Posts by Reiny

Total # Posts: 39,963

Math
when it hits the ground, h = 0 so solve: -16t^2 + 144t + 160 = 0 divide each term by -16 t^2 - 9t - 10 = 0 easy to solve, use factoring.

Math
Use Pythagoras. Let me know what you find and how.

math
Just a simple ratio question: 45/30 = x/45 x = 45(45/30) = .... km

Math - Steve
Steve may not be online right now. Going with his equation, 2.9046(1.9798)^x = 13000000 first divide both sides by 2.9046 1.9798^x = 4475659.299.. (keep in your display) take log of both sides, and use your log rules x log 1.9798 = log 4475659.299 x = log 4475659.299/log 1....

math
2.6×1000 shows up on my computer as illegible. Volume = area of base x height but of course we must have the same units 5.2 cubic metres = 5,200,000 cm^3 so divide 5200000/(2.6×1000 ) to get the height in cm.

math
You must have meant: lim (1 + ?n)/(1-?n) as n ---->? divide top and bottom my ?n = lim (1/?n + 1)/(1/?n - 1) as n ---->? Now look at the 1/?n term as as n ---->? , 1/?n -----> 0 e.g. let n = 10,000,000 , 1/?10,000,000 = .00031... getting small So you are left with ...

Calculus
looks like a decimal place error, check that. Here is what Worlfram says: http://www.wolframalpha.com/input/?i=riemann+sum+9-x%5E2+between+x%3D-2+and+x%3D3

Algebra
I see 5k^2 as the GCF, the last term does not contain b

Math
cost = 100(.25) + 8 = 33 number sold ---- x 2n - 33 > 0 2n > 33 n > 16.5 , so they sell at least 17 chains, or the fewest number they must sell is 17 if they sold all 100, their profit is 200 - 33 or $167 Am I missing something here ? looks pretty straightforward.

Math
original area = 1 x .8 = .8 m^2 new length = 1.4 m new width = 1.2 m new area = 1.4(1.2) or 1.68 m^2 finish it up

Math
algebra solution: let the unit digit be z let the tens digit be y let the hundred digit be x x+y+z = 20 y = (1/4)(x+z) 4y = x+z original number is 100x + 10y + z reversed number is 100z + 10y + x difference of those two is 198 100x + 10y + z - 100z - 10y - x = 198 99x - 99z = ...

Math
find y for each of the given x values. list them in brackets such as {?,?,...}

PreCalc
I assume you have studied the remainder theorem. Then you must know that for your conditions, f(-1/2) = (-1/8)a + (1/4)b + 4 = 0 ---> a - 2b - 32 = 0 f(1) = a + b + 4 = 0 ----> b = -4-a sub that into the first: a - 2(-4-a) - 32 = 0 a + 8 + 2a - 32 = 0 3a = 24 a = 8 , ...

Math
looks like linear programming. let's look at each region. 2x + 3y > 30 the boundary is 2x + 3y = 30 when x = 0, y = 10 when y = 0 , x = 15 , so we have (0,10) and (15,0) plot these points on the axes and draw a dotted line, shade in the region above this line 2x+y < ...

Algebra
You have a very common mistake. Notice there is no x^2 term, so you need a 0 as a placeholder correction: -3 | 1 -2 0 -4 4 .....| -3 15 -45 147 -------------------- .....| 1 -5 15 -49 151 hard to line up the columns , isn't it ?

Algebra
Difference implies subtraction sum implies addition product implies multiplication, and quotient implies division so "a number" is an unknows difference between "the unknown" and 10 could have been x-10 or 10-x, but they didn't show a 10-x

Algebra
The product of 3 and the difference of a number and 10 is 15 The product of 3 and the difference of a number and 10 is 15 The product of 3 and (x-10) is 15 The product of 3 and (x-10) = 15 3(x-10) = 15 can you see what I did there ?

geometry
Nice question, and I could see your diagram. Several ways to do this, here is what I thought: easy to get the equation of BD : y = -x + 4 and the equation of AQ = (1/2)x so for the intersection: (1/2)x = -x + 4 x = -2x + 8 3x=8 x = 8/3 so if we consider AB as the base and 8/3 ...

algebra
x^3 + 3x^2 + 3x + 2 let f(x) = x^3 + 3x^2 + 3x + 2 f(1) = 1+3+3+2 ? 0 f(-1) = -1 + 3 - 3 + 2 ?0 f(2) = ..... ? 0 f(-2) = -8 + 12 - 6 + 2 = 0 , so x+2 is a factor do a long division to get the remaining quadratic factor.

sorry - math
Your equation was correct. For some reason I wrote down your equation as y = 1/2x-8 to do my calculation, and I then carried through the calculations with my typo. yes, it is y = (1/2)x - 9

math
nope, your slope is right, but when I substituted x = 2, I got y = (1/2)(2) - 8 = 1 - 8 = -7 so the point does not lie on your line. Furthermore, since the original equation was written in standard form, I think the same style of equation would be expected.

Algebra
disagree. if the first chooses orange juice, then the second can only choose from the remaining 9 oranges out of the remaining 19 so prob(both have orange) = (10/20)(9/19) = 9/38

Algabra
My money is on Scott .... unless you were to do 0/0, then all bets are off e.g. 12÷3 = 4, because 3 x 4 = 12 12 ÷ 0 = k, because 0xk = 12 ? , but that is false since zero times anything = zero but 0 ÷ 0 = k, because 0 x k = 0 , hehh, I could put anything I...

Algebra
You will have to use "completing the square". y = 2x^2-8x+11 = 2(x^2 - 4x+ .... ) + 11 <---- took out the coefficient of the square term from the first two terms = 2(x^2 - 4x + 4 - 4) <--- took half of the coefficient of the x term, then squared it, added it ...

math
It always helps to make a sketch before you start a problem. In this case, notice that RS is a horizontal line, so it is easy to that RS = 5 let's make RS the base, then since T is 6 units below that line, the area = (1/2)(base)(height = ....

maths
Each rotation is 1.4? m so number of rotations = 1100/(1.4?) = ...

Pre algebra
X/4+1=-5 x/4 = -6 x =-24

Calculus
looks like Steve and I have the same answer

Calculus
using the quotient rule, by first line derivative is y' = (1/3)[(5z+6)/(3-9z)]^(-2/3) [ (5(3-9z) - (-9)(5z+6) ]/(3-9z)^2 = (1/3)[(5z+6)/(3-9z)]^(-2/3) [ 69/(3-9z)^2 ] = 23 (3-9z)^(2/3) / (5z+6)^2/3 [ 1/(3-9z)^2 ] = not getting your answer let's try the product rule y...

Algebra
i = .0645/12 = ..... n = 8(12) = 96 paym = p p( 1 - (1+i)^-96 )/i = 45000 - you should know that formula as the PV , present value, formula Once you have the payment p , use your Amount formula to find the amount of 96 payments of p

Maths
So wouldn't the length be reduced by 8 cm, and the width reduced by 8 cm ? mmmmhhhh? What is the new area vs the old area ? show me your work.

algebra
We had a very similar question yesterday https://www.jiskha.com/display.cgi?id=1512043982 In that one, I had found the slope Using (30,14) as a point, find the equation in the form y = mx + b then sub in 45 for x to get the number of gallons

math
from the first: 2x-6y=26 --> x = 3y + 13 sub into the 2nd and away you go ....

Math
obviously x + y ? 1000 and just as clearly: 2x + 5y ? 3000 Now show me the efforts you made in the next problem.

prealgebra
just plug in the numbers.. m/n +m/2p = (-4/7) / (5/3) + (-4/7) / (16/5) = (-4/7)(3/5) + (-4/7)(5/16) = -12/35 + (-20/112) = -12/35 - 5/28 now 35 = 5 x 7 and 28 = 4 x7 so the LCD = 5x4x7 = 140 carry on from here

algebra
Simplest way to understand this is to make a table of values. Pick any x to find the matching y, then plot those points the |... anything ..| simply means to take the positive result of 'anything' e.g. |5| = 5 , |-5| = 5 your graph should look like this: http://www....

algebra
Whenever you have a direct variation of something like (.....y....) varies directly with (.....x.....) we can say y = kx Usually you will be given one case where that is true, in your case x = 5 and y = 15. So sub that in ... 15 = 5k k = 3 so now we know the variation equation...

Algebra
775.5 is the correct answer. Trust yourself and Ms Sue.

MATH
nope, Use Pythagoras ... x^2 + 5^2 = 13^2 etc

Geometry
Steve and I answered this same question way back in 2011 https://www.jiskha.com/display.cgi?id=1324327824

Math
let the length be x let the width be x/2 let the height be x-5 x(x/2)(x-5) > 1125 x^2(x-5) ? 2250 let's solve x^2(x-5) = 2250 with the help of Wolfram http://www.wolframalpha.com/input/?i=solve+x%5E2(x-5)+%3D+2250 x = 15 x(x/2)(x-5) < 3000 x^2(x-5) = 6000 and that ...

Geometry
good! You got it

Geometry
You are correct, but do you understand why not ?

Math
Woahh there. looking at the function, it will have a maximum of 37+25 or 62 and a minimum of -37+25 or -12 Since this is apparently Alaska, those units can only be in Fahrenheit units and not Celsius. The units I was talking about are "radians" vs "angles ...

Math
btw, make sure your calculator is set to radians, and not degrees

Math
just plug in 342 for the x, and grind it out. let me know what you get. Here is a graph to help you check your answer. http://www.wolframalpha.com/input/?i=plot+y+%3D+37sin%7B2%CF%80%2F365(x%E2%88%92101)%7D%2B25

Math
nope rate of draining = (9-14)/(60-30) = -5/30 gallons/sec or -1/6 gallons/sec the negative shows the volume is decreasing or "draining" remember, slope is (the difference in the y's)/difference in the x's I think you had it backwards, and also ignored the ...

Math
You first must define your ordered pairs. let my general ordered pair be (time, volume) secondly, make sure you have the same units, e.b. seconds or minutes. I would have: (30,14) and (60,9) now find the slope, and your answer would be gallons/second let me know what you get.

geometry
I am sure you made a sketch let triangel APC = x then triangle PBC = 3x the whole triangle ABC = 4x Since M is the midpoint, triangle BPM = (1/2) of 3x = 3x/2 ratio of ?BPM : ?ABC = 3x/2 : 4x = 3/2 : 4 = 3 : 8 you had C, so correct

Math
speed downstream = x+2 speed upstream = x-2 4(x+2) = 6(x-2) solve for x, then sub into 4(x+2) to get your distance

math
A: cost = 25 + .8x B: cost = 44 + .6x set them equal to find out when the cost is the same. then decide when A is cheaper

Calculus
take the derivative, set it equal to zero and solve for x Plug that x back into P(x) to get your maximum profit. b) ?x^2+36x?26 ? 40 x^2 - 36x + 66 ? 0 let's use the = sign x^2 - 36x + 66 = 0 use the quadratic formula, you will get two positive x's lower ? x ? larger ...

Math
No, there is a solution .... 4 - t = (t - 1) -5 4 - t = t - 1 - 5 -2t = -6-4 2t = 10 t = 5

Algebra pleaseee helppp
Thanks Steve, you are right, I missed the duplications I was thinking something along the lines of dividing by 2^52 , since we have pairs 52 times. I don't know enough about jokers. Are the all the same or distinct? I did count them in my 108 = 2x52+4 If they are the same...

Algebra pleaseee helppp
so you want 11 of the 108 cards, which would be C(108,11) = appr 3.4 x 10^14 quite a few i would say

Math
so our x = 20 set your calculator to radians and find 50 cos(60) + 75 = appr 27 rabbits Strange question. The max population would be 125 and the minimum would be 25 repeatedly during that time, and it would go from a max to a min in a period of (1/2)(2?/3) years or appr. ...

Algebra
15 correct 16 the discriminant is b^2 - 4ac for yours we get 16-4(1)(-32) = 144 which is a positive number and a perfect square, so we have to different rational x-intercepts. Remember if the discriminant is > zero , you have two real roots if the discriminant is = zero, ...

math
let the point be P(x,y) you don't say if AP : PB = 2 : 3 or 3 : 2 I will assume the first. If otherwise it is very easy to change If you make a sketch and draw the right-angled triangles, you can see .... for the x: (x-2)/(18-x) = 2/3 3x - 6 = 36 - 2x 5x = 42 x = 8.4 find ...

algebra
Just did this for you in your earlier post

Math
.77..... = 7/9 test with your calculator

math
But I want you to factor the bottom, and my hint was that one of the factors is (x-2) so (x^2 + 3x - 10) = (x-2)( ...... ) and the x-2 will cancel

math
You will definitely need brackets to properly show these expressions, I will assume you meant: (3x-6)/(x-2) = 3(x-2)/(x-2) = 3, x ? 2 You take over to do (x-2)/(x^2 +3x-10) hint: become very suspicious that perhaps one of the factors in the bottom might be (x-2)

Algebra
1. slope = (y2 - y1)/(x2 - x1) so , please recalculate the slope, it is not a I think you have it "upside down" 2. correct

math
6. ?75 + ?3 = ?25?3 + ?3 = 5?3 + ?3 = 6?3 7. ?7(?14 + ?3) = ?98 + ?21 = ?49?2 + ?21 = 7?2 + ?21

Math
correct I would have preferred if you had said, "I know the answer is A"

Math
Wow, what garbled language !! Fortunately, I am guessing you are talking about perfect numbers. As far back as Euclid it was know that if if p is prime, then 2^p - 1 is a prime number, then (2^p -1)(2^(p-1) ) is a perfect number. e.g. p = 2 ---->(2^2 - 1)(2^(2-1)) = 3(2) = ...

college algebra
similar to your other question let the amount invested at 6% be x then the amount at 7% is 2x let the amount invested at 4% be y so x + 2x + y = 24900 y = 24900 - 3x .06x + .07(2x) + .04(24900-3x) = 1412 proceed as before

Algebra 1
Just translate, if her present rate is x mph, then 2(x+15) > 3x

college algebra
first equation: x+y = 6600 or y = 6600-x .09x + .055y = 468 how about multiplying each term by 200 18x + 11y = 93600 use substitution: 18x + 11(6600-x) = 93600 carry on ....

Algebra
step 1 multiply each term by 6 to eliminate the fraction 6y = x + 24 step 2 re-arrange to the form required.

Geometry
easiest way: Since the slopes must be negative reciprocals of each other, the new equation must look like this y = (-1/2)x + b plug in your point (-4,7) 7 = (-1/2)(-4) + b 5 = b y = (-1/2)x + 5

math
Sure looks like we are dividing a term by -4 to get to the next one, so .....

math
If the average of the original 20 men is 50 years, what is the total sum of their ages? What is the total sum of the new 5 men ? Find the total sum of the ages of the 25 men, which will lead you to the average age of all of them.

math
since the time is 6 years, I will assume you are using compound interest, simple interest normally would not be used for that length of time Let the interest rate be i 1500(1+i)^6 - 1200(1+i)^6 = 90 isolate (1+i)^6 take the 6th root of both sides and you have it

algebra
good grief, this is as fundamental as it gets. Parallel lines have the same slope. In y = mx + b form, which your given line and all choices are shows as, the slope is m I see only one of the choices having the same slope.

algebra
for the 6 and 3, it would be 6 for the a and a^2 , it would be a^2 for the b and b^2, it would be b^2 so .......

Mathematics
by "easy enough" ole means that you have similar right-angled triangles, so use ratios.

Algebra
major error from 6000=3000 (1+.10/12)^12t to 6000-3000=3000-3000(1+008333333)^12t which in turn is NOT equal to the next line 3=1.008333333^12t propter steps: 6000 = 3000(1.0083333)^t, where t is in months 2 =1.0083333^t take ln of both sides ln2 = t ln1.083333. t = ln2/ln1....

Algebra
I agree, assuming the question was, "how long would it take for money to double at 10% compounded continuously?" ( In the good ol' days we had something called the rule of 72. Money doubles approximately if you multiply the time by the rate and you get 72. So 72/...

Math
If by e you mean the Euler number 2.718281828... and your x is a multiplication sign, then 3e = 8.154845...

math
number of advance --- x number of same day --- y x+y = 55 y = 55-x 40x + 20y = 1800 40x + 20(55-x) = 1800 continue strange price for tickets, usually at the door they are more expensive

Math
You will have to use your distance formula three times. Add the lengths of PQ , QR, and RS I will do QR, you do the other distances , PQ and RS Q(1,2), R(1,-1) QR = ?( (1-1)^2 + (-1-2)^2 ) = ?( 0 + 9) = 3 units Just noticed that all your trips are either horizontal or vertical...

ALGEBRA
First of all they should have reduced your given 3x+6y=9 to x + 2y = 3 quickest way: since the new equation is perpendicular to the old one, it should be 2x - y = c , (realizing that for ax + by = c, the slope is -a/b ) plug in your point (-4,2) -8 - 2 = c c =-10 new equation...

Math
I did this same question https://www.jiskha.com/display.cgi?id=1511672005

Algebra
suppose they were all positive: 2,1,4,7,10,13,16 that general term would be 3n-5, from the second term on It looks like the first term is an outlier if I make that change, let's hope it works out but we want to make the terms alternate between + and - this can be done by...

geometry
Ok, I saw you diagram, a pyramid with a square base of sides a, and height h, with h1 as the height of each of the 4 triangles. given : (1/3) a^2 h = V, where V is a constant h = 3V/a^2 SA = total surface area covered by marble = 4(1/2) a h1 = 2(a)(h1) I can also see that : h1...

Math
yes, the pennies might be off slightly depending on the calculator. I did: .10/12 = +1 = y^x 480 = x 100000 = 5,370,066.31

Math
for your given starting value of 100,000 n = 40(12) = 480 i = .10/12 = .008333... amount = 100000(1.008333...)^480 = .... use your calculator, and yes, you can retire quite nicely.

Linear Algebra
let Q(x,y,z) be that closest point. then vector PQ = <x+5 , y-1 , z+4 > we also know the given line has direction vector <3, -2, 1> The shortest distance is when PQ is a perpendicular which means that the dot product between the two vectors is zero <x+5, y-1, z+...

algebra 2
The (-(2)/(3)) part is just (1/3)(-2) so we can write it as [ 27^(1/3) ]^-2 ----> 27^(1/3) is the cube root of 27 or 3 = 3^-2 = 1/3^2 = 1/9

math
let the quarterly rate be j (you will have to multiply j by 4 at the end to get the annual rate) 8700(1+j)^52 = 11100 (1+j)^52 = 1.275862.. take 52nd root, that is 1+j = 1.275862^(1/52) = ..... I matched one of your choices

Math
what is 100(1.085)^100 ??

math
since we are estimating, by the rule of 72 time = appr 72/7.3 = 9.86 so what is your estimation?

Math
Since M is the midpoint, area AMC = area BMC , they have the same height and base so BMC = (1/2)(56) = 28 now look at triangles AMD and CMD, they have the same height and their bases are in the ratio of 2 : 5 so triangle AMD = (2/7)(28) = 8 and triangle CMD = (5/7)(28) = 20

math
Jim's share --- 15x Jack's share --- 30x Tom's share ---- 3(15x) = 45x 15x+30x+45x = 360 90x = 360 x = .... find x, sub back into my definitions

math
sum to infinity = a/(1-r) but a/(1-r) = 4a divide both sides by a 1/(1-r) = 4 continue

@Emily - Calculus
Damon had answered this and 4 others for you, why are you switching names? I pointed out your error here. https://www.jiskha.com/display.cgi?id=1511687459

Calculus
Where did you get 4500 from ? Damon correctly found w = 5 and his cost equation was c = 4500/w + 18 w^2 = 4500/5 + 18(25) = 1350

math (correct my work to see if it's right please?
This is a complicated question. To use our general formulas, the payment period must coincide with the interest period. With your data it doesn't. Your payments are made semi-annually, while the interest is compounded biweekly. I will take the definition of "bi-weekly...

Math
it asked "how many square feet are added to the area" square feet are the units for area !

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