Wednesday

October 7, 2015
Total # Posts: 31,225

**Urgent math**

remember we can take logs of only positive numbers, so ... domain: x> -3 range : y is any real number asymptote : x = -3
*August 3, 2015*

**Precaculculus**

you are correct. An interesting question now would be ... what is the value of 'a' ?
*August 3, 2015*

**Math**

I agree, good work
*August 3, 2015*

**math**

Why do "the wheels on a bus go round and round" ??
*August 3, 2015*

**pre-cal**

just use the formula let a = 10, so we can use your standard base 10 logs on your calculator log14 41 = log 41/log 14 = appr 1.407158.. = 1.407 correct to 3 decimals check by evaluating 14^1.407 on your calculator. What did you get?
*August 3, 2015*

**Urgent math**

n(t) = 19000 e^(.07t) , where t is the number of years since 2005 in 2010 , t = 5 n(5) = 19000 e(.07(5)) = 26962 use the method I showed you in your previous post do answer c)
*August 3, 2015*

**Urgent math**

general equation: number = a e^(kt) , where a is the initial amount, t is the time in hours and k is a constant. case1: when t = 2, number = 400 400 = a e^(2k) case2: when t = 6 , number = 25600 25600 = a e^(6k) divide the 2nd equation by the 1st 64 = e^(4k) 4k = ln64 k = ln64...
*August 3, 2015*

**College Algebra**

you were not quite done, 3.4 is the difference in the Richter scale values, so the relative strength of the quakes is 10^(3.4) = appr 2512 times as large remember that the Richter scale is a base 10 logarithm relationship
*August 3, 2015*

**College Algebra**

general equation amount = a (1/2)^(t/5730) , where t is in years .8 = 1 (1/2)^(t/5730) .8 = 1 (.5)^(t/5730) log .8 = (t/5730) log.5 t/5730 = log.8/log.5 t = 5730(log.8/log.5) = appr 1844.6 years
*August 3, 2015*

**College Algebra**

4 + 5^6x = 8 I will assume you meant 4 + 5^(6x) = 8 5^(6x) = 4 log both sides and use rules of logs 6x log5 = log4 x = log4/(6log5) b) x = appr .143559
*August 3, 2015*

**stadistic**

for any question, prob(correct guess) = 1/4 prob(wrong guess) = 3/4 To have exactly 7 of 15 correct, prob = C(15,7)((1/4)^7 (3/4)^8 = 6435 (1/16384)(6561/65536) = appr .039
*August 2, 2015*

**gnmps**

let their ages be 6x and 7x (6x+12)/(7x+12) = 12/13 78x + 156 = 84x + 144 -6x = -12 x = 2 they are now 12 and 14
*August 2, 2015*

**Math ho.**

You have not indicated if the given number has any repeating decimals. The way you typed it, it appears to terminate. Thus it would be rational. An irrational number has decimals than neither repeat nor terminate. The way you typed it, we can't tell.
*August 2, 2015*

**Math ho.**

nope, each length is 25/2 m which is a rational number.
*August 2, 2015*

**Algebra**

I will read that as: 4/(x^2 - 4x + 1) + 2/(x^2 - 1) We usually "solve" equations, but you have no equation. Are you simplifying? If so, I was expecting the first denominator to factor like the second one, so we can find the LCD. The way it stands, the simplification ...
*August 1, 2015*

**MATH**

I agree with Bosnian that the question contains a typo. If the sum of n terms is 225 as stated we could solve for r = 2.309.. but then the solution for n is not a whole number. Bosnian assumed correctly that sum(8) = 255
*August 1, 2015*

**alpha**

secØ = x - tanØ for a trivial solution, but .... If you want secØ in terms of x, then you have a mess Secø + tanø=x 1/cosØ + sinØ/cosØ = x (1+sinØ)/cosØ = x 1 + sinØ = xcosØ square both sides 1...
*August 1, 2015*

**MTH 157**

x(1.04)^5 = 50000
*July 31, 2015*

**Math**

first get you results to sine and cosine of x since you are in II, from your diagram, sinx = 15/17 tanx = -15/8 use the formula for tan(3x) you just found in your other post. then apply the formula for tan(A/2) actually that is a nice one: tan (A/2) = (1 - cosA)/sinA good luck
*July 31, 2015*

**Math**

easy to look up, here is one such page http://www.trans4mind.com/personal_development/mathematics/trigonometry/multipleAnglesTangent.htm If you have to actually develop it, use tan(A+B) = (tanA + tanB)/(1 - tanAtanB) on tan(3x) = tan(2x+1) after doing tan2x first.
*July 31, 2015*

**math**

let his income be x after food expenses he is left with (2/3)x he then spends (1/4+1/5)(2x/3) = (3/10)x which leaves him with 2x/3 - 3x/10 or 11x/30 (11/30)x = 1760 x = 4800 which is choice c)
*July 31, 2015*

**math**

so you want: √a + √b = √c just take any two perfect squares, add their square roots and square that to get c e.g. a = 1 , b=1, c = 4 ----> √1 + √1 = √4 a = 1 , b = 4, c = 9 a = 4, b = 9, c = 25 ---> √4 + √9 = √25 ...
*July 30, 2015*

**math**

amount of the 30% alloy to be added --- x ounces .3x + .05(10) = .2(10+x) .3x + .5 = 2 + .2x .1x = 1.5 x = 15
*July 30, 2015*

**math**

let the side of the square be x let d be the diagonal, d^2 = x^2+x^2 = 2x^2 d = √2 x "the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400" x^2+x^2+x^2+x^2 + 2(2x^2) = 400 8x^2 = 400 x^2 = 50 x = 5√2 area of ...
*July 30, 2015*

**Probability**

Is the password case sensitive ? It usually is, so number of ways to arrange 5 letters = 52^5 also assuming that letters can be repeated only one of these is correct prob(getting it right) = 1/52^5 = 1/380204032
*July 30, 2015*

**Probability**

prob(A/C) = 1/2 prob(not A/C) = 1/2 prob(that 5 out of 10 have A/C) = C(10,5)(1/2)^5 (1/2)^5 = 252 (1/2)^10 =252/1024 = 63/256 or appr .246
*July 30, 2015*

**Probability**

So he already has 1 penny, which means he can only draw another penny or another nickel Prob(as stated) = 3/8 + 2/8 = 5/8
*July 30, 2015*

**Cones**

V = (1/3)π r^2 h = 36π r^2 h = 108 Now if we cut the height in half, then the radius is also cut in half new volume = (1/3)π(r/2)^2 (h/2) = (1/24)π r^2 h = (1/24)π(108) = 9π/2 or the volume of similar solids is proportional to the cube of their ...
*July 30, 2015*

**Math**

b men earning D dollars = bD remaining men = m-b each earning D/2 so they earn D/2(m - b) = mD/2 - bD/2 total = bD + mD/2 - bD/2 = 2bD/2 + mD/2 - bD/2 , using a common denominator = bD/2 + mD/2 = D/2(b+m) , using a common factor of D/2 which is B D/2 is the same as (1/2)D
*July 30, 2015*

**Math**

It would be a good idea if you familiarize yourself with Pascal's Triangle, the 4th row has values 1 4 6 4 1 so (2x-1)^4 = (2x)^4 + 4(2x)^3 (-1) + 6(2x)^2 (-1)^2 + 4(2x) (-1)^3 + (-1)^4 the term that will yield x^2 is 6(2x)^2(-1)^2 = 24x^2 confirmed by Wolfram: http://www....
*July 30, 2015*

**GCF**

pick out the factor with the lowest exponent for each variable e.g. for the b's it would be b^5 etc
*July 30, 2015*

**What did I did wrong MATH**

number of $1 coins --- 3x number of half-dollars --- 4x Your second sentence does not make any sense to me taking your equation ... cross-multiply 9x - 18 = 4x+6 5x = 24 x = ???? , x must be a whole number Fix your second sentence.
*July 30, 2015*

**math**

I find it odd that you made the same typo in this question as somebody else did back in Nov 2014. http://www.jiskha.com/display.cgi?id=1416116940
*July 30, 2015*

**Math**

You will need brackets to establish the correct order of operations. The way you typed it, the +1 -1 would cancel and you are left with 4 /X^2 – 4x + 2/ x^2 = 4/x^2 - 4x^3/x^2 + 2/x^2 = (6 - 4x^3)/x^2 I have a strong feeling that is not what you meant.
*July 30, 2015*

**math**

I started it as a simple calculus question ... first number: x 2nd number : 48/x sum = x + 48/x d(sum)/dx = 1 - 48/x^2 = 0 for a min of sum x^2 = 48 x = √48 = appr 9 but you want the numbers to be whole numbers so possible ordered pairs: (1,48) (2,24) (3,16) (4,12) (6,8...
*July 30, 2015*

**maths**

Why not just say: the volume equals the surface area (4/3)πr^3 = 4πr^2 times 3/π 4r^3 - 12r^2 = 0 r^3 - 4r^2 = 0 r^2(r - 4) = 0 r = 0 (trivial solution) or r = 4 or the diameter is 8 Your actual question is strangely worded.
*July 30, 2015*

**Mathematics**

The zeroes of a function indicate where the corresponding graph touches or crosses the x-axis.
*July 30, 2015*

**math**

check your typing, right now your post makes no sense. "... find the length if its worth (16x^2y^2) dm ?? " did you mean , if it width is .... ? In that case just divide 256x^4y^4-169c^4y^4 by 16x^2 y^2 to get 16x^2 y^2 - 169c^4 y^2/(16x^2) btw, the units for the ...
*July 30, 2015*

**Math**

you must mean "simplify" ((1/x)-(1/y))/(y^2-x^2) = ( (y-x)/(xy) ) / ((y-x)(y+x) ) = (y-x)/( (xy)(y+x)(y-x) ) = 1/(xy(y+x) ) , y≠x
*July 29, 2015*

**Math**

or for #3 you have 1*(1+2+3+...+9+10) + 2*)1+2+3+...+9+10) + ... 10*(1+2+3+...+9+10) add them: (1+2+3+...+9+10)(1+2+3+...+9+10) = 55*55 = 3025
*July 29, 2015*

**Maths**

In your first case , there were 4 children and the answer was 4! or 24 So if there are 5 children .... ??
*July 29, 2015*

**Math**

width --- x length --- 3x x^2 + (3x)^2 = (8√10)^2 10x^2 = 640 x^2 = 64 x = 8 width = 8 length = 24 area = (8)(24) = 192
*July 29, 2015*

**College Algebra**

I am sure you meant: m(t) = 9 e^(-.012t) so if t = 0 , remember that anything^0 = 1 so m(0) = 9
*July 29, 2015*

**Data management**

my interpretation of a face card is either Jack, Queen, or King number(spade or face) = number(spade) + number(face) - number(spade AND face) = 13 + 12 - 3 = 22 prob(spade or face) = 22/52 = 11/26
*July 29, 2015*

**rd. math**

I will assume that by the "division method" you are referring to what is generally call Euclid's Algorithm find the HCF of the first two numbers by following this Youtube clip, then use that answer with the third number https://www.youtube.com/watch?v=AJn843kplDw...
*July 29, 2015*

**Math**

present age of Joy --- x present age of Drew --- 2x five years ago: Joy = x-5 Drew = 2x-5 (x-5)(2x-5) = x-7 2x^2 -15x + 25 = x-7 2x^2 - 16x + 32 = 0 x^2 - 8x + 16 = 0 (x-4)^2 = 0 x = 4 Joy is now 4, and Drew is 8 check: 5 years ago: Joy = -1 ?? Drew = 3 product of their ages...
*July 29, 2015*

**Math**

amount spent = 1/12 + 1/4 = 1/3 So (2/3) of his money is left (2/3)x = 240 x = 240(3/2) = 360 so he spent (1/4)(360) or $90 on books
*July 29, 2015*

**Algebra**

Really? Then what does this mean ? "How in the world do I solve for x without using a calculator?"
*July 28, 2015*

**Algebra**

If the question says to solve without a calculator, then admittedly this is a very unreasonable question. Not even in my olden days, (you know when we had to rely on slide rules and log tables) would they have expected a solution. I ran it through Wolfram and it shows that you...
*July 28, 2015*

**Algebra 2 CP**

100000(1+i)^11 = 196000 (1+i)^11 = 1.96 take 11th root of both sides 1+i = 1.96^(1/11) = 1.06309 i = .06309 or appr 6.3% check: 100000(1.06309)^11 = 196006 , not bad
*July 28, 2015*

**math**

I don't understand the question √1000000 = 1000 why express 1000 as a square root did you mean? = 1*√1000000 = √10*√100000 = √100*√10000 = √1000*√1000
*July 28, 2015*

**math**

the last term in the expansion of (2x^2+3x+2)^n is 2^10 and .... we know 2^10 = 1024 (1 kb = 1024, recall your computer science stuff) so n = 10
*July 28, 2015*

**math**

I think you have a typo and meant 1 - 2 + 3 - 4 + ... + 1997 - 1998 + 1999 - 2000 (all odds are positive and all evens are negative) take them in pairs: 1-2 = -1 3-4 = -1 5-6 = -1 .. 1999-2000=-1 so you have 1000 of these pairs, and the sum is -1000
*July 28, 2015*

**math**

slope RS = (-d-b)/(-c+a) or (d+b)/(c-a) test for slope going through T slope TA = (b+d)/(c-a) ----> that is correct slope TB = (b+d)/(-c-a) slope TC = (-b+d)/(c-a) slope TD = (-b+d)/(-c-a) use an actual example to illustrate: a=3, b=4, c=2 , d=5 let R be (-3,4) and S be ( -...
*July 28, 2015*

**Math**

from the 2nd, y = x-8 now sub that into the 1st: -3x - 2(x-8) = 16 -3x - 2x + 16 = 16 -5x = 0 x = 0 y = 0 - 8 = -8
*July 28, 2015*

**Math**

H -- hit M -- miss possible outcomes HH -- (.6)(.8) = .48 HM -- (.6)(.2) = .12 MH -- (.4)(.4) = .16 MM -- (.4)(.6) = .24 notice the sum = 1 , as expected
*July 28, 2015*

**Maths**

volume = (1.4)(.8)(.5) m^3 = .56 m^3 = 560 L of water , 1 m^3 holds 1000 L leak is 40 cl or .4 L/min ( 100 cl = 1 L) number of minutes to drain = 560/.4 =1400 minutes or 23 hrs, and 20 minutes
*July 28, 2015*

**maths**

same problem four times! and still typed incorrectly .... Don't you read previous replies to this question??
*July 28, 2015*

**Geometry**

Since it is isosceles, we can construct a right-angled triangle with an altitude to the base of 3 then cosØ = 1.5/√3 = 3/2√3 = 3/2√3 * √3/√3 = √3 /2 ahhh, do you recognize the 30-60-90° triangle (if not, use your calculator) &...
*July 28, 2015*

**mathematics**

Other than changing the "subject" heading, you have not answered any of my concerns, and posted the problem in the same confusing way. http://www.jiskha.com/display.cgi?id=1438088880
*July 28, 2015*

**Physics**

The circumference of the wheel is 50π cm = π/2 m 1 rotation covers π/2 m x rotations cover 26 m x/1 = 26/(π/2) x = 52/π = appr 16.55 the wheel is turning at 16.55 rotations/second or appr 993 rpm
*July 28, 2015*

**government secondary school abuja**

Wow, before I start, some clarification: I will assume that you meant: (x^4+3x-2)/( (x^2+1)^3 (x-4) ) My second concern: In your break-down your last term is h/(x-4)^2, yet the original denominator showed only (x-4) Besides that, if the denominator did contain (x-4)^2, then ...
*July 28, 2015*

**math**

volume = (9)(16)(√25) = 720 cubic units none of your choices are correct unless your dimensions are √9, √16, and √25 Then the volume would be 60 cubic units, but that is not what you said.
*July 27, 2015*

**algebra**

ok up to 50-100+5 which is -45
*July 27, 2015*

**Maths**

let then number of sugar bags be x then the number of salt bags is 100-x now for the cost: 2x + 5(100-x) = 380 2x + 500 - 5x = 380 -3x = -120 x = 40 so he bought 40 bags of sugar and 60 bags of salt or, using two variables sugar bags --- x salt bags ----- y x + y = 100 2x + 5y...
*July 27, 2015*

**Maths Problem**

When the car catches up with the van, they would have both traveled the same distance let the time from 7:30 am to the catch-up time be t hrs. distance covered by car = 80t distance covered by van = 60t + (1/2)(60) = 60t + 30 80t = 60t + 30 20t = 30 t = 3/2 3/2 hours added to ...
*July 27, 2015*

**math**

Make a sketch of your finished quad and enter all the information. Notice that adjacent angles add up to 180°, so AT || MH, and it is easy to see that MAH must be an equilateral triangle. You should see that MATH must be a rhombus, with all sides equal to 8 cm I assume you...
*July 27, 2015*

**Maths**

time for first part = d/15 time for 2nd part = d/30 total time = d/15 + d/30 = d/10 avg speed = total distance/total time = 2d/(d/10) = 20 km/h notice we can't just average the two speeds.
*July 27, 2015*

**Maths**

speed of slower train --- x km/h speed of faster train ---- x+20 km/h 6 minutes = 6/60 or 1/10 hour (1/10)x + (1/10)(x+20) = 11 times 10 x + x+20 = 110 2x = 90 x = 45 the slower train goes at 45 km/h the faster at 65 km/h
*July 27, 2015*

**Maths**

Let the length and width be x and y, both x and y positive xy = 6 and x^2 + y^2 = (2√5)^2 from xy=6, y = 6/x x^2 + (6/x)^2 = 20 x^2 + 36/x^2 = 20 x^4 + 36 = 20x^2 x^4 - 20x^2 + 36 = 0 (x^2 - 18)(x^2 - 2) = 0 x^2 = 18 x = √18 = 3√2, and y = 6/√18 = &#...
*July 27, 2015*

**Math**

I assume you made a sketch In mine, 36/x = tan30° x = 36/tan30 , but I know from my basic 30-60-90 triangle that tan30 = 1/√3 x = 36/(1/√3) = 36√3 m or appr 62.35 m
*July 27, 2015*

**math**

I will assume your expression is a complex number of the form a + bi , let me know if you give it a different meaning. (2+j4)*(-3-j4) = -6 - 8j - 12j - 16j^2 = -6 - 20j + 16 = 10 - 20j tanØ = -20/10 = -2, with Ø in quad IV Ø = 5.176 argument = √(10^2...
*July 27, 2015*

**College Algebra**

If 4i is a zero, then -4i must also be a zero, since complex zeros come in conjugate pairs. a possible polynomial is f(x) = (x-4i)(x+4i)(x+1)^2 a general solution would be f(x) = a(x-4i)(x+4i)(x+1)^2 , where a is a non-zero integer. If necessary, your can expand this.
*July 27, 2015*

**Algebra**

The way you typed it , we would get 5m + 7/m^2 - 21 I have a feeling you meant: (m+7)/(m^2+4m-21) = (m+7)/( (m+7)(m-3) ) = 1/(m-3) , m ≠ -7 See how extremely important those brackets are ??
*July 26, 2015*

**math**

The way you typed it ..... -8/15 a = 9/10 would mean: (-8/15) a = 9/10 , by the order of operation -80a = 135 a = -135/80 = - 27/16 = - 1.6875 Ms Sue interpreted it as the way you probably meant it ... -8/(15a) = 9/10 a = -16/27 = -.59259259.. (the 592 is repeated) See how ...
*July 26, 2015*

**math- partial fractions**

What you typed is really just (s^2 +2s +3)/s^2 which is = 1 + 2/s + 3/s^2 I don't know if this is what you needed.
*July 26, 2015*

**algebra**

My name is Billy vs Billy is my name If I recall, it is called the transitive property
*July 26, 2015*

**Data management**

prob(getting a six) = 1/6 prob(not getting a six) = 5/6 a) prob (at least 1 six in 6 tries) ---> we don't want all non-sixes prob(no six in 6 tries) = C(6,0)(1/6)^0 (5/6)^6 = .3349 so prob of at least 1 six = 1 - .3349 = .6651 b) this time we exclude the case of no ...
*July 26, 2015*

**Math**

let m be the number of minutes cost1 = .20m + 14 cost2 = .15m + 18 When is .20m + 14 = .15m + 18 ? .05m = 4 m = 4/.05 = 80
*July 25, 2015*

**maths**

ahhh, see http://www.jiskha.com/display.cgi?id=1437880873 Looks like I assumed correctly
*July 25, 2015*

**circle**

You are missing an operator in your line equation, I will assume you mean 5x + 12y = 1 or 5x + 12y - 1 = 0 we know that the equation must be (x-3)^2 + (y-4)^2 = r^2 , so the only thing missing is the value of r using the distance from a point to a line method, r = |5(3) + 12(4...
*July 25, 2015*

**11th maths**

I read that as log3 243 - log2 64 - log√3 3 notice that 3^5 = 243 , 2^6 = 64 and (√3)^2 = 3 then: log3 243 - log2 64 - log√3 3 = 5 - 6 - 2 = -3
*July 25, 2015*

**math**

let the longest side be x shortest side = (1/3)x + 2 other side = x-5 x + (1/3)x + 2 + x - 5 = 53 times 3 3x + x + 6 + 3x - 15 = 159 7x = 168 x = 24 longest side = 24 shortest = 10 other = 19 check: 24+10+19 = 53
*July 25, 2015*

**Deogiri**

1 mile = 1.60934 km so 150 miles = appr 241.4 km 150 mph = 241 km/h
*July 24, 2015*

**Algebra**

divide each term by 81 to get (x+1)^2/9 + (y-1)^2/3 = 1 so a = 3, and b = √3, which means that the major axis is parallel to the x-axis (since a > b)
*July 24, 2015*

**maths**

argggghhh! go with Steve's method, I'm going back to bed
*July 24, 2015*

**maths**

speed of boat --- x km/h speed of current -- y km/h case1: 30/(x-y) + 44/(x+y) = 10 times (x+y)(x-y) .... 30(x+y) + 44(x-y) = 10(x+y)(x-y) 30x + 30y + 44x - 44y = 10x^2 - 10y^2 10x^2 - 10y^2 = 74x - 14y ----> #1 case2: 40/(x-y) + 55(x + y) = 13 40(x+y) + 55(x-y) = 13(x+y)(x...
*July 24, 2015*

**sets**

Make a Venn diagram, and enter your data. Let the number of people who like only tennis be x x + 10 + 30 = 65 x = 25 so number who like tennis = 10+25 = 35 check: N(C or T) = N(C) + N(T) - N(C and T) LS = 65 RS = 40 + 35 - 10 = 65 = LS All is good!
*July 23, 2015*

**statistics**

What is (3/10)^5 ??
*July 23, 2015*

**Trigonometry**

You would be correct if you had x^2+y^2-7x+5y = 0 remember, you want an equation, not just an expression.
*July 23, 2015*

**Math quadratic function**

Your vertex is indeed (70,17) Other points would be (142,0) and (0,1.2) Since the vertex must lie midway between the two intercepts and the distance between 70 and 142 is 72, the other intercept must be (-2,0) h(x) = a(x-70)^2 + 17 must be the equation use (142,0) to find a 0...
*July 23, 2015*

**Math**

"My ten thousand digit is the highest odd number" What is the highest odd number ?
*July 20, 2015*

**Math**

Didn't it say that your unit digit is zero ?
*July 20, 2015*

**Math**

"My thousand digit is the second odd number. " 2 is not an odd number.
*July 20, 2015*

**Math**

Did you check if your answer matches all the conditions ?
*July 20, 2015*

**Math**

yes, see http://www.jiskha.com/display.cgi?id=1435211710
*July 20, 2015*

**math**

Of course all sides are the same let the side be x given: "the sum of the cubes of two sides is equal to the square of the third side" ... just translate into math 2x^3 = x^2 2x^3 - x^2 = 0 x^2(2x - 1) = 0 x = 0 , which would make an interesting triangle or x = 1/2 ...
*July 19, 2015*

**math**

When it reaches the ground, h(t) = 0 -4.9t^2 + 9.5t + 1.2 = 0 don't think it will factor, so let's use the formula I got t = 2.0578 or a negative, the latter does not make sense It will hit the ground after appr 2.06 seconds
*July 19, 2015*

**math**

Then tan is +, and the cos is -, so you must be in quadrant III tan a = 15/8 = y/x so y = -15 , x = -8, and r = 17 [sin(-a)-cosa]/[tan(-a)+sec(-a)] = (-sina - cosa)/(-tana + seca) = (15/17 + 8/17)/(-15/8 - 17/8) = (23/17)(-8/32) = -23/68
*July 19, 2015*

**@ Nick - calculus**

Nick, with a little effort on your part to complete the solution I gave you and some small adjustment for this question, you could have saved the duplication of this solution by Damon.
*July 19, 2015*