Sunday

April 20, 2014

April 20, 2014

Total # Posts: 26,030

**To: Reiny**

what question?

**permutation and combination**

so we only use 24 cards, of which 12 are red number of 5-card hands = C(24,5) = 42504 let's exclude number with no reds and only one red number with no reds = C(12,0) x C(12,5) = 792 number with 1 red = C(12,1) x C(12,4) = 5940 no number with at least two reds = 42504 - 79...

**math**

let the width be w length = 2w-5 w(2w-5) = 25 2w^2 - 5w - 25 = 0 (2w+5)(x-5) = 0 w = -5/2 or w = 5, but the width could not be negative, so the width is 5 and the length is 2(5)-5 or 5 your rectangle is a square.

**math**

done before, look back

**Math!**

35/26.25 = 8/h 35h = 8(26.5) h = .....

**math**

16^(1/3) e^4

**Algebra 2**

welcome

**Algebra 2**

8+64n = 8n 64n - 8n = -8 56n = -8 n = -8/56 = -1/7

**Math**

1. area = s^2 = 81/100 s = 9/10 2. area = 484 so side + √484 = 22 so sum of 4 sides = 88

**algebra**

multiply each term by z 2az + 2b = 5cz 2az = 5cz-2b a = (5cz - 2b)/(2z)

**algebra**

19-π

**algebra**

-4x - 48 ≥ -30 -4x ≥ 18 x ≤ -9/2

**math**

green apples --- x red apples ------ 4x x+4x=50 x = 10 so 10 green and 40 red

**Math**

1. correct Be definition, |anything| has to be a positive result so how can "+something" < -3 ? NO WAY! 2. how about this: -4 < -2t + 6 < 10 subtract -6 -10 < -2t < 4 divide by -2, must reverse signs 5 > t > -2 add 6 ---> we needed t+6 in the ...

**Math**

you will have to use logs 4( 7^(x-2) ) = 8 divide both sides by 4 7^(x-2) = 2 take logs of both sides log (7^(x-2) ) = log 2 by rules of logs (x-2)(log 7) = log 2 x-2 = log 2/log 7 x = 2 + log2/log7 = appr 2.3562

**Math**

remember all you need to draw a straight line is 2 points, the intercepts are 2 good points to use I just showed you in a previous point how to find those intercepts x+y = 4 let x = 0 --->y = 4 or the point (0,4) let y = 0 ---> x = 4 or the point(4,0) piece of cake!!! y-...

**Math**

1. Perpendicular to what? -- missing information there must have been some original line given, or else the slope

**Math**

You did well. Some small errors from y-3 = 3(x+1) y-3 = 3x + 3 at this point you did: y-3+3 = 3x+3 should have been y-3+3 = 3x+3 + 3, then y = 3x + 6, which you have (so there were actually two errors here) #2, looking at y-3 = 3(x+1) and comparing it to the point-slope form o...

**math-advanced functions**

f(g(x)) = f(2cos(x) ) = 3(2cosx)^2 + 2cosx - 1 = 12 cos^2 x + 2cosx - 1 we want 12 cos^2 x + 2cosx - 1 = 1 12 cos^2 x + 2cosx - 2 = 0 6 cos^2 x + cosx - 1 = 0 (3cosx -1)(2cosx + 1) = 0 cosx = 1/3 or cosx = 1/2 since the domain is given in radians, our angle should be in radian...

**Math**

assume that the train travels at a uniform rate. between 12:45 and 2:15 ---> 1.5 hrs the train went 90 miles rate = 90/1.5 or 60 mph now use a simple ratio, if x is the distance traveled from noon to 12:45 x/.75 = 90/1.5 x = .75(90/1.5) = 45 miles but the train at this poin...

**Equation solving**

1. given: x - 3y = 2 -3y = -x + 2 y = (1/3)x - 2/3 so the slope of the given line is 1/3 then the slope of a perpendicular line is -3 new equation: y = 3x + b but (2,4) must lie on it, so 4 = 3(2) + b 4 = 6 + b -2 = b new equation: y = 3x - 2 2. I assume we are dealing with th...

**math**

changing them to direction vectors with standard angle notation. 50 yards N30°W = 50(cos120,sin120) = (-25,43.30) 80 yards N35E = 80(cos55,sin55) = (45.89 , 65.53 200 yds N10W = 200(cos100,sin100) = (-34.73 , 196.96) r yds at Ø = r(cosØ,sinØ) = (rcos&O...

**to REINY**

You are welcome

**in desperate need of help, PRECALC**

Found my error. from : = 200 (xy)/(100y+100x) = xy/(y+x) should be = 200 (xy)/(100y+100x) = 2xy/(y+x)

**For Damon**

Damon, I am having a brain freeze. I know you answer is correct. Can you see the error in my solution?

**in desperate need of help, PRECALC**

time going = 100/x ---> from Time = distance/ rate time going = 100/y total time = 100/x + 100/y = (100y + 100x)/(xy) total distance = 200 avg speed = total distance / total time = 200/( (100y+100x)/(xy) ) = 200 (xy)/(100y+100x) = xy/(y+x) but avg speed = 50 xy/(x+y) = 50 x...

**Pre-calc**

f) time for whole trip = 200/50 = 4 hrs time to go one way at 20 mph = 100/20 = 5 hrs. oops, whole trip only took 4 hrs. so ......

**math**

see http://www.jiskha.com/display.cgi?id=1389913970

**solid mensuration**

volume = base x height area of base: construct a right angled triangle by drawing an altiude to the longer diagonal. x^2 + 36 = 144 x = √108 there are 4 congruent right-angled triangles area of base = 4((1/2)(6)(√108) = 12√108 volume = 12√108 h once you...

**Pre-Calc**

you must mean N = 20(5+3t)/(1+.04t) plug in t = 5 N = 20(5+15)/(1 + .04(5)) = 400/1.02 = 2000 Do the others likewise. as t ---> large n = (100 + 60(large))/(1 + .04 large) = appr 60large/.04large = appr 60/.04 ---> 1500 the limiting size = 1500 e.g. let t = 100,000 N = 2...

**Math**

Easy if you know calculus. h ' (t) = -10t + 22 = 0 for a max/min of h(t) 10t = 22 t = 2.2 h(2.2) = -5(2.2)^2 + 22(2.2) = appr 24.2 m If you don't know Calculus, the x of the vertex of your parabola is -b/(2a) = -22/-10 = 2.2 sub in 2.2 into h(t) , same as above If you ...

**Math**

first rebound = .75(200) 2nd rebound = .75(.75(200)) =.75^2 (200) 3rd = .75^3 (200) 4th = .75^4 (200 = appr 63.28 ft

**Pre-Calc**

you must have a method of solving 800000 = -76x^3 + 4830x^2 - 320000 Wolfram yields two answers, one of appr 18 , the other appr 59.3 http://www.wolframalpha.com/input/?i=solve+800000+%3D+-76x%5E3+%2B+4830x%5E2+-+320000

**Pre-Calc**

if the page is x by y then the printable area = x-4 by y-4 so (x-4)(y-4) = 30 xy -4x - 4y + 16 = 30 xy - 4y = 4x + 14 y(x-4) = (4x+14) y = (4x+14)/(x-4) Total area = xy = x(4x+14)/(x-4) = 2x(2x+7)/(x-4) ---> that would be b) c) clearly x> 4 d) your job with the graphing ...

**Pre-Calc**

let me say right away, that defining x to be the length of the wire used for the square is a poor choice. But ... let the piece used for the square be x then the piece used for the circle = 100-x side of square = x/4 area of square = x^2 /16 perimeter of circle = 100-x perimit...

**Algebra 1**

Ratio of win : lost = 2 : 1 = 2x : x 2x+x = 96 3x = 96 x = 32 won = 2x = 64 lost = x = 32

**math**

i = .045/12 = .00375 what is 12000(1.00375)^48 ?

**Math**

let the number of grandchildren he has be n so total money = 17n + 7 20n = 17n+7 + 62 3n = 69 n = 23 total money = 17(23)+7 = $ 398 And he has 23 grandkids check: if he wanted to give each $20, he would need $ 460, But he has only 398, which is $ 62 short of what he needs. He ...

**Math**

so you want the specific order, RGRG prob(of that order) = (20/60)(40/59)(19/58)(39/57) = 260/5133 reduced to lowest terms or = appr .05065

**Math**

John's present age ---- x John's age 5 yrs ago = x-5 Loretta's present age = 2(x-5) in 3 yrs from now: John = x+3 Loretta = 2(x-5) + 3 x+3 + 2(x-5)+3 = 50 x+3 + 2x - 10 + 3 = 50 3x = 54 x = 18 NOW: john = x = 18 yrs Loretta = 2(x-5) = 26 yrs check: 5 years ago, Joh...

**Math**

375n = (25)(15)(n) = (5x5)(15 x n) to have a perfect square, each of my brackets must be a pair of same numbers. I need a 15 in my second bracket so n = 15

**Math**

multiples of 6: 6 12 18 .... 198 ---> 33 of them multiples of 9 9 18 27 ... 198 ----> 22 of them multiples of 18 , their LCM 18 36 ..198 ----> 11 of them number of multiple of 6 OR 9 = 33 + 22 - 11 = 44 prob(multiple of 6 OR 9) = 44/200 = 11/50 or .22

**algebra 1**

yes width = 400/25 = 16 Prm= 2(25+16) =82 , which is your answer

**unit rate**

time = 1 : 18 : 27 = 1 hr + 18/60 hrs + 27/3600 hrs = 1.3075 hrs speed = 26.5/1.3075 mph = 20.26768 mph

**Math**

yes, x(2x) = 2x^2 for the 2nd, we cannot add "unlike" terms, one is x^3, the other is x^5, not the same

**math**

enter your data into http://davidmlane.com/hyperstat/z_table.html to get .8327

**add maths**

f(x) = 4-x g(x) = px^2 + q g(f(x)) = g(4-x) = p(4-x)^2 + q = p(16 - 8x + x^2) + q = px^2 - 8p x + 16p+q if px^2 - 8p x + 16p+q = x^2 - 8x + 11 then p = 1 16p+q = 11 16 + q = 11 q = -5 and -8p = -8 p = 1, which checks out

**Algebra 1**

the same question was answered by bobpursley back in October http://www.jiskha.com/display.cgi?id=1382315986 I suggest you simply do what it says to do.

**math**

angle of depression and angle of elevation are concepts that should have been explained to you in your text or in class. If not, google "angle of depression"

**trigonometry**

Sketch the 2 buildings, mark the window on one of them. Draw a horizontal from the window to the other building, mark it as 15m (any horizontal line between the two buildings will be 15m ) From the window draw in lines to the top and bottom of the opposite building. Mark your ...

**algebra 2**

solve by completing the square ?? first divide by 2 and move the constant to the right ... x^2 - 2x = 1 add 1 to both sides x^2 - 2x + 1 = 1 + 1 (x-1)^2 = 2 x-1 = ± √2 x = 1 ± √2

**math**

Basic trig, if the length of the ladder is h ft 3/h = cos 80° h = 3/cos80° = appr 17 ft

**Calculus**

V= (l)(w)(h) since the length and width do not change, only V and h. dV/dt = (lw) dh/dt We must have the same units, 20 cubic feet = 20(12^3) or 34560 cubic inches when V = 34560 and dV/dt = -4 34560 = (lw) h lw = 34560/h -4 = 34560/h dh/dt dh/dt = -h/8640 inches/second Are yo...

**Math**

number of additional miles --- x .2x + 2.4 + 2 = 10 .2x = 5.6 x = 28 So you can ride 28.5 miles

**Math help asap!!!**

correct

**Math help asap!!!**

5(x – 9) = 5x 5x - 45 = 5x -45 = 0 If your variables drop out and you end up with a true statement, such as 4 = 4, there will be an infinite number of solutions. If your variables drop out and you end up with a false statement, such as our -45 = 0, there will be no soluti...

**Algrebra**

bird's air speed ---- x mph wind speed -------- y mph x+y = 3 x-y= 1.5 add them 2x = 4.5 x = 2.25 mph y = 0.75 mph

**geometry**

Didn't you just state that gcb = 13x - 9 ? I have no clue what gcb is, or what m fcg is.

**math**

width--- x length --- 5x "would be" situation: width = x+24 length = 5x - 24 then 5x -24 = x+24 4x = 48 x = 12 the rectangle is 12 by 60 check: had it been 24 shorter ---> length = 60-24 = 36 had it been 23 wider -----> width = 12 + 24 = 36 all is good!

**math**

solve: x + 2x+25 = 150

**Nadine -Miranda -Eleyan-Algebra**

Why are you switching names?

**Algebra**

http://www.jiskha.com/display.cgi?id=1390189178

**add maths**

find g^-1 (x) the way I showed you from that get f^-1(p) , then find f(4) set those two equal to each other and solve

**add maths**

Ok, your turn for #2, I have given you several examples. It is really easy. See if you can get p = 2

**add maths**

huh?? for your first ... /(x+2) , x is not equal to -2 so in " .. x is not equal to k" , I guess k must be -2

**add maths**

define f^2 (x) is it ( (x+1)/(x-1) )^2 ??

**add maths**

remember how I did the last one for you? original: y = (x+10)/(x-8) inverse: x = (y+10)/(y-8) xy - 8x = y+10 xy - y = 8x + 10 y(x-1) = (8x+10)/(x-1) f^-1 (x) = (8x+10)/(x-1) so we want: (8x+10)/(x-1) = x x^2 - x = 8x + 10 x^2 - 9x - 10 = 0 (x-10)(x+1) = 0 x = 10 or x = -1 chec...

**Algebra**

I just did 2 very similar problems for you. Follow my method and let me know what you got

**Algebra**

I just did 2 very similar problems for you. Follow my method and let me know what you got

**Algebra**

NOw: Macky --- x Mimie --- x+12 4 years from now: Macky --- x+4 Mimie --- x + 16 x + 4 = (2/3)(x+16) times 3 3x + 12 = 2(x+16) 3x + 12 = 2x + 32 x = 20 Now, Macky is 20 and Mimie is 32 check: 4 years from now, Macky will be 24 and Mimie will be 36 Is 24 equal to 2/3 of 36 ?? YES

**Algebra**

List their ages at the two different times NOW: Mike's age --- x father's age -- 2x 7 YEARS AGO: Mike ---- x-7 father ---- 2x-7 It said: " (7 yrs ago) the father was 7 years less than thrice as old as Mike was ---> 2x-7 = 3(x-7) - 7 2x - 7 = 3x - 21 - 7 -x = -2...

**add maths**

yes, but in this form of typing you have to use brackets. f^-1 (x) = 3x/(x-3) or else the 3x is divided by x only

**add maths**

What would happen if you sub x = 1 into our new denominator? Can we divide by zero ?

**add maths**

I will do the 2nd, you do the 1st in the same way f(x) = (2x+4)/(2x-1) or y = (2x+4)/(2x-1) inverse by switching x's and y's x = (2y+4)/(2y-1) simplify and solve this for y .... 2xy - x = 2y+4 2xy - 2y = x+4 y(2x - 2) = x+4 y = (x+4)/(2x-2) f^-1 (x) = (x+4)/(2x-2) , x ...

**Mathh**

your first part is correct for the 2nd part, I would have it as T(x) = .0175x - 3000 , x ≥ 400,000 (so I have taken 1.75% on the whole thing, but then subtracted the 0.75% part for the first 400,000 which is 3000. Where did you get your $500 from ? )

**calculus**

I would solve it for y first 1-xy = x-y y - xy = x-1 y(1 - x) = x-1 y = (x-1)/(1-x) = -1 , x ≠1 Well, isn't that special !!! so y' = 0 and of course y '' = 0 Wolfram took it as a pair of intersecting lines. Notice the horizontal line y = -1 The vertical l...

**Calculus**

f'(x) = 6x - 3 f'(a) = 6a - 3

**math**

(3*((-5)+7))+((19-7/4) there are mis-matched brackets at the right of the expression, ignoring this type we get = 3(2) + 19 - 1.75 = 23.25 if you want the answer to be 9, you would have brackets in this way: (3*((-5)+7))+((19-7)/4) = 3(2) + 12/4 = 6 + 3 = 9

**Math Help**

l -(-5)^2 l [( -5) - (-2)] + [(-5)^3 + (-2)] = |-25| [ -5 + 2] + [- 125 - 2] = 25(-3) + (-127) = -202

**algebra 2**

so you would want 3 = -.2x^2 + 1.3x .2x^2 - 1.3x + 3 = 0 times 10 2x^2 - 13x + 30 = 0 x = (13 ±√-71)/4 which is not a real number, so NO, the mouse cannot jump over that fence or the x of the vertex is 1.3/(2(.2)) = 1.3/.4 = 13/4 when x = 13/4 y = -.2(13/4) + 1.3(...

**Math! Ms.Sue Please**

check this later post http://www.jiskha.com/display.cgi?id=1390271913 I missed that set of inside brackets.

**Math! Ms.Sue Please**

just plug in the values x = -5 and y = 3 l-x^2l (x - y) + (x^3 + y) = |-25| (-5-3) + (-125+3) = 25(-8) + (-122) = -322

**Math**

[f(2 + h) − f(2)]/h if h ≠ 0 if f(x) = x^2 - 3x f(2+h) = 4+4h+h^2 - 3(2+h) = h^2 + h - 2 f(2) = 4-6 = -2 [f(2 + h) − f(2)]/h if h ≠ 0. = (h^2 + h - 2 - (-2))/h = (h^2 + h)/h = h + 1

**Algebra**

Gustav -- x his father -- 7x One year ago: Gustav -- x-1 his father -- 7x-1 7x-1 = 9(x-1) 7x-1 = 9x - 9 -2x = -8 x = 4 Gustav is now 4 years old check: his father is now 28 one year ago, Gustav was 3 and his father would have been 27, which is 9 time Gustav's age

**Algebra**

10 years ago: son --- x father --- 3x NOW: son --- x+10 father --- 3x+10 12 years from now: son --- x+22 father -- 3x + 22 x+22 = (3/5)(3x + 22) times 5 5x + 110 = 9x + 66 -4x = -44 x = 11 so 5 years ago: son = present age - 5 = (11+10) - 5 = 16 father = 3x+10 - 5 = 38 So 5 ye...

**finance**

17700( 1 - (1+i)^-300)/i = 2700000 (1 - (1+i)^-300 )/i = 152.5423729 nasty.. going to use Wolfram http://www.wolframalpha.com/input/?i=%281+-+%281%2Bx%29%5E-300+%29%2Fx+%3D+152.5423729 I = .0051528 annual rate compounded monthly = .0618.. or appr 6.18%

**MATH**

adults --- x children -- 82-x 8x + 3(82-x) = 431 take over from here.

**math URGENT**

sin 2x - sinx = 0 , 0 < x < 2π 2sinx cosx - sinx = 0 sinx(2cosx - 1) = 0 sinx = 0 or cosx = 1/2 for sinx = 0 x = 0 , π , 1π for cosx = 1/2 x = π/3 or x = 5π/3

**Math**

(-3)^-4 = 1/(-3)^4 = 1/81

**Calculus**

domain of f(x) : any real number, x ≠ 3 lim (x-3)/(x^2 - 9) , x --->3 = lim (x-3)((x-3)(x+3)) = lim 1/(x+3) , as x -->3 = 1/6

**Algebra 1 (Reiny)**

no, anything^0 = 1 so 2x^0 y^-3 = 2(1)/y^3 = 2/y^3 How in the world did you get -1/64? What happened to your variables.?

**Math**

let distance covered by the 40 mpg car be x miles let the distance covered by the 30 mpg car be 1250-x miles gas used by the 40 mpg car = x/40 gas used by the 30 mpg car = (1250-x)/30 x/40 + (1250-x)/30 = 35 times 120 3x + 4(1250-x) = 4200 -x = -800 x = 800 So the more efficie...

**Maths**

Ok, then .... If the slope is undefined, you have a vertical line. All vertical lines can be defined only by their x value. since x = 3 the equation of your line is x = 3 Furthermore, if the slope is undefined, that is, if the line is vertical it CANNOT be written in the form ...

**Maths**

equation is y = (UD)x + b Until you reveal more information about this mysterious UD , that's all I can give you.

**mathIV**

tanØ + secØ - 1 / tanØ - secØ + 1 = tanØ + secØ Surely , you must have meant (tanØ + secØ - 1) / (tanØ - secØ + 1) = tanØ + secØ I will use x instead of Ø for easier typing LS = (sinx/co...

**algebra**

parallel lines have the same slope. Pick out the pair that has the same slope.

**algebra**

slope of first line = (8-2)/(6+1) = 6/7 slope of 2nd line = (y-5)/(5+1) = (y-5)/6 to be perpendicular, (y-5)/6 = -7/6 y-5 = -7 y = -2

**algebra**

If it is parallel, then it must have the form y = (1/2)x + b , with (4, -3) on it -3 = (1/2)(4) + b -3 = 2 + b b = -5 y = (1/2)x - 5

**math**

y^2 x^2 = 2x y^2 = 2x/x^2 y^2 = 2/x , clearly x > 0, (something squared could not be negative) y = ± √2/√x y = ± √2/√x * √x/√x = ± √(2x) / x Whenever you have an equation of the form x^2 = k, where k is a positi...

**math**

Not clear what you meant because of your typo I see no equal sign. Secondly did you mean (x-2)^2 or √(3x-2) ?

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