Wednesday

July 27, 2016
Total # Posts: 35,358

**Logarithm**

I answered this further up the listing
*April 9, 2016*

**Logarithm**

Ln2+Lnx=1 ln(2x) = 1 by definition of ln e^1 = 2x x = e/2
*April 9, 2016*

**Math: Parametric Equations**

does this help? https://www.wolframalpha.com/input/?i=plot+x+%3D++cos(4t),+y+%3D+sin(6t)
*April 9, 2016*

**MAth**

let n be the number of half-years i = .072/2 = .036 73,000(1.036)^n = 100,000 1.036^n = 1.36986... log both sides and use log rules n log 1.036 = log 1.36986.. n = 8.898.. half-years = appr 4.45 years
*April 9, 2016*

**algebra**

number of whites --- x number of yellows --- 18-x 995x + 1250(18-x) = 22245 (I changed the $'s to cents) solve for x, has to come out as a whole number
*April 9, 2016*

**Canadian finances**

I have placed *** behind my choices. If you see no *** or no comment, I agree with your answer. which of the following services do banks not provide? a. lines of credit b. health insurance *** c. currency exchange d. none of above (THIS ONE) which institutions does not offer ...
*April 9, 2016*

**Math**

x(x+5) = 350 x^2 + 5x - 350 = 0 too bad it doesn't factor. By the formula x = (-5 + √1425)/2 = appr 16.37 ft take over remember perimeter = 2width + 2length
*April 9, 2016*

**math**

i = .038/365 n= 365(4) = 1460 principal = 3500 amount = 3500( 1 + .038/365)^1460 = 4074.53 So interest earned = 4074/53-3500 = 574.53 which is choice a)
*April 9, 2016*

**Geometry**

width ---- x length ---- 2x+5 x(2x+5) = 1375 2x^2 + 5x - 1375 = 0 solve the quadratic hint: it factors, but it may be just as fast to use the formula
*April 9, 2016*

**Precalculus**

How about this way: Since AC supports a 45 degree angle at the circle, AC must support a 90 degree angle at the centre. let the radius be r r^2 + r^2 = 8^2 2r^2 = 64 r^2 = 32 Area = pi r^2 = 32 pi or appr 100.53 Notice just as Damon pointed out, we don't even need to know ...
*April 9, 2016*

**karki**

let the AP be a, a+d, a+2d so 3a + 3d = 45 a+d = 15 ---> d = 15-a and a(a+d)(a+2d)=300 a(a^2 + 3ad + 2d^2) = 300 a(a^2 + 3a(15-a) + 2(15-a)^2) = 300 a(a^2 + 45a - 3a^2 + 450 - 60a + 2a^2) = 300 a(- 15a + 450) = 300 -15a^2 + 450a - 300 = 0 a^2 - 30a + 20 = 0 a = (30 ±...
*April 9, 2016*

**Trigonometrt**

sin ( 810- theta) I am sure you meant: sin(180 - θ) which is sinθ cot(θ - 360) .... recall that tan(-x) = -tanx and tan(360-x) = -tanx and of course the cot behaves just like the tan cot(θ-360) = -cot(360-θ) = -(-cotθ) = cotθ cos(-180 - θ...
*April 9, 2016*

**Probability (Math)**

You are correct
*April 9, 2016*

**math**

Since Mathematics is a precise language, it requires precise and correct English to express a problem to be solved. Please re-type your problem using correct and proper English so that it makes sense to me. "Texting" English doesn't cut it.
*April 9, 2016*

**gemoetry**

I don't see any diagram but by a simple trig ratio, we have cos 75.5 = 20/L L = 20/cos75.5 = appr 79.9 ft Wow, a ladder to go up about 8 stories high???
*April 9, 2016*

**Math**

If x = 2√2 and x = -2√2 then two of the factors are (x - 2√2) and (x + 2√2) or (x^2 - 8) must be a factor of your polynomial. Do a long algebraic division to get x^4+4x^3-4x^2-32x-32 = (x^2 - 8)(x^2 - 4x + 4) we can get more roots from x^2 - 4x + 4 = 0...
*April 9, 2016*

**math**

Just replace the units with their equivalents. 24 miles / 1 hour = 24*1760 yards / 60 minutes = (42240/60) yards/min = 704 yards/min I agree with your answer
*April 9, 2016*

**MATH**

I agree with your equation and I get $4011.25. Beyond that, I can't help you since I don't know what you mean by "syntax" error.
*April 9, 2016*

**I NEED HELP!!!**

arrange it in more standard form 2x^2 + 6x - 5 = 0 use the formula: x = (-6 ± √76)/4 = (-6 ± 2√19)/4 = (-3 ± √19)/2
*April 9, 2016*

**Algebra**

you are basically looking for the vertex of this downwards opening parabola the t of the vertex is -b/2a = -64/-32 = 2 seconds it will take 2 seconds to reach the maximum height when t = 2 h = -16(4) + 64(2) + 9 = 73 ft
*April 8, 2016*

**Algebra**

the real parts of the left side must match the real parts of the right side, and the imaginary parts .... your steps are correct, so x = -4, y = 1
*April 8, 2016*

**Algebra**

A(t) = 3- 2t^2 + 4^t A(2) - A(1) = 3 - 2(4) + 4(4) - (3 - 2(1) + 4(1)) = 3 - 8 + 16 - 3 + 2 - 4 = 6 you are correct
*April 8, 2016*

**Math**

let y = (3x - 7)/(x + 1) for the inverse , exchange the x and y's x = (3y-7)/(y+1) now solve this for y ... xy + x = 3y - 7 xy - 3y = -x - 7 y(x-3) = -x - 7 y = (-x - 7)/(x - 3) = (x+7)/(3-x) f^-1 (x) = (x+7)/(3-x) check: f(1) = (3-7)/(2 = -2 f^-1 (-2) = (-2+7)/(3-(-2)) = ...
*April 8, 2016*

**MATH**

Your formula is a creative variation of the real one amount = 60000( (1 + .07/2)^50 - 1)/(.07/2) = 60000( 1.035^50 - 1)/.035 =
*April 8, 2016*

**Math**

8% per annum compounded semi-annually ---> 4% every half year so i = .04 number of half-years in 18 years = 36 amount = 20,000( 1.04^36), as Bob had = $82,078.65
*April 8, 2016*

**math**

number of small trucks --- x number of vans ----- 2x number of large trucks = 280 - 3x 30,000x + 25,000(2x) + 40,000(280-3x) = 8,000,000 divide by 5000 6x + 10x + 8(280-x) = 1600 carry on
*April 8, 2016*

**Algebra 1-HELP!**

(6^3/8)^2/5 = 6^((3/8)(2/5)) = 6^(3/20)
*April 8, 2016*

**math**

original fraction : x/y new fraction = .9x/(.5y) = 9x/5y (9x/5y) / (x/y) = 9x/5y * y/x = 9/5 = 1.8 so it increased by 80% e.g suppose we had 100/200 or 1/2 new fraction = 90/100 or 9/10 new ratio = (9/10) / (1/2) = 9/5
*April 8, 2016*

**math**

increases expressed as a single increase = 1.2(1.15) = 1.38 it increased by 38%
*April 8, 2016*

**math**

correct
*April 8, 2016*

**math**

Distance walking --- x distance by cab ---- 31-x time walking = x/4 time by cab = (31-x)/50 Your "formula", we call it an equation x/4 + (31-x)/50 = 2 solve for x, plug x into 31-x
*April 8, 2016*

**geometry**

The radius of the whole circle = 2πr = 10π Now, what fraction of that circumference is a 45 degree sector?
*April 8, 2016*

**Math w/business apps**

solve for x x(1 + .06/12)^12 = 20000
*April 8, 2016*

**Algebra 1-HELP!**

Did you first look for the HCF ? I see: 8(4a^2 + 12a^2 + 9) hint#2: Did you notice the perfect squares at front and end of the trinomial?
*April 8, 2016*

**Algebra 1**

hint: if there are x cans and you have 800 cans and bottles, wouldn't the number of bottles be 800-x ?
*April 8, 2016*

**algebra**

As Bob noted you don't have an equation. you probably have the expression (x - 1/x)/(1 + 1/x) and are asked to simplify it. Hint: how about multiplying the fraction by x/x
*April 8, 2016*

**math**

Why would "guess" for math problems Surely you could have tried to work them out #6 is trivial #8-12 deal with the rules of multiplying and dividing powers When multiplying powers with the same base, keep the base and add the exponents e.g. x^4 * x^8 = x^12 When ...
*April 8, 2016*

**math {sequences}please help**

#3 is geometric with a common ratio of 1/3 your other answers are correct
*April 8, 2016*

**GEOMETRIC SEQUENCES**

No Think of how you would obtain the next term you could take .18 of the previous term and subtract or just take .82 of it so the sequence is: 20000 , 20000(.82), 20000(.82)^2 , .... so r = .82 I am sure you can now answer the question
*April 8, 2016*

**math**

No interest ? Give it to me and after 35 years, my estate will pay you back 1000(12)(35) or $ 420,000
*April 8, 2016*

**math**

let the tens digit be x then the unit digit is 3x so the number is 10x + 3x = 13x the number reversed is 10(3x) + x = 31x 31x + 13x = 88 44x = 88 x = 2 3x = 6 The original number was 26 check: is 26 + 62 = 88 ? YES my answer is correct
*April 8, 2016*

**linear equation in one variables**

let unit digit be x then tens digit is 9-x the number is : 10(9-x) + x = 90 - 9x the number reversed is 10x + 9-x = 9x + 9 9x+9 - (90-9x) = 27 18x - 81 = 27 18x = 108 x = 6 unit digit is 6 tens digit is 3 The number is 36
*April 8, 2016*

**elementary quantitative methos**

This is just finding the P of a PV. Same formula, same story.
*April 8, 2016*

**elementary quantitative methos**

beginning of 2nd year ---> end of first year. I will assume the 12th payment has been made outstanding balance = 230000(1.01625)^12 - 3817.23( 1.01625^12 - 1)/.01625 = ....
*April 8, 2016*

**elementary quantitative methos**

subtract 100,000 from 240,000, that is your PV i = .195/12 = n = 240 P = ? straight formula application ( I got 3817.23 )
*April 8, 2016*

**elementary quantitative methos**

Use the PV formula I showed you in your previous post
*April 8, 2016*

**elementary quantitative methos**

i = .085/4 = .02125 n = 20 amount = A = 30000 payment = P = ? You must memorize the formulas A = P( (1+i)^n - 1)/i and PV = P (1 - (1+i)^-n )/i, where PV is the present value just sub in all your data and solve for the missing variable. 30000 = P( 1.02125^20 - 1).02125 30000...
*April 8, 2016*

**Math**

number of stickers ---- x number of ballons --- 6x bubbles ----- (1/3)(6x) = 2x x + 6x + 2x = 135 solve for x
*April 7, 2016*

**Math**

I assume you mean by just guessing. he must get 8 right, or 9 right or 10 right = C(10,8)(1/2)^8 (1/2)^2 + C(10,9)(1/2)^9(1/2) + C(10,10) (1/2)^10 = (1/2)^10 ( 45 + 9 + 1) = 55(1/2)^10 = 55/1024 not good, better study
*April 7, 2016*

**Math**

let the side of square ABCD be x then area = x^2 area of square EFGH = 2x^2 side of square EFGH = √2 x EF = √2 x AC^2 = x^2 + x^2 = 2x^2 AC = √2 x AB/AC = x/√2x = 1/√2 AB/EF = x/√2x = 1/√2 thus AB/AC = AB/EF
*April 7, 2016*

**Math**

original price ----- x dollars .85(1.08)x = 688.50 solve for x
*April 7, 2016*

**Math**

In a refection over the x-axis, the x coordinate would stay the same, but the y would turn into its opposite that is, (x,y) ---> (x, -y) A(2,-5) ---> A'(2,5) find the choice that matches this
*April 7, 2016*

**pre ap math**

If it is lauched from a height of 48 ft, then the equation should be h = -16t^2+32t+48 I will assume a typo you want h = 0 (at ground level h=0) 0 = -16t^2+32t+48 t^2-2t-3 = 0 It factors, (t-3)(t+1) = 0 t = 3 or t = -1, rejecting the negative time it took 3 seconds
*April 7, 2016*

**linear equations in one variable**

Let the number of ₹5 coins be x then the number of ₹2 = 3x and the number of ₹1 = 160 - x - 3x = 160 - 4x Now for the value: 5x + 2(3x) + 1(160 - 4x) = 300 5x + 6x + 160 - 4x = 300 7x = 140 x = 20 You have 20 ₹5 coins 60 of the ₹2 coins and 80 of ...
*April 7, 2016*

**math probability**

The prob that you get a 7 when rolling two dice = 1/6 so when two friends roll , (the same result as you rolling twice) prob(2 7's ) = (1/6)(1/6) = 1/36
*April 7, 2016*

**math**

area of trap = (1/2)(sum of parallel sides)(distance between them) (1/2(a + 12)(6) , where a is the other parallel side. (1/2(a + 12)(6) = 48 3(a+12) = 48 3a + 36 = 48 3a = 12 a = 4
*April 7, 2016*

**math**

Am I looking at 3 equations? separate them with commas. what is 3y+x-×=10-x ? is x-× a power like x^-x ??
*April 7, 2016*

**Precal**

Don't you have a calculator? make sure you catch the double negative in the last term since cos 135 is negative
*April 7, 2016*

**Math-soh cah toa**

make a sketch. label the ends of the bridge A and B make angle A = 41° and angle B = 48°. label the point on the river P and Q on AB so that PQ is at right angles to AB. Let PQ = h let QB = x , the AQ = 140-x tan41 = h/(140-x) h = (140-x)tan41 tan48 = h/x h = xtan48 So...
*April 7, 2016*

**Math**

I will do one of the components, you do the other , then subtract them a(x) = 3x - 7 and b(x) = 2 - x^3 a(b(3)) = a(2-3^3) = a(-25) = 3(25) - 7 = 68
*April 7, 2016*

**Math**

just follow the definition: f(a,b) = 2a - 3b^2 + 7 f(b,3) = 2b - 3(3)^2 + 7 = 90 2b - 27 + 7 = 90 2b = 110 b = 55
*April 7, 2016*

**Math**

y = 5x-12 inverse: x = 5y-12 5y = 12-x y = (12-x)/5 f^-1 (x) = (12-x)/5 f(x+1) = 5(x+1) - 12 = 5x - 7 5x-7 = (12-x)/5 25x - 35 = 12 - x 26x = 47 x = 47/26 check my arithmetic
*April 7, 2016*

**Math**

We are told : a#b=ab-a-b+1 so x#7 = 7x - x - 7 +1 = 42 6x = 48 x = 8
*April 7, 2016*

**Math**

x^2 + 12x = 73 let's complete the square, the easiest way to solve this particular one x^2 + 12x + 36 = 73+36 (x + 6)^2 = 109 x + 6 = ± √109 x = -6 ± √109 the positive one looks like √109 - 6 so a = 1, b = -6 a+b = -5
*April 7, 2016*

**Math**

What part of my solution I gave you here did you not like ? http://www.jiskha.com/display.cgi?id=1459995714
*April 7, 2016*

**Geometry**

did you notice that you are given two angles in each of the triangles ? Did you notice that their sum is 180 degrees? So they are similar, thus the corresponding sides are proportional. What are we supposed to find ?
*April 7, 2016*

**Algebra II**

Show Thomas a simplified example of why his idea is wrong 3^2 + 4^2 = 5^2 ---- true then 3 + 4 = 5 ????? If you want to take the square root, you have to take it of the whole side, not the individual terms
*April 7, 2016*

**Calculus**

f'(-4) = 9 f'(0) = 6 f'(x) = 3ax^2 + 2cx f'(-4) = 48a - 8c = 9 f'(0) = 0 + 0 = 6 Oh, oh, something fishy here. Check your typing or check the question
*April 7, 2016*

**Calculus**

f(x) is increasing if f'(x) is positive so (x−8)^7(x−1)^4(x+19)^8 > 0 we know that (x−1)^4(x+19)^8 is always positive since we have even exponents. So all we have to do is look at (x-8)^7 > 0 if x > 8 then (x-8)^7 > 0 if x < 8 it is ...
*April 7, 2016*

**Calculus**

f(x) = √(36-x^2) = (36-x^2)^(1/2) f ' (x) = (1/2)(36-x^2)^(-1/2) (-2x) = 0 for a max/min thus x = 0 , f(0) = 6 but f(1) = √(36-1) = √35 which is < 6 f(6) = √0 = 0 So the absolute minimum is 0
*April 7, 2016*

**math**

in a), b), and d) the first points don't work leaving c) in c) the 2nd point does not work so none of triples have all 3 correct
*April 7, 2016*

**math**

the way you typed according to BEDMAS (1/15)(6+x)=(1/6)(x+3) multiply both sides by 30 2(6+x) = 5(x+3) now it is easy, carry on What Bob meant was: did you mean, 1/(15(6+x)) =1/(6(x+3)) ? then we have an entirely different ballgame
*April 7, 2016*

**math**

All of them are NOT a solution
*April 7, 2016*

**check this - maths**

I must have made some kind of error in this big mess. I can't reconcile the fact that k = 6 will produce the 45 degree angle, but both of our solutions somehow showed that k = 2 I will look at it again later on today
*April 7, 2016*

**maths**

x^2 + xy - Ky^2=0 To have this equation represented by two straight lines, we must have it in a factored form such as (x + ay)(x - by) = 0 so that a+b = 1 and ab=-k e.g. if we had x^2 + xy - 6y^2 = 0 (x+3y)(x-2y) = 0 our two lines would be x+3y = 0 or x-2y = 0 slope of first...
*April 7, 2016*

**Algebra**

Winner of the most nonsensical question of the day.
*April 6, 2016*

**Math**

amount = 1500 + 1500(1.05^4 - 1)/.05 = 7965.19
*April 6, 2016*

**Math**

x^2 - 5x - 4 < 10 x^2 - 5x - 14 < 0 (x-2)(x+7) < 0 if y = (x-2)(x+7) we have a parabola opening upwards with x-intercepts of 2 and -7 the parabola would be below the x-axis, that is y < 0 , for -7 < x < 2
*April 6, 2016*

**Math**

the maximum area is obtained when your rectangle is a square. so let the side be s 4s = 24 s = 6 area = 36
*April 6, 2016*

**Math**

again, just like in your last post, just do it m/n@p/q = (m)(p)(q/n) 7/69@23/24$ , other than the confusing $ = 7(23)(24/69) = 56
*April 6, 2016*

**Math**

What's wrong with just plugging in the numbers and adding the fractions?
*April 6, 2016*

**math**

the last one looks just like http://www.jiskha.com/display.cgi?id=1459986016 but you changed the first term so the answer is not 2779 like in your previous question for the bagel question, which I did for you here http://www.jiskha.com/display.cgi?id=1459985491 how did you get...
*April 6, 2016*

**Math**

A(2) = 3 - 2(2)^2 - 4^2 = 3 - 8 - 16 = -21 find A(1) the same way, then subtract them
*April 6, 2016*

**Geometry**

Follow my steps in your previous post http://www.jiskha.com/display.cgi?id=1459994336
*April 6, 2016*

**Trig**

let the length of the chord be 2x ft Drop a perpendicular from the central vertex to the chord then sin 12.5 = x/30 x = 30sin12.5 2x = 60sin12.5 = 12.9864 or by cosine law: let the length of the chord be c c^2 = 30^2 + 30^2 - 2(30)(30)cos25 = 168.64598.. c = 12.9864 , same as ...
*April 6, 2016*

**Geometry**

let the width of the uniform border be x ft new width = 10+2x new length = 15 + 2x area of whole thing = (10+2x)(15+2x) (10+2x)(15+2x) - 150 = 100 150 + 50x + 4x^2 - 15 - 100 = 0 4x^2 + 50x - 100 = 0 2x^2 + 25x - 50 = 0 doesn't factor, so use the formula x = (-25 ±...
*April 6, 2016*

**Math**

let number of boys be 5x let numbe of girls be 3x after change: boys --- 5x+1 girls --- 3x+3 (5x+1)/(3x+3) = 4/3 15x + 3 = 12x + 12 3x = 9 x = 3 new class : boys = 16 girls = 12 total = 28
*April 6, 2016*

**math**

-3/4-(3/-8) = -3/4 + 3/8 = -6/8 + 3/8 = -3/8
*April 6, 2016*

**correction - Math**

scrap the 7,5,1,1 combination, they don't add up to 12 also scrap the 7,1,1,1,1, there should only be 4 digits.
*April 6, 2016*

**Math**

add = odd ?? notice that 12 = 7+5+1+1 or 12= 3+5+3+1 12 = 7+3+1+1 12 = 9+1+1+1 see if you can find any others. now each of my choices can be arranged in different orders 7,5,1,1 ---> yields 4!/2! or 12 of them 3,5,3,1, yields 4!/2! = 12 of them 7,1,1,1,1 etc one of them is ...
*April 6, 2016*

**Geometry**

Algebraic way: original width = x original length = 2x+3 x(2x+3) = 434 2x^2 + 3x - 434 = 0 (x - 14)(2x + 31) = 0 x = 14 or x = -31/2 , which I will reject original width is 14 ft original length is 31 ft new width = 18 new length = 35
*April 6, 2016*

**Algebra**

notice for each increase of 2 units of tem, the level drops 10 rate of change = -10/2 ft/h = -5 ft/hr
*April 6, 2016*

**Algebra**

between which readings ?
*April 6, 2016*

**Geometry**

ok, ok I stand corrected, there is a way, we have an angle. The apothem is the distance from the centre to the midpoint of a side Let's look at one of the triangles of the hexagon. It has a central angle of 60 so in a right-angled triangle formed by the apothem and half ...
*April 6, 2016*

**Geometry**

So, I guess we can't find the area, since we need the side
*April 6, 2016*

**Geometry**

Area = 1/2 x perimeter x apothem = 1/2 (6s)(6√3) once you tell me what the side (s) of the hexagon is, we an finish the question
*April 6, 2016*

**Algebra**

confusing wording Anyway, for y = mx + b m is the slope, or the rate of change the greater the value of m, the greater the rate of change.
*April 6, 2016*

**math**

looks like an AS with a = 4.5 and d= .5 term(5550) = a + 5549d = 4.5 + 5549(.5) = ....
*April 6, 2016*

**math**

2c + 4b = 600 2c + 7b = 825 subtract them: 3b = 225 b = 75 sub b = 75 back into the firs equation and solve for c let me know what you get.
*April 6, 2016*

**Precal**

We don't "work this out" I believe this is an identity, so we have to prove LeftSide = RightSide If it is an identiy, if we attempt to "solve" it, we end up 0=0 LS = cot^3 x+ cotx = cotx(cot^2 x + 1) = (cosx/sinx)((cos^2 x/sin^2 x + 1) = (cosx/sinx)(cos...
*April 6, 2016*