Saturday

April 30, 2016
Total # Posts: 34,395

**Math(Quadratic Functions)**

For days ???? since the x-intercepts of a function are the same as the roots of the corresponding equation x=7 ----> a factor of (x-7) x=-2 ---> a factor of (x+2) so f(x) = a(x-7)(x+2) we are told that (0,5) lies on it, so 5 = a(-7)(2) a = -5/14 f(x) = (-5/14)(x-7)(x+2) ...
*April 25, 2016*

**Roots, complex numbers**

This question must be a popular one. Did it yesterday http://www.jiskha.com/display.cgi?id=1461490844
*April 25, 2016*

**Math**

A = 800(3)^3.12 = appr 24644 bacteria
*April 25, 2016*

**Math**

90000 = 45000(1.075)^n 2 = 1.075^n log both sides log 2 = nlog1.075 n = log2/log1.075 = appr 8.58 years
*April 25, 2016*

**Calculus**

let the height along the wall be y m let the distance from the wall along the ground be x x^2 + y^2 = 6^2 2x dx/dt + 2y dy/dt = 0 x dx/dt + y dy/dt = 0 when x = 4 16 + y^2 = 36 y = √20 , and dx/dt = 1 4(1) + √20 dy/dt = 0 dy/dt = -4/√20 m/sec the negative ...
*April 25, 2016*

**algebra 2**

see this similar question http://www.jiskha.com/display.cgi?id=1461613740
*April 25, 2016*

**algebra 2**

see this similar question http://www.jiskha.com/display.cgi?id=1461613740
*April 25, 2016*

**math**

volume = πr^2 h = π(25)(10) cm^3 = appr 785.4 cm^3 by the beauty of the metric system, that would be .7854 kg of water so the empty container weighs 2 - .7854 or aprr 1.21 kg
*April 25, 2016*

**algebra 2**

follow the same steps I just showed you in your previous post
*April 25, 2016*

**algebra 2**

you will need to find the vertex of this parabola, a) and c) can then be answered the t of the vertex is -b/(2a) = -64/-32 = 2 s(2) -16(4) + 64(2) + 80 = 144 the vertex is (2,144), what does that vertex tell you? b) when it reaches the ground, s = 0 -16t^2 + 64t + 80 = 0 ...
*April 25, 2016*

**Math/Precsl**

log(8y+12)=2 <-----> 8y + 12 = 10^2 8y = 88 y = 11
*April 25, 2016*

**math**

number of 100 rupee winners ---- x number of 25 rupee winners --- 63-x 100x + 25(63-x) = 3000 100x + 1575 - 25x = 3000 75x = 1425 x = 19 state your conclusion
*April 25, 2016*

**Math**

amount at 3% --- x amount at 8% --- 9000-x .03x + .08(9000-x) = 580 solve for x
*April 25, 2016*

**geometric sequences**

to find r, (90/17) / 9 = 10/17 and (900/289) / (90/17) = 10/17 a = 9 r = 10/17 term(n) = 9(10/17)^(n-1) term(10) = 9(10/17)^9 = appr .07589
*April 25, 2016*

**Math/precal**

for the y-intercept, let x = 0 y = 7b^0 = 7 for the x-intercept, let y = 0 0 = 7b^x no solution for x (normally we would take the log of both sides, but we can't take log0)
*April 25, 2016*

**Maths**

a + ar = 9 a(1+r) = 9 a = 9/(1+r) a/(1-r) = 12 a = 12(1-r) 12(1-r) = 9/(1+r) 1 - r^2 = 3/4 4 - r^2 = 3 -r^2 = -1 r = ± 1
*April 25, 2016*

**maths**

Just add them, the 1/y's will drop out 2/x = 6 6x = 2 x = 1/3 sub into the original first 1/y + 1/(1/3) = 5 1/y + 3 = 5 1/y = 2 y = 1/2
*April 25, 2016*

**Math**

For the volume I got 538.8 ft^3 to the nearest tenth of a foot. (you should really use a better value for π than 3.14, most calculators have it built in correct to 10 decimals) Your SA is made up of 2 circles + a rectangle SA = 2π(3.5)^2 + 2π(3.5) = 384.8 ft^2
*April 25, 2016*

**Algebra**

Where does the 4 come from? There are 36 cookies in 6 bags, so the number of cookies in each bag = 36/6 = 6
*April 25, 2016*

**Calculus**

let the length of line be L ft let the horizontal distance of the boat from the dock be x ft You have a right-angled triangle, thus x^2 + 3^2 = L^2 2x dx/dt = 2L dL/dt for the given case: x = 4 L^2 = 4^2 + 3^2 L = 5 2(4)(7) = 2L dL/dt dL/dt = 2(5)/(56) = 5/28 ft/s
*April 25, 2016*

**MATH**

What am I missing here? Isn't the circumference of the cylinder simply the circumference of the circle? which would be 3.2π inches. The height of 8 inches would have nothing to do with it.
*April 25, 2016*

**Math**

volume of cubes is proportioanl to the cube of their corresponding sides so V/729 = 4^3/3^3 27V = 46656 V = 1728 notice the sides increased by a ratio of 4:3 and 1728/729 = 64/27 = 4^3 : 3^3
*April 25, 2016*

**Algebra**

Ok, multiply the first by 4, then subtract the 2nd multiply the first by 3, then subtract the third. Now you have two equations with y's and z's carry on
*April 25, 2016*

**Algebra**

Why eliminate x when the obvious choice would be to eliminate z ?? #2 - #1 ---> 3x - 4y = 1 ** #2 - #3 ---> x - y = 2 or x = y+2 sub that into ** 3(y+2) - 4y = 1 3y + 6 - 4y = 1 -y = -5 y = 5 , then x = 7 back into #1: 7 + 5 + 5z = 2 5z = -10 z = -2 so the solution is (7...
*April 25, 2016*

**Maths**

2nd term = a+d 7th term = a+6d a+d + a+6d = 20 2a + 7d = 20 ** (a+d)/(a+6d) = 1/3 3a + 3d = a + 6d 2a = 3d *** sub that into ** 3d + 7d = 20 10d = 20 d = 2 then 2a = 6 a = 3 "Calculate The Sum Of The 1st Terms Of The G.P" HUH? I thought we were dealing with an AP. ...
*April 25, 2016*

**algebra**

short leg --- x longer leg --- x+2 x^2 + (x+2)^2 = 8^2 x^2 + x^2 + 4x + 4 - 64 = 0 2x^2 + 4x - 60 = 0 x^2 + 2x - 30 = 0 let's complete the square: x^2 + 2x + 1 = 30+1 = 31 (x+1)^2 = 31 x+1 = ± √31 x = -1 ± √31 but x has to be positive, so x = &#...
*April 24, 2016*

**Math**

take 1/2 of the -7 and square that so (-7/2)^2 = 49/4 we should add 49/4 to both sides
*April 24, 2016*

**Math**

herding my way through that first "sentence" .... I got the obvious: h = -16t^2 + 96t + 3 a) plug in t = 0 b) find the vertex and both b) and c) are answered.
*April 24, 2016*

**Math**

what is 7! ?
*April 24, 2016*

**Math**

That's a lot of fencing.. No diagram can be used in this format. Check your post for typos and grammar before posting.
*April 24, 2016*

**Math**

3 -> 9 5 -> 25 2 -> ? 7 -> 49 if x is input and y is output, it sure looks like y = x^2
*April 24, 2016*

**Math**

prob(all 4 boys) = (1/4)^4 = 1/256 = .... you do the button-pushing
*April 24, 2016*

**Algebra 1**

No, your choice is not correct It is B If I multiply the first equation by -2, don't I get the 2nd equation??? So one is a multiple of the other.
*April 24, 2016*

**Algebra 1**

let's look at the 2nd equation. −2x − 6y = 2 multiply by -1 2x + 6y = -2 divide by 2 x + 3y = -1 , well, isn't that the first equation??? So, do you want to change your choice?
*April 24, 2016*

**Math**

the diameter of the large cookie is 4 times that of the smaller cookie. The area is proportional to the square of their diameter, (or their radii) so the larger one is 16 times the area, thus it should cost 16 times the smaller, or 80 cents. B would be my choice.
*April 24, 2016*

**Math**

you are right
*April 24, 2016*

**Algebra**

I will assume from looking at the answers that you meant y = √(3x+3) Since we only take √'s of non-negative numbers, 3x+3 ≥ 0 3x ≥ -3 x ≥ -1
*April 24, 2016*

**calculus**

I would simplify it first f(x) = 1 + 9/x - 3/x^2 f ' (x) = -9/x^2 + 6/x^3 = 0 for a max/min 6/x^3 = 9/x^2 9x^3= 6x^2 9x^3 - 6x^2 = 0 3x^2(3x - 2) = 0 x = 0 , but that would make f(x) undefined, or x = 3/2 f(3/2) = 1 + 9/(3/2) - 3/(9/4) = 1 + 6 - 4/3 = 17/3
*April 24, 2016*

**calculus**

f(x) = 2x(x-1)^(-1/2) f ' (x) = 2x(-1/2)(x-1)^(-3/2) + 2(x-1)^(-1/2) = 0 for critical values, (max/mins) x/(x-1)^(3/2) = 2/(x-1)^(1/2) times (x-1)^(3/2) x = 2(x-1) x = 2x - 2 x = 2 f(2) = 4/sqrt(1) = 4 the critical number, in this case a minimum is (2,4)
*April 24, 2016*

**Anti-Derivatives**

distance = -16t^2 + h velocity = -32t but we know that is -170 so -32t = -170 t = 85/16 seconds so how far his it fallen in 85/16 seconds? distance = 16(85/16)^2 = 7225/16 ft or appr 451.56 ft
*April 24, 2016*

**Algebra**

original amount -- x x - (x/8 + x/5 + x/10) = 15 x - 17x/40 = 15 40x - 17x = 600 23x = 600 x = 26.09 , correct to 2 decimals
*April 24, 2016*

**Math**

what is 270/450 ?
*April 24, 2016*

**math**

ar^2 + ar^3 = -4/3 ar^2(1 + r) = -4/3 ** ar^3 + ar^4 = -4/9 ar^3(1 + r) = -4/9 *** divide *** by ** ar^3(1+r)/(ar^2(1+r)) = (-4/9) / (-4/3) r = 1/3 plug back into ** a(1/3)^2 (1 + 1/3) = -4/3 a(1/9)(4/3) = -4/3 a = -9 term(6) = ar^5 = -9(1/3)^5 = -1/27 check: sequence is: -9...
*April 24, 2016*

**math**

done here http://www.jiskha.com/display.cgi?id=1461503265
*April 24, 2016*

**Maths**

what is 20 - (2/5)(20) - (1/5)(20) ? or they ate 3/5 of your chocs so you have 2/5 of 20 left
*April 24, 2016*

**math**

P = k L^2 when P=108, L=6 108 = 36K k = 3 P = 3L^2 75 = 3L^2 L^2 = 25 L = 5
*April 24, 2016*

**math**

you are choosing all possible pairs from 40 to shake hands, that would be C(40,2) = 780 or think of it this way: each of the 40 people can shake hands with 39 other people which is 40x39 = 1560. BUT, that includes identical pairs, e.g. A shaking with B is the same as B shaking...
*April 24, 2016*

**math**

Your Taylor expansion of f(x) is correct I disagree with your derivative, it should be (-1/4)((1/16 + x)^(-5/4) why not just integrate ʃ(1/16 +x)^(-1/4) dx to get (4/3)(1/16 + x)^(3/4) + C
*April 24, 2016*

**maths**

let z^5 = rcosθ + rsinθ i = -1 + 0 we have r = 1 θ = 180° so z^5 = 1(cos180° + isin180°) by de Moivre's theorme z = 1^(1/5)(cos 180/5 + i sin180/5) = 1(cos 36° + isin36°) or cis36° repeating at 360/5 or 72° z = cis 36° z = ...
*April 24, 2016*

**math**

(3.3x10^3)(1.8x10^4) = 5.94 x 10^7
*April 23, 2016*

**Math**

the prob that the biased coin is tails = .4 so prob(3tails) = .4^3 = .064 So what do you think?
*April 23, 2016*

**Pre-Calc**

we can only take logs of positive numbers so 3x-8 > 0 3x > 8 x > 8/3 I will let you write it in the new-fangled notation. In my time we used the above simple way of stating it.
*April 23, 2016*

**maths**

x^3 + y^3 = 72 x^2 - y^2 = 12 We could just do this by listing the cubes less than 72 : 1, 8, 27, 64 the only combination for a sum of 72 is 8 + 64 so x=2, y=4 so the numbers are 2 and 4 is the difference property ok? is 16-4 = 12 ?? YES
*April 23, 2016*

**math**

the largest prime < 50 is 47 the smallest composite > 10 is 12 so what is the difference between those ?
*April 23, 2016*

**Math**

s = t(t^2 - 8t + 16) = t^3 - 8t^2 + 16t v = 3t^2 - 16t + 16 a = 6t - 16 for zero of a, 6t-16=0 t = 16/6 = 8/3 seconds when t = 8/3 v = 3(64/9) - 16(8/3) + 16 = -16/3 s = (8/3)(8/3 - 4)^2 = 128/27 work these answers in with your concluding statements
*April 23, 2016*

**maths**

When it falls down, the distance is zero so 0 = 30t - 4.9t^2 t(30 - 4.9t) = 0 t = 0 , that would be at the beginning or t = 30/4.9 or appr. 6.12 seconds 2nd part: 20 = 30t - 4.9t^2 4.9t^2 - 30t + 20 = 0 t = (30 ± √508)/9.8 = .761 seconds, on its way up or = 5.36 ...
*April 23, 2016*

**algebra**

did you mean an = (3)^(n−1) ? if so, follow the same steps I showed you in your previous post.
*April 23, 2016*

**sequence**

If n = 1, term(1) = 4 if n = 2, term(2) = 8 if n = 3, term(3) = 12 etc
*April 23, 2016*

**Math**

Unless I see an obvious identity I can replace, I usually change everything to sines and cosines. LS = (1/cosx - cosx)/(sinx/cosx - sinx) = ( 1 - cos^2 x)/cosx )/( (sinx - sinxcosx)/cosx ) = ( 1 - cos^2 x)/cosx )* cosx/( (sinx - sinxcosx) = (1 - cos^2 x)/(sinx(1 - cosx)) = (1...
*April 23, 2016*

**math**

shares bought at RS140 --- x shares bought at RS125 --- y amount invested at 6% --- 140x amount invested at 5% --- 125y 140x + 125y = 6750 ** .06(140x) + .05(125y) = 280 8.4x + 6.25y = 280 times 20 168x + 125y = 5600 *** subtract ** from *** 28x = -1150 not possible. Unless ...
*April 23, 2016*

**geomentry**

I drew a line AB, with A to the left of B I marked P and Q on the left side of the midpoint. "Point P divides AB in the ratio 2:3" ---> let AP = 2x and PB = 3x then AB = 5x "Q divides AB in the ratio 3:4" --> let AQ = 3y and QB = 4y then AB = 7y ...
*April 23, 2016*

**Maths**

The altitude in an isosceles triangle right-bisects the base, so BD = DC let BD = x then BC = 2x AB = 4x in the right-triangle ABD AD^2 + x^2 = (4x)^2 = 16x^2 AD^2 = 15x^2 AD^2 = 15BD^2 , not 15 BC^2 as you stated.
*April 23, 2016*

**Finance**

amount at 4% compounded quarterly = 1500(1.01)^20 = .. amount at 4% compounded semi-annually = 1500(1.02)^10 = .. amount at 4% per annum = 1500(1.04)^5 = ...
*April 23, 2016*

**Math**

let the number be x x/2 + 4 = 10 carry on
*April 22, 2016*

**Math, NEEDS HELP EMEDIETLY!**

To me the method of your solution is much more important than the answer. Since your method makes no sense, it would benefit you to actually care more about how the answer is obtained. 7/12 of the students take martial arts, and (7/12)(144) = 84 sample size?? well, how many ...
*April 22, 2016*

**Science/Math**

a = -4 m/s^2 v = -4t + k when t = 0, v = 3- thus k = 30 v = -4t + 30 when the vehicle stops, v = 0 0 = -4t + 30 4t = 30 t = 30/4 or 7.5 seconds
*April 22, 2016*

**Calculus Help**

lim (5 - √x)/(x-25) as x ---> 25 = lim (5-√x)/((√x-5)(√x+5)) = lim -1/(√x+5) as x ---> 25 = -1/(5+5) = -1/10
*April 22, 2016*

**math**

√-1 , also called i , is a complex or imaginary number. Every other complex number can be expressed in terms of i
*April 22, 2016*

**math**

Your start would be to make a diagram of the right-angled triangle. Then you should see that if L is the length of the ladder, sin76° = 10/L L = 10/sin76° = 10.306 m
*April 22, 2016*

**Mathematics**

let u = e^x then u^2 = e^(2x) and du/dx = e^x dx = du/e^x = du/u ʃ e^x /sqrt[e^(2x) -1] dx = ʃ u/√(u^2 - 1) du/u = ʃ 1/√(u^2 - 1) du = ln (√(u^2 - 1) + u) , from my old integration formulas = ln((√(e^(2x) - 1) + e^x) + C
*April 22, 2016*

**Geometry**

circumference of whole circle = 2pi r = 6pi so : arc/6pi = 20/360 arc = 120pi/360 = pi/3 = appr 1.047 units or arc = rθ , where θ is the angle in radians so 20 degrees = 20pi/180 radians = pi/9 arc = 3(pi/9) = pi/3 , same as above
*April 22, 2016*

**Math (Calculus)**

Yes, it does work, let's set -6x^2+20.4x+202.275 = 0 6x^2 - 20.4x - 202.275 = 0 I used the formula and got x = 7.75 or x = -4.35 remember that the function is increasing when the derivative is postive, and decreasing when .... so the function is increasing for -4.35 < x...
*April 21, 2016*

**Math Pythagorean**

northern direction = 3 - 1 + 2 = 4 eastern direction = 2 + 4 = 6 h^2 = 4^2 + 6^2 = 52 the hypotenuse is √52 = appr. 7.2 miles
*April 21, 2016*

**Math**

older sister --- x younger sister --- 19-x in 5 years: (x+5)(24-x) = 208 -x^2 + 19x + 120 - 208 = 0 x^2 - 19x + 88 = 0 (x-11)(x-8) = 0 x = 11 or x = 8 older sis is 11, younger is 8 check: in 5 years: 16(13) = 208 , all is good
*April 21, 2016*

**Math**

expand: (x-5) log19= (x+2) log3 xlog19 - 5log19 = xlog3 + 2log3 xlog19 - xlog3 = 2log3 + 5log19 x(log19 - log3) = 2log3 + 5log10 x = (2log3 + 5log19)/(log19 - log3) = appr 9.1663
*April 21, 2016*

**algebra 2**

(21 − 4i) − (16 + 7i) + 28i just like basic algebra ... = 21 - 4i - 16 - 7i + 28i = 5 + 17i
*April 21, 2016*

**math 1**

8p^2 + 56p + 98 = 2(4p^2 + 28p + 49) = 2(2p + 7)^2 ----> notice the perfect square in the 2nd last line
*April 21, 2016*

**Math**

–1, 9, 19, 29, . . . looks like you are adding 10 each time, so the next 3 terms would be 39, 49, 59 None of your choices match that, unless C contains a typo Your choice of D is definitely wrong
*April 21, 2016*

**Math- Check my answers please!**

#3 4^4/4^6 = 1/4^2 = 1/16 #5 7^4/7^2 = 7^2 = 49 #6 –2r(8r + 5) = -16r^2 - 10r #7 4a(a^2 + 7a + 4) = 4a^3 + 28a^2 + 16a #8 (2y-3)(3y-2) = 6y^2 - 4y - 9y + 6 = 6y^2 - 13y + 6 Looks like somebody has some major review ahead of them.
*April 21, 2016*

**maths-I only need the solution**

To me, the actual solution is less important than the method of getting that solution. We should assume that all values would be whole numbers. More than that, all numbers would have to be perfect squares or else we would have decimals suppose we subtract the second from the ...
*April 21, 2016*

**Math**

What part of yesterdays solution did you not like? http://www.jiskha.com/display.cgi?id=1461201861
*April 21, 2016*

**math0**

We have to know how many gumballs there are and how many of each colour.
*April 21, 2016*

**maths**

P = k/Q + C given: P=3, Q=9 3 = k/9 + C 27 = K + 9C *** P=9, Q = 18 9 = k/18 + C 162 = k + 18C ** subtract *** from ** 135 = 9C C = 15 in *** k+135 = 27 k = -108 P = -108/Q + 15 so when Q = 12 P = -108/12 + 15 = 6
*April 21, 2016*

**sequences and Series**

I have now answered 6 of your questions without any effort on your part showing me that you have attempted these. What do you think about this one? Why not just follow the rules of the sequence as you stated them?
*April 21, 2016*

**Maths**

Ok so far simplify your expression a bit and use proper brackets = 11Ck (1/4)^(11-k) (-16)^k x^(11-k) y^k so y^k <----> y^4 thus k = 4 the coefficient comes from 11Ck (1/4)^(11-k) (-16)^k = 11C4 (1/4)^7 (-16)^4 = 330(1/16384)(65536) = 1320 confirmation: https://www....
*April 21, 2016*

**sequences and Series**

geeesh, why not just list the berries handed out for each house? There are only 5 identical steps
*April 21, 2016*

**Sequences and Series**

appears to go 6,5,1,2 ..... a cycle of 4 terms. the 21st term must be 6
*April 21, 2016*

**Sequences and Series**

add 1 to each even numbered term add 5 to each odd numbered term 25,5,30,6,35,7,40,8,45,...
*April 21, 2016*

**Series and Sequences**

Not enough data to tell for the first 3, there is an increase of 20 from one to the other for the last three, there is the same increase but we can't tell what happened from term3 to term4
*April 21, 2016*

**please math help**

T/F ---- x multiple choice --- y x+y = 20 ----> y = 20-x 3x + 11y = 100 3x + 11(20-x) = 100 3x + 220 - 11x = 100 -8x = -120 x = 15 and then y = 5 There are 5 multiple choice questions
*April 21, 2016*

**Math linear equations**

large pitcher --- x small pitcher --- y x + 2y = 8 x - y = 2 subtract them: 3y = 6 y = 2 then x = 4 large holds 4 cups, the smaller holds 2 cups
*April 21, 2016*

**Math**

radius of circle = 1450 ft circumference of whole track = 2π(1450) = 2900π ft angle of sector between them = 90 + arctan(1440/170) = 173.267° Distance Robin has to make up is 173.267/360 = x/2900π x = 4384.9155 ft He is gaining on him at a rate of 1.3 ft/sec...
*April 20, 2016*

**Math**

prob(grow) = .65 prob(not grow) = .35 prob(1 of 11 will not grow) = C(11,1)(.35)(.65)^10 = .05183
*April 20, 2016*

**NEED HELP MATH QUESTION ASAP**

Prob(rolling a two) = 1/6 number of expected times of getting a 2 in 6 rolls = 6(1/6) = 1
*April 20, 2016*

**Math**

I assume you meant:Volume = 4(c)^3(b)^8 Base area = 16(ab)^3 let the height be h h(16(ab)^3) = 64(c)^3(b)^8 h = 4 c^3 b^5 /a^3 No choice is correct
*April 19, 2016*

**math**

age of son ---- x age of woman --- 4x 5 years from now: son : x+5 woman : 4x+5 4x+5 = 3(x+5) solve for x
*April 18, 2016*

**Trig**

This same post has been declared as muddled and garbled several times. It has been answered by both Steve and I and you should not expect any more replies until you fix the wording so that the question makes sense http://www.jiskha.com/display.cgi?id=1460596777
*April 18, 2016*

**Math/algebra**

Cutting through the chase: 60 + -25x = 35x + 20 -25x - 35x = 20 - 60 -60x = -40 x = 40/60 = 2/3
*April 18, 2016*

**Trigonometry**

draw your triangles in the correct quadrantIs. Use Pythagoras in each case. if cosu = 3/5, in IV, then sinu = -4/5 if cosv = 12/13, then sinv = -5/13 sin(u-v) = sinu cosv - cosu sinv = (-4/5)(12/13) -(3/5)(-5/13) = (-48 + 15)/65 = -33/65
*April 17, 2016*

**Ms Sue please helpp**

4356/9999 = 484/1111
*April 17, 2016*