# Posts by Reiny

Total # Posts: 38,645

**Math**

let f(x) = x^3 + kx - 4 if x-2 is a factor, then f(2) = 0 f(2) = 8 + 2k - 4 = 0 2k = -4 k = -2

**Grade 6: money and measures**

combined rate is 15 litres per minute. amount in 6 min = 6(15) = 90 litres. volume in tank = 2400h cm^3, where h is the height = 2.4h litres, since 1000 c^3 = 1 litre so 2.4h = 90 h = 90/2.4 cm = 37.5 cm <--- the depth of water after both taps ran for 6 minutes b) Does the ...

**algebra**

let the time form 11:00 to the time of overtaking be t hrs distance gone by the truck = 54t distance gone by the van = 64(t-1) but they went the same distance, so ... 54t = 64(t-1) solve for t, and add it to 11:00

**math**

3s + 4j = 360 s + 3j = 220 -----> s = 220 - 3j sub that into the first and solve for j then find s

**algebra**

Plane's speed --- x mph wind speed ----- y mph 2(x-y) = 180 x-y = 90 1(x+y) = 180 x+y = 180 add them: 2x = 270 x = 135 back in x+y= 180 135+y=180 y = 45 state a proper conclusion.

**Algebra**

"and" usually suggests addition, e.g. what is 5 and 6 ? let the number be n "the sum of 4 times a number and 30" --> 4n+30 now twice that ---> 2(4n+30) = 8n + 60

**Cal 1**

S(-3) = 6(-27) + 8(9) + 5 = -85 S(-1) = 6(-1) + 8 + 5 = 7 avg velocity = (7 + 85)/(-1 + 3) = 46

**Math-Geometry**

Good job, you have 1. shown that opposite sides are parallel 2. adjacent sides form a right angle.

**Math-Geometry**

I would first of all plot the points. That would give you an idea which sides would form the rectangle. Since in a rectangle: 1. opposite sides are parallel, you can show this by finding the slopes 2. slopes of adjacent sides are negative reciprocals of each other. Use your ...

**Math**

or number of bags needed --- n amount of peanuts he bought 2n lbs number of bags he needs to buy = 2n/(5/6) = 12n/5 <---- must be a whole number the smallest number of n to make it so, is n = 5 number of bags needed = 5

**Math**

all 3 digit number divisible by 6: 102 108 114 120 126 132 138 144...978 984 990 996 How many of those are there ? (996-102)/6 + 1 = 150 or: An AG with a=102, d = 6, term(n) = 996 term(n) = a+(n-1)d 996 = 102 + 6(n-1) 6n-6 = 894 6n = 900 n = 150 Of those which ARE divisible by...

**math**

so shaded part = 6/20 = 3/10 or 30%

**math**

prob(yellow) = 1/6= x/36, so x = 6 , 6 yellows prob(orange) = 3/4 = y/36, so y = 27, 27 orange remaining 3 must be orange or 1/6 + 3/4 = 11/12 leaving 1/12 for the purple (1/12)(36) = 3 purple

**Maths**

midpoint of (-5,12) and (-1,-12) = ( (-5-1)/2 , (12-12)/2 )) = (-3, 0) I will use vectors to find the points of trisection i.e. in the ratio of 1:2 one point = (1/3)(7,10) + (2/3)(-8,-5) = (7/3, 10/3) + (-16/3 , -10/3) = (-9/3 , 0) = (-3,0) which is the midpoint of above other...

**Math**

In your sketch that you made, you will notice that the diagonals right-bisect each other, creating 4 congruent right-angled triangles. Each of them has angles 30:60:90 degrees the ratio of sides for such a triangle is 1:?3:2 where 2 is the hypotenuse Our hypotenuse is 8 so the...

**math**

I am sure you meant: f(x) = e^x b) f(6) = e^6 f(4) = e^4 avg rate of change from x=4 to x=6 = (e^6 - e^4)/(6-4) = ... , use your calculator

**Algebra**

invested at 2% --- x invested at 3% --- 7000-x .02x + .03(7000-x) = 184 carry on

**Trigonometry**

When you say "a 10 inch wheel" I will assume you have a radius of 10 arc length = rØ, where Ø is in radians 225° = 5?/4 radians 450 = r(5?/4) r = 360/? inches = appr 114.59 inches (big wheel) A point on the smaller wheel has to move 450 inches as ...

**Algebra**

4^4 x 8^8 x 16^16 are all powers of 2 = (2^2)^4 x (2^3)^8 x (2^4)^16 = 2^8 x 2^24 x 2^64 = 2^96 so what do you think?

**Algebra**

looks pretty standard to me. Perhaps you mean: |y|-2=0 |y| = 2 y = 2 or y = -2

**college algebra**

from your data, if h is the height above the water h = -4.9t^2 + 28t + 38 set h = 7 4.9t^2 - 28t - 31 = 0 use the quadratic formula to solve for t, use the positive result

**college math**

At a time of t hours after the action started, - distance remaining for the northbound car before reaching intersection is 3 - 20t - distance remaining for the westbound car before reaching the intersection is 4 - 30t let d be the distance between them d^2= (3-20t)^2 + (4-30t...

**Algebra (answer check)**

y = -x^2 + 2x + 5 the x of the vertex is -b/(2a) = -2/(-2) = 1 plug in x = -1, y = -1+2+5 = 6 vertex is (1,6) -4x^2+7x+5=0 4x^2 - 7x - 5 = 0 x = (7 ± ?129)/8 = appr (7±11)/8 = appr 18/8 or -4/8 or appr 2.5 or -1/2 your choice is good 5x^2 - 20 = 15x x^2 - 3x - 4...

**Math; Calculus**

from the given data: h = -16t^2 + 55t + 6 this is a parabola, we need its vertex. the t of the vertex is -b/(2a) = -55/-32 = 55/32 seconds plug that into equation to find max height it is in the air for h > 0 let's see when h = 0 0 = -16t^2 + 55t + 6 16t^2 - 55t - 6 = 0...

**Algebra**

speed of current --- y speed of swimming ---- x x+y = 5 x-y = 2 solve, I suggest adding them, etc

**Algebra**

amount of cashews --- x lbs amount of raisins ---- 4.5 - x lbs 2.5x + 1.25(4.5-x) = 2(4.5)

**math**

let the second be x ft long then the first is x+4.25 the third is x+2.24 x + x+4.25 + x+2.24 = 10 carry on

**math**

cost price = 525 18 eggs = 1.5 dozen selling price = 23.5(26) = ... profit or loss = selling price - 525 = .... percent profit = ....

**math**

collins meant: (a+b+c)/2 = s

**number base help plz**

Steve is simply using the definition of a number with a different base. Just like 57810 = 5(10^2) + 7(10^1) + 8(10^0) 1234 = 1(4^2) + 2(4) + 3 = 16 + 8 + 3 = 24 + 3 ---> Steve noticed the multiples of 8 = 3(8) + 3 = 338

**Math**

Say what ?

**algebra**

your function is a straight line - from your equation we can tell that the slope is -2 and the line passes through (-8,7) All you need is another point and you can draw it. Why not pick something nice like x = 0 So we get: y-7 = -2(8) y = -16+7 = -9 take over

**Calculus**

A rough sketch of the two functions y = x , and y = 1+sinx will show that y = x clearly crosses y = 1 + sinx only once. So your statement is not correct. evidence: http://www.wolframalpha.com/input/?i=solve+x%3D1%2Bsin(x)

**Algebra**

x/3 + 5 = 3x/2 times 6. 2x + 30 = 9x 7x = 30 x = 30/7 check: (1/3)(30/7) + 5 = 45/7 3/2(30/7) = 45/7 my answer is correct

**math**

They do not intersect at (3,4) (3,4) does not satisfy g(x) = 2^x - 1 RS = 2^3 - 1 = 7 LS = 4, no good (3,4) work in f(x) = -5/3x + 9 RS = -5/3(3) + 9 = 4 So it does work in the other equation. did you mean g(x) = 2^(x-1) ?? RS = 2^2 = 4 = RS you must have meant that! so ...

**math**

Did you make a sketch?? The difference in their connection points is 4 m. and you have a triangle with base 10, height 4 and missing hypotenuse x^2 = 4^2 + 10^2 carry on

**Math**

Maria "guessed" correctly, I got the same answer. So none of the answers supplied are correct. Either typo or misprint.

**Matj**

I will assume the difference to be between pairs of coupons possible cases: 5,1 6,1 6,2 7,1 7,2 7,3 8,1 8,2 8,3 8,4 9,1 9,2 9,3 9,4 9,5 10,1 10,2 10,3 10,4 10,5 10,6 total 21 number of pairs = C(10,2) = 45 prob(of your event) = 21/45 = 7/15

**math**

Hint: The diagonals of a rhombus right-bisect each other. Another hint: Make a sketch. What type of triangles do you see? Do you know the legs of those triangles?

**Math**

What is the LCM of 2, 6, and 9 ?

**algebra**

time spent cyling --- x hrs times spent running --- (2.5 - x) hrs 10x + 6(2.5-x) = 21 carry on

**math**

Scott is absolutely right, if you had taken the 10 seconds to complete his calculations.

**n**

Let's use a sine curve, we could use a cosine as well amplitude is 10, so h = 10sin kt the period is 6 minutes, so 2?/k = 6 ----> k = ?/3 sofar: h = 10sin (?/3 t) this has a min of -10, but our min is to be +1, so we have to raise everything up by 11 so far: h = 10sin...

**Math**

Number of Yen remaining = 110682 - 87438.78 = 23243.22 $1100US = 110682 Yen 1 Yen = 1100/110682 = $.009938382 so 23243.22 Yen = .009938382(23243.22) = $231 or 1100/110682 = x/23243.22 x = 231

**math**

correct, only a = 0 if x = 0 then in x/y=2 0/y = 2, which cannot be, so x ? 0 if y = 0, we would be dividing by zero to get 2, which is rather silly, so y ? 0 if a = 0, x/y =2 has nothing to do with it, but x*y*0 = 0, which is true

**math**

size of original piece of material: x cm by x cm after cut-out base is (x-8) by (x-8) height = x V = x(x-8)^2 = 576 x^3 - 16x^2 + 64x - 576 = 0 Nasty equation to solve. Have you learned any methods to solve a cubic? Newton's Method is probably the best way, but you have to...

**Algebra**

x=3, so Alysia is 3 and Adam is 33 3+33 = 36

**Algebra**

Ms. Sue meant to say: x + 30+x = 36

**Algebra 1**

Yes, except since this is money in dollars you would round it to the nearest cent. $500,637.91

**Algebra 1**

What is 20000(1.05)^66 ?

**Math**

rate of first ---- x rate of 2nd ---- y 1500(3)x - 1500(3)y = 13.50 x-y = .003 the difference is .3%

**polynomial**

I don't understand how looking at the graph of y=2x³+x²+x+8 , which does not have a "nice" rational solution, will help you in solving y = 2x^3 + x^2 - x + 5. The latter also has an irrational solution. http://www.wolframalpha.com/input/?i=y%3D2x%C2%B3%...

**Maths**

you are solving, 6750(1.05)^t = 8000 1.05^t = 1.185185.. take log of both sides, and use log rules t = log 1.185185.../log 1.05 = 3.482239 so that is 3 years and .482239 years multiply the decimal part by 12 to get 3 years, 5.7868.. months so 3 years, 5 months and .7868 months...

**maths**

graphing utility?? why? 6sinx + 3cosx = 0 divide by cosx 6sinx/cosx + 3 = 0 6tanx = -3 tanx = -1/2 we know that the tangent is negative in II or IV and we know tan (.4636) = +.5 x = ?-.4636 = appr 2.678 or x = 2? - .4636 = appr 5.820 If you insist: http://www.wolframalpha.com/...

**Math**

12.5 litres takes the car 168.75 km then 1 L takes the car 168.75/12.5 km then 15 L will take the car .....

**Math**

Why do you think this question might deal with the concept of a Lowest Common Multiple ?

**Math**

How many square cm are there in 1 square metre? - then how many in 1/2 square metre ?

**Math**

simplify and re-arrange ... y-5 = (2/7)(x-11)

**Math**

of course it isn't right x = 3 would be a vertical line. A quick sketch will show you that your 2 points do not lie along a vertical line slope = m = (-8-8)/(5-3) = -16/2 = -8 equation: y-8 = -8(x-3) re-arrange to whatever form you learned.

**Slopes**

slope = m = (7-4)/(-5-0) = ... once you find m, replace it in the equation y-4 = m(x+6) arrange into the form that you are familiar with.

**Algebra II**

Don't understand your question. Don't understand your answer.

**Math**

p5^y + 5^-y = 5 p5^y + 1/5^y = 5 now replace px + 1/x = 5 times x px^2 + 1 = 5x px^2 - 5x + 1 = 0 which is what we want

**calculus**

V= (4/3)? r^3 dV/dt = 4? r^2 dr/dt when V = 64 64 = (4/3)? r^3 48/? = r^3 r = (48/?)^(1/3) = appr 2.4814 ---> I stored the 10 decimal answer in dV/dt = 4? r^2 dr/dt 20 = 4?(2.4814..)^2 dr/dt dr/dt = appr .2585 inches/min

**Math**

You must know the binomial expansion and the general term of the expansion!! 5th term = C(9,4) (4^4)(-x/5)^5 = 126 (256)(-x^5)/3125 = -32256/3125 x^5 oops, just did in descending powers, so C(9,5) 4^5 (-x/5)^4 = 126(1024)(x^4/625) = 129024/625 x^4 , in ascending order

**Maths**

distance at original speed = (1/4)(60 km = 15 km time at reduced speed = 15/36 hours = 5/12 hr = 25 minutes

**Geometry**

clearly the largest circle will have a diameter of 4 ft, or a radius of 2 ft area = ?(2^2) = 4? ft^2 = ...... In this time of calculators, using 3.14 for ? and then rounding off that rounded constant is rather silly. Most calculators have a special key for ?, use it.

**Maths**

correct your spelling and incomprehensible gibberish

**Math**

Yes, could have been easily checked by taking 20% of it.

**Math**

regular price ---- x it said the 20% discount came to $15 well, .2x = 15 x = 15/.2 = ......

**Aice Math**

(5-x/2)^6 I assume you know how to expand using the binomial theorem. (5-x/2)^6 = 5^6 + 5^5(-x/2) + 5^4(-x/2)^2 + ... = 15625 - (3125/2)x + (625/4)x^2 + ... so matching up terms: -3125x/2 = px ----> p = -3125/2 (625/4)x^2 = qx^2 ----> q = 625/4

**Math**

Using the binomial expansion (x^2-b/x)^4 = (x^2)^4 + 4(x^2)^3 (-b/x) + 6(x^2)^2 (-b/x)^2 + 4(x^2) (-b/x)^3 + (-b/x)^4 = 4x^8 - 4x^6 (b/x) + 6x^4 b^2/x^2 - ... = 4x^8 - 4x^5 b + 6x^2 b^2 - ... so the term containing x^2 is 6x^2 b^2 , which is equal to 294 6v^2 = 294 b^2 = 49 b...

**Math**

I = PRT you told me I = 1/9P --> P = 9I you told me r = t, where r is a stated percent I = 9I(r/100)(r) 1 = (9/100)r^2 r^2 = 100/9 r = 10/3 = 3.3333.. the rate is 3 1/3% check: suppose we have $1000 for 10/3 years at 3 1/3 % I = 1000(10/3)(10/300) = 111.11 and 1/9 of 1000...

**algebra**

Compare this question to your previous one. What is your answer ?

**algebra**

The product of 5 and 6 = 30 the product of 7 and 8 = 56 the product of 31 and g = 31g

**Math**

Your post makes absolutely no sense to me.

**Maths**

equation: x^2 - bx + c roots: ?a and ?b sum of roots = ?a + ?b = b product or roots = ?a?b = c --> ab = c^2 ?a + ?b = b square both sides (?a + ?b)^2 = b^2 a + 2?(ab) + b = b^2 then a+b = b^2 - 2?(ab) = b^2 - 2c DONE a^2 + b^2 = (a+b)^2 - 2ab = (b^2 - 2c)^2 - 2c^2 treat ...

**correction - Algebra 1**

Eddie's answer is not correct after 8 months, x = 8 y = 3(2^8) = 3(256) = 768 or: 3 6 12 24 48 96 192 384 768 now: 3 after 1 month -- 6 ---> 3(2^1) after 2 months -- 12 --> 3(2^2) ... after 8 months -- 768 = 3(2^8)

**Math**

(w^-2 j^-4) ^-3 (f^7 f^3) = (w^6)(j^12)(f^10)

**Math**

3 apples + 2 oranges + 2 apples - 1 orange = 5 apples + 1 orange 3x + 2y + 2x - y = 5x + y 3?3 + 2?5 + 2?3 - ?5 = 5?3 + ?5

**Ms. Sue! Math**

You should know that linear functions can be written in the form y = mx + b , (the y-intercept form), except vertical lines which have the form x = c so let's pick any slope from -1 to 0. How about m = -1/4 Equations with such a slope are y = (-1/4)x + 7 or y = (-1/4)x + 3...

**Algebra**

Extraneous roots mostly occur after squaring an equation. Since you verified your solution by subbing it back into the original equation, there are no extraneous roots LS = x/(5x+4) = (-6/7) / (5(-6/7) + 4) = (-6/7) / (-2/7) = (-6/7)(-7/2) = 42/14 = 3 = RS

**maths equation too hard**

you mean Newton's "iterative" method sure, why not? x^3 = 3^x let y = x^3 - 3^x dy/dx = 3x^2 - ln3(3^x) newx= x - (x^3 - 3^x)/(3x^2 - ln3 (3^x) ) start with x = 2.9 newx = appr 3.0471... using that newx = appr 3.0081... using that newx = appr 3.00006996 , not bad

**maths equation too hard**

Steve did this for you earlier. What did you not like about his reply? http://www.jiskha.com/display.cgi?id=1486532823 You could graph: y = x^3 and y = 3^x and see where they cross

**Maths**

prob(defect) = .05 prob(no defect) = .95 a) I read that as exactly 10 out of the 100 = C(100,10) (.05)^10 (.95)^90 = appr .0167, according to my calculator b) unreasonable question, you would have to do prob(exactly 0 defective) + prob(1 effective) + ...+ prob(10 defective) If...

**Mathematics**

case 1: the circumference of the cylinder is 30, and the height is 18 2?r = 30 r = 15/? V = ?(15/?)^2 (18) = 4050/? case 2: the circumference is 18 and the height is 30 2?r = 18 r = 9/? V = ?(9/?)^2 (30) = 2430/? volume of case1 : volume of case2 = 4050/? : 2430/? = 5 : 3 Just...

**math**

I read that as area = -x^2 + 7x + 30 this has to be positive, so -x^2 + 7x + 30 > 0 x^2 - 7x - 30 < 0 (x - 10)(x+3) < 0 so you know that -3 < x < 10 that is, x must be between -3 and 10 Possible values : let x = 1, then area = -1 + 7 + 30 = 36 the rectangle is 1...

**Continuity Calculus Help**

limit ?( (x^2 - 64)/(x-8)) as x -->8 = lim ?( (x-8)x+8)/(x-8) , as x ---> 8 = lim ?(x+8) , as x---> 8 = ?16 = 4

**Math**

I used to illustrate this problem to my students by taking a cone-shaped drinking cup from a water dispenser and cutting it open to show just that kind of a sector. It was easy to see that the arc of that sector becomes the circular base of the cone, so .... since the angle is...

**Calculus-derivatives**

Bob forgot to find the derivative first dy/dx = 12x + 4 12x+4 = -2 12x = -8 x = -8/12 = -2/3 f(-2/3) = 6(4/9) + 4(-2/3) - 9 = -25/3 We have a parabola shown below with a tangent at (-2/3 , -25/3) having a slope of -2 http://www.wolframalpha.com/input/?i=plot+y%3D6x%5E2%2B4x-9

**Math interest**

So the interest on your $5000 should amount to $5000 5000(.05)t = 5000 t = 1/.05 = 20 or, interest for 1 year = 5000(.05)(1) = $250 Since that stays constant (simple interest), it would take 5000/250 or 20 years

**physics/calculus**

h = -16t^2 + 12t + 600 a) sub in t=6 b) set -16t^2 + 12t + 600 = 0 divide by -4 4t^2 - 3t - 150 = 0 use the formula to find t = .... (use the positive answer only) c) v = -32t + 12 plug in your answer from b)

**math**

father's age ----- x Mark's age ---- x-32 x + x-32 = 72 easy to solve for x

**Maths**

first term is 3+2a common difference = d = 3+4a - (3+2a) = 2a term(5) = first term +4d = 3+2a + 4(2a) = 73 10a = 70 a = 7 check: d = 14 terms are: 17, 31, 45, 59, 73 all looks good

**Math**

sum of interior angles of a hexagon = 180(6-2) = 720 , from 180(n-2) 5x + 155 = 720 5x = 564 x = 113°

**Maths**

taking differences 1 2 1 5 3 2 11 6 3 1 21 10 4 1 the third differences are constant, so we could represent it as a cubic function. Lots of work, so I went to Wolfram: http://www.wolframalpha.com/input/?i=pattern+%7B1,2,5,11,21,....%7D

**Algebra**

1st term --- a 15th term = a + 14d = 9a 14d = 8a d = 4a/7 sum(35) = (35/2)(2a + 34d) = (35/2)(2a + 34(4a/7) = (35/2)(150a/7) = 375a

**Algebra**

a=10 a+(n-1)d = 62 10 + nd - d = 62 nd-d=52 n=(52+d)/d or d = 52/(n-1) sum(n) = (n/2)(2a + (n-1)d) = (n/2)(20 + (n-1)(52)/(n-1)) = (n/2)(20 + 52) = (n/2)(72) = 36n sum(n) = 36n so sum(n) varies directly as the number of terms

**Math**

33750 = 50*25*27 = 2*3*3*3*5*5*5*5 So the question becomes: in how many ways can these digits be arranged We have 8 digits , of which 4 are the same and another 3 are the same number of arrangements = 8!/(3!4!) = 280 e.g. 23535355 would be one of them

**Math**

please use t^2 to show exponents. the * symbol is traditionally used for a multiplication sign h = -16t^2 + 40t + 3 , note the - sign! dh/dt = -32t + 40 = 0 for a max of h 32t = 40 t = 40/32 = 1.25 seconds when t = 1.25 h = -16(1.25)^2 + 40(1.25) + 3= 28 when it hits the ...

**Algebra**

3b = a(B + b) 3b = aB + ab 3b - ab = aB (3b - ab)/a = B