Sunday
April 20, 2014

Posts by Reiny


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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