pizzas in 1.5 hours 9 teens...

18 years ago

clearly the cost of the notebooks plus the calculator has to be equal to or less than $20 Now translate this into "math" 12 + 2n ≤ 20

18 years ago

subtract 12 from both sides 2n ≤ 8 now divide both sides by 2 to get your answer.

18 years ago

I will assume that "0-7" means none out the seven choses has back problems. then.. it is simply : (0.54)^7

18 years ago

#1,10 and 12 are correct, you probably meant to type "x varies inversely as y^2.." in #12 for #4 all you have to do is say y = k/x , sub in the x and y values given so 2=k/6 k = 12 then the equation you are asked for would be y = 12/x

18 years ago

To get the x intercept for any equation let y=0 and solve. You should recognize your equation to be that of a standard hyperbola, with symmetrical x and y intercepts. so the other x intercept would be x=-2 the other 3 points would be (3,-4.5), (-3,4.5) an...

18 years ago

12% of budget=300 1% of budget = 300/12 = 25 so 100% of budget = 25*100 =2500

18 years ago

The correct answer is x ≤ 21/7 When you divide (or multiply) by a negative number, which you did in your second-last line, you have to reverse the inequality sign. BTW. to get the ≤ sign, hold down the Alt key, at the same time press 243 on the number pad...

18 years ago

I think they are saying that there are 12 eggs in a carton So the mean of a carton is 780 g with a standard deviation of 24 g. We need the z-score for both 825 and 750 z-score for 825 = (825-780)/24 = 1.875 z-score for 750 = (750-780)/24 = - 1.25 Now go t...

18 years ago

You are so right drwls, I don't know how I possible got 5 x 12 to be 24, it should have been 60 so let me try again: I think they are saying that there are 12 eggs in a carton So the mean of a carton is 780 g with a standard deviation of 60 g. We need the...

18 years ago

The exterior angle of a triangle is equal to the sum of the 2 interior and opposite angles. so.. angle Q + 4/5 angle Q = 144 (multiply by 5) 5angle Q + 4angle Q = 720 9angle Q = 720 angle Q = 80

18 years ago

The square root enters the picture as we calculate standard deviation. But unless I am missing something here, the standard deviation is given, thus already calculated. Suppose I change the question a bit and look only at one egg instead of one carton. Th...

18 years ago

you are correct in all cases

18 years ago

Check your typing of the question. There had to be an exponent somewhere in "find the numerical value of x in 3x+2 = 405", otherwise there would have been no need to give you the log of 2 and 3

18 years ago

In the expansion of (3x - 5/x)^n there is no term independent of x, (a constant term), if n is odd, in your case 9 the general term would be C(9,r)(3x)^r(-5/x)^9-r =C(9,r)(3)^r (-5)^^-rx^r-9 =C(9,r)(3)<sup...

18 years ago

As suggested by bobpursley, use the cosine law to get c, I got 8.1 Now use the Sine Law to find angle A, which I got to be 43.16º Let P be the centre of the incsribed triangle. A property of that circle is that its centre is the intersection of the angle...

18 years ago

Clearly the person in front and the person behind the wall know nothing So it is left to either the second or third person. If the third person sees two identical colours in front of him, either both blue or both brown, then he knows his is the opposite,...

18 years ago

Here is another very easy way: Your new equation will only differ in the constant, so it must be 4x+y=c put in (5,3), 20+3=c so your equation is 4x+y=23

18 years ago

Most computer languages have a command that assigns a numerical value to a character variable, such as VAL($A) in Visual Basic. I used to assign such a problem as you stated and found the "bubble method" to be the easiest to use for most students. Assign...

18 years ago

I will assume you meant the following: (14x-7)/(x^2+3x-4) * (x^2+6x+8)/(2x^2+5x-3) ÷ (x^2+2x)/(x^2+2x-3) Then everything factors very nicely and my answer was 7/x Don't forget the restrictions of x not= -4,1,-3,1/2,-2,0 Hint:(my restrictions should give y...

18 years ago

At a rate of 8 m/min, after 2 minutes the radius will be 16 m. Now sub r=16 into your dA/dt you had in a)

18 years ago

Let the midpoints of XY,YZ, and XZ be P,Q, and R respectively Did you get P(2,2), Q(6,0) and R(4,-2) ? XQ is obviously y = 0, the equation of the x-axis YR has undefined slope, so its equation is x=4 Right there you already have the coordinates of the cen...

18 years ago

Your question makes no sense to me. How long is EF, do we know the endpoints E and F? You want the circumcentre of triangle DEF, but D is not mentioned in your data. Please restate correctly.

18 years ago

(4,0) would be the correct centre for the circumcentre of the original triangle ABO in general, the circumcentre is the intersection of any two of the rightbisectors of two of the sides of the original triangle. The right bisector of a side goes through t...

18 years ago

Each traveled 5.5 hours I made a chart ..........Distance....rate........time trav#1......5.5x......x km/h.....5.5 hrs trav#2....5.5(x+20)...x+20 km/h..5.5 hrs ...total...220 so 5.5x + 5.5(x+20) = 220 solve, it is easy from here on. (I got 30 km/h)

18 years ago

the first one is correct, the 2nd is not try f(4) in your equation, you do not get zero. I had f(x) = a(x^2+1)(x-4) then for f(-3)=60 60 = a(10)(-7) a= -6/7 so f(x) = -6/7(x^2+1)(x-4) expand it for your answer

18 years ago

"poly" is many in Greek and "nomial" means number so a polynomial is 'several terms' In highschool mathematics, a polynomial is an expression made up of two or more terms, where each term has an exponent n, so that n is a whole number. A "graph that is li...

18 years ago

to find k: 24 = k(6)(4)/√49 which gave me k=7 then y = 7ab/√c and for the second data values: y = 7(2)(5)/51√16 = 70/4 =17.5

18 years ago

Let the distance from the sideroad be x miles, let the distance between the car and the house be y miles. You have a right-angled triangle where x^2 + 8^2 = y^2 then 2x dx/dt = 2y dy/dt (1) when x=7, y^2 = 49+64 = 113 so when x=7, y= √113 and dx/dt = 80 s...

18 years ago

8. Clearly it must be y-9 = 11(x-2)^2 10. sketch y = x^2, then move it 6 units to the left and 3 units up

18 years ago

for any parabola of the form f(x) = a(x-h)^2 + k the vertex is (h,k) and the axis of symmetry is x = h Make use of that fact for #1 and #3 The range is the set of y values that the graph covers. so in #5 first rewrite it as f(x) = -(x+4)^2 - 7 Wouldn't th...

18 years ago

#15 and #30 open downwards, so they have a maximum #20 and #19 open upwards, so they have a minimum. change the equations to the form f(x) = a(x-h)^2 + k by completing the square You should have learned how to do this, and read the vertex from that form.

18 years ago

To find the x-intercept, set y=0 and solve for x To find the y-intercept, set x=0 and solve for y the domain of a standard parabola that opens either up or down is x "is an element of" R the domain is either y ≥ "the y value of the vertex", if it opens up...

18 years ago

Let the foot of the ladder be x feet from the wall let the height of the ladder be y feet then x^2 + y^2 = 225 differentiate with respect to t, this is a "related rate problem" 2x dx/dt + 2y dy/dt = 0 (1) when t=3 sec, x = 9 feet (you knew the rate) then...

18 years ago

................. . . . . . . . . . . . . . . . y . . . . . ................. ------4x------- let the length of the original rectangle be 4x (so that each of the smaller rectangles is x ) let the width be y After it is folded, the volume would be y(x^2) b...

18 years ago

looks like my diagram did not come out correctly. It was supposed to be a large rectangle 4x by y, divided into 4 equal rectangles each x by y

18 years ago

Let C = ax + b, from the data 60 = 160a + b and 90 = 280a + b solve these two, you should get a=1/4 and b=20 then C = (1/4)x + 20

18 years ago

first find the slope slope = (8-6)/(3-2) = 2 now use one of the points, eg A(2,6) and m=2 to sub into y=mx+b 6=2(2)+b solve for b, put that back into y=2x+b and you are done

18 years ago

NO from my previous post: y=mx+b 6=2(2)+b then 6=4+b b=2 then y = 2x + 2

18 years ago

4th degree functions can have a maximum of 4 x-intercepts (in general a nth degree function can have at most n x-intercepts) They tend to look like a W for 1. the factors are (x+1)(x-3)(x-1)^2 so there are x-intercepts at -1 and 3. The factor (x-1)^2 or (...

18 years ago

you are correct for all questions. I like how you actually did the questions and asked for verification, rather than asking how to do it. This is what most tutors on here would like to see

18 years ago

correct

18 years ago

let the speed of the train be x miles/hour then the speed of the car is 1.5x miles/hour. Time taken by train = 300/x hours Time taken by the car = 300/1.5 hours So 300/x - 300/1.5x = 2 solve for x (I got x=50, so car = 50, train = 75)

18 years ago

For the first one, since Area = LxW and W = 2x+5 then L = (2x^4 + 9x^3 - 12x^2 - 79x - 60)/(2x+5) the rest of your answers are correct

18 years ago

Your answer makes no sense. If the second worker works twice as fast than the first, then his time should be HALF of that of the first, not double the time. so first takes 30 minutes, rate is Tree/30 the second takes 15 minutes, rate is Tree/15 combined r...

18 years ago

let the speed of the wind be x mph so the speed of the plane with the wind is 220+x and against the wind it would be 220-x The time taken against the wind is 780/(220+x) and the time taken with the wind would be 780/(220+x), remember Time = Distance/Rate...

18 years ago

correct!!!

18 years ago

use x^3 to say x cubed use brackets to enclose the denominators and / to show division, * to show multiplication e.g. (x^2-64)/(x+2)

18 years ago

Very easy Recall that the slopes of perpendicular lines have slopes that are negative reciprocals of each other, or in other words, the product of their slopes is -1 Your first line is x + 3y = 12 So the perpendicular line must be 3x - y = c , the only th...

18 years ago

If Nora is n years old NOW, then Kevin is NOW n-3 so 4 years ago Kevin was (n-3) - 4 = n - 7 , (E)

18 years ago

1 mile/hour = 5280 feet/3600 seconds so 168 miles/hour = ......

18 years ago

168*5280/3600 = 246.4

18 years ago

no! the slope of the given line was -1/3, the slope of your new line is +1/3 So they are not even perpendicular!! from your line: 3y/3 = -x/3 + 12/3 so far so good now y = (-1/3)x + 4 so the new slope must be +3 y + 5 = 3(x - 9) y + 5 = 3x - 27 y = 3x - 3...

18 years ago

(continued) so the slope of the new line must be +3 then the new equation is y = 3x + b but (9,-5) lies on it so -5 = (3)(9) + b b = -32 for y = 3x - 32

18 years ago