# 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**

2.6Ã—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/(2.6Ã—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 !