Sunday
April 20, 2014

Posts by Reiny


Total # Posts: 26,042

Algebra 2
the way you typed it, multiply each term by 2 x^2 + 4x + 6 = 0 complete the square ... x^2 + 4x + 4 = -6+4 (x+2)^2 = -2 x+2 = ± √-2 x = -2 ± i√2

For Sam - math
Even if tossing around a few numbers often yields the "correct answer", the statements must be mathematically correct and logically sound look at your statement: 3/5 = 2+4 , now that is news to me, I always thought 2+4 is 6 and not 3/5 Do you see what I mean ? .........

math
tan E = y/x = (4/5) / (3/5) = 4/3

Algebra
in standard form we usually lead with the x term with a positive coefficient, so I wanted a +x as my first term, it was -x . to change a standard form to slope- yintercept form usually takes 2 steps: 1. move all terms except the y term to the right e.g. 4x - 5y = 8 ---≥ ...

Algebra
your slope is correct as +1 your equation of y+1 = 1(x+2) is also correct then y+1 = x+2 y = x+1 ---> slope-yintercept form y-x = 1 x - y = -1 ----> standard form ( I multiplied each term by -1)

math
first round: x --> 3x --- >3x-2 2nd round: 3x-2 ---> 9x-6 ---> 9x-8 3rd round: 9x-8 ---> 27x - 24 ---> 27x - 26 27x - 26 = 271 27x = 297 x = 11

math question grade 8!!
Wow, those rooms are pretty small even for a doll-house.

Math - Calculus I
Draw a side view of the situation (The cone will look like an isosceles triangle with a rectangle (the cylinder) sitting on its base and touching the sides) let the radius of the cylinder be r and let the height of the cylinder be h Look at the small right-angled triangle at t...

Math
A new number is obtained by adding the 3 previous ones.

Math
let the 6 consecutive multiples of 6 are 6x , 6x+6 , 6x+12, 6x+18, 6x+24 and 6x+30 their sum is 36x + 90 the LCM of 13 and 18 is 234 36x + 90 = 234 36x = 144 x = 4 So the number are : 24, 30, 36, 42, 48, and 54

Algebra 1
Let the time traveled by each one be t hrs distance gone by first = 125t miles distance gone by 2nd = 120t miles 125t + 120t = 735 245t = 735 t = 3 After 3 hrs, they will be 735 miles apart

Algebra
You must mean y = x^2 - 2x - 15 , note how we show exponents. =(x-5)(x+3) so the zeros are -3 and 5

Math
1. (4/5)(5/7) = 4/7 2. -1 1/6 ÷ 2/9 = (-7/6)(9/2) = -63/12 = -21/4 or -5 1/4 3. (-32/5) ÷ (-16/7) = (-32/5)(-7/16) = 14/5 or 2 4/5 4. You do this one the same way I showed you

Statistics
true

Statistics
true, but your answer should be reduced to 1/6

TO REINY
You are very welcome

Advanced Functions/Precalculus
2. 7sin^2x - 4sin2x/cosx = -1 7sin^2 x - 4(2sinxcosx)/cosx = -1 7sin^2x - 8sinx + 1 = 0 (7sinx - 1)(sinx - 1) = 0 sinx = 1/7 or sinx = 1 if sinx = 1 x = 90° or π/2 if sinx = 1/7, then x = aprr 8.2° or 171.8° 3. cos 2Ø = cos^2 Ø - sin^2 Ø g...

Advanced Functions/Precalculus
will you take a look at the fun that even Wolfram had in solving the equation the way you typed it ??? http://www.wolframalpha.com/input/?i=solve+sin2x%2B1%3D-2sinx I have a feeling that you meant: sin^2 x + 1 = -2sinx then sin^2 x + 2sinx + 1 = 0 (sinx + 1)^2 = 0 sinx +1 = 0 ...

math
slope = (7-2)/(3-(-5)) = 5/8 y-7 = (5/8)(x-3) 8y-56 = 5x - 15 -5x + 8y = 41 5x - 8y = -41 in standard form 5x - 8y + 41 = 0 in general form y = (5/8)x + 41/8 in slope - yintercept form

math
We can't do diagrams in this forum Possible paths to get from lodge to entrance via dock AC AD BC BD I will do one length , you do the others; BC = 2/3 mile + 1/4 mile = (8+3)/12 = 11/12 miles

Algebra 1
1. Area of a square = (x^2)^2 = x^4 (each side is x^2, area of a square = side^2 so (x^2)(x^2) = x^4 ) 2. when x = 5 area = 5^4 = 625 3. when x = 10 area = 10^4 = 10000

Math
number of short-sleeved shirts --- x number of long-sleeved shirts --- 63-x 15x +22(63-x) = 1134 15x + 1386 - 22x = 1134 -7x = -252 x = 36 so 36 short-sleeved and 27 longsleeved shirts

Calculus
the shape you will get is half a torus. A torus is a donut or bagel shaped solid. We have cut ours in half (to make a tasty cream-cheese bagel) the y-intercepts: 0 = y(9-y) so y = 0 or y = 9 , You had that so we need the radius of the outer and the inner rings: y^2 - 9y = -x y...

Math (PreCalculus)
I get log(1584893) = 6.199999 or 6.2 not 6.268

Can anyone help me with this?
Disagree with 1. My Canada is the 2nd largest country in terms of area, but has only 35 Million, about 1/10 of yours. I would pick C

help please math
i = .06/24 =.0025 n = 5(24) = 120 Let the payment be P P( 1 - 1.0025^-120)/.0025 = 18000 I get P = $173.81

math
payment -- P P( 1 - 1.17^-20)/.17 = 250000 I get P = $44,422.59

math
Where are you getting these magical 18% and 17% ?? Amount = 10( 1.015^540 - 1)/.015 = $2,067,433.43

Advanced Functions/Precalculus
11π/12 is π/12 short of 2π so tan 11π/12 = -tan π/12 I know tan 2π/12 = tan π/6 = 1/√3 tan 2π/12 = 2tanπ/12/(1 - tan^2 π/12) let x = tan π/12 for easier typing so 1/√3 = 2x/(1 - x^2) 2√3x = 1 - x^2 x^2 + ...

MATH.
C(9,6) = 9!/(6!3!) = 362880/(720 x 6) = 84 you should have a C(n, r) key on you r calculator sometimes shown as nCr on mine it is found under the "5" key so enter 9 nCr 6 = to get 84

Geometry
measured along the diagonals, so diagonal is twice as big

Geometry
I will do the 1st one you do the 2nd method 1. check to see if it is right -angled, then it would be real easy is 3.5^ + 4.8^2 = 6.1^2 ? , NO --- so forget that method method 2: find the angle opposite the smallest side using the cosine law 3.5^2 = 4.8^2 + 6.1^2 - 2(4.8)(6.1)c...

math
You must have a typo If you want me to use the stated property, then you must have meant 9^(-x+15) = 27^x if as assumed, then (3^2)^(-x+15) = (3^3)^x 3^(-2x + 30) = 3^3x -2x + 30 = 3x , using your stated property -5x = -30 x = 6

math
You will also have to insert brackets to clarify the order of operation here e.g. I will do the 2nd one assuming you meant: 7√(2x) + 2√(72x^3( - √(162x^5) = 7√(2x) + 2√(2x) √(36x^2) - √(2x) √(81x^4) = 7√(2x) - 12x√(2x...

Math
area of circle = π(7^2) = 49π prob of landing in circle = 49π/420 = 7π/60 = appr .3665 ignoring any leaves that fall partially either on the circle or the edge of the yard

GEOMETRY CIRCLES PLEASE
This is just too easy. Remember that both tangents to the same circle from an exterior point are equal. so AB = AC but AC is also tangent to the small circle so AC = AD but AD is also a tangent to the circle at the right so AD = AE Since the are all equal , and AB = 15 each on...

Math-Trig
make a diagram showing a sideview. remember the angle of depression from the helicopter view is equal to the angle of elevation from groundview. So I have a right-angled triangle, with a height of 105 (opposite side), the adjacent side of x and an angle of 30.5 take it from there

calc
first of all use the rules of logs y = ln (1 - x^2)^(1/2 = (1/2) ln (1 - x^2) now ... dy/dx = (1/2) (-2x)/(1-x^2) = -x/(1-x^2)

finance
My interpretation of the wording first year = 47500 2nd year = 47500(1.23) third year = 47500(1.23)^2 fourth year = 47500(1.23)^2 (1.12) = .....

Algebra 1
You have the same base, so (8^6/8^4)(8/2) = 8^(6-4+2) = 8^4

prealgebra
when is .15t + 26.50 = .25t + 14.50 multiply by 100 to clean up the numbers 15t + 2650 = 25t + 1450 -10t = -1200 t = 120 minutes at 120 minutes the charge would be the same

prealgebra
Four times a number is 21 more than the number ----> 4x = 21 + x 3x = 21 x = 7 Anna "thought" the answer is 7 Now you can be 100% sure that the answer is 7

Math
Ummmh, the ratio of radius to diameter is always 1 : 2

ALGEBRA 1
z^-9 is the same as 1/z^9 both answers are correct

Trigonometry/Geometry
Start by drawing a reasonably accurate rhombus on a piece of paper. Remember a rhombus has 4 equal sides and opposite angles equal, ( A square is a special kind of rhombus, so don't use a square) cut your rhombus out with scissors. Surprisingly, you will be able to form a ...

math formula help needed
let her payment be p i = .065/52 = .00125 p( (1.00125^312 - 1 )/.00125 = 15000 solve for p You should get p = 78.68

Fault in "education" - the cay(help)
Let me understand this ! You have an assignment due on a book which you have not read or even seen. That assignment was due tonight, and you expected us to just give you the answers. Call me old-fashioned, but when I was teaching I would have called that "cheating" Y...

math
Use that same fantastic webpage I just gave you.

math
One of the best webpages available for this topic http://davidmlane.com/hyperstat/z_table.html It replaces your tables at the back of your text. enter mean of 170 enter sd of 5 a) click on 'between' and enter 170 and 180 multiply that by 60 b) what do you think?

math
i = .06/4 = .015 n = 4(6) = 24 What is the "future" value .... So which formula do you think you should use ? What is your equation? Let me know what you got.

math
You want the present value of 20 payments of 5500 at the end of each quarter for 5 years i = .08/4 = .02 n = 4(5) = 20 PV = 5500( 1 - 1.02^-20)/.02 = $89932.88

annuities..math
i = .06/12 = .005 n =2.5(12) = 30 amount = 100( 1.005^30 - 1 )/.005 = $3228.00

geometry
mmmhhhh http://www.jiskha.com/display.cgi?id=1386103063

geometry
let the outer segment of the 2nd secant be x then the inner segment is 28-x 8/6 = x/(28-x) 6x = 224 - 8x 14x = 224 x = 16

algebra
prob(2) = 1/6 prob(not 2) = 5/6 prob (four 2's out of 6) = C(6,4) (1/6)^4 (5/6)^2 = 15(1/1296)(25/36) = appr .008

Geometry
2.54 cm = 1 inch (official definition of inch since 1959) 1 cm = 1/2.54 inches 1 m = 100/2.54 inches 1 km = 1000(100/2.54) inches = 100000/(2.54*12*5280) miles = .62137 miles which is the same as your other definition correct to 2 decimals.

Math
Good Grief !! http://www.wolframalpha.com/input/?i=plot+y+%3D+ln%7CSin2X-CosX-1%7C+ First of all, if ln (something) = 0 then (something) = 1 so sin 2x - cosx - 1 = 1 or -1 easy one first: sin 2x - cosx - 1 = -1 2sinxcosx - cosx = 0 cosx(2sinx - 1) = 0 cosx=0 or sinx= 1/2 x = &...

incorrect - math answer check please
the interest rate is 5% per annum compounded monthly that means you get .05/12 each month, NOT .05 I did this question for you , look back to see the solution. Your solution and answers above make absolutely no sense.

math
value of 125000 6 months from now = 125000(1.00416666...)^6 = 128157.73 Pr value of 135000 x(1.00416666..)^6 = 135000 x = 131673.68 So both solutions show that he should take the 135000 six months from now. At he present time, the difference is worth = 131673.68 - 125000 $ 667...

Algebra!
#2 done the same way as the first x+y = 41 ---#1 12x + 17y = 582 ---> #2 #1 times 12 12x + 12y = 492 12x + 17y = 582 subtract them: 5y = 90 y = 18 then x = 23 23 short-sleeved and 18 long-sleeved shirts

Go with Kuai - Algebra 1 (Reiny or Kuai)
sorry about my arithmetic error when I copied your diagram to paper, I had point Q as (3,6) instead of (2,6)

Algebra 1 (Reiny or Kuai)
I did this for you , it was #5 of http://www.jiskha.com/display.cgi?id=1386029033 Ok, once more, very simple: slope PQ = (6-4/(2-1) = 2 slope QR = (6-3)/(2-8) = -3/5 So there is no right angle at Q but a rectangle must have 4 right-angles I have shown that one of them is not, ...

Algebra 1 (Reiny or Kuai)
in a trapezoid, one pair of opposite sides are parallel Make a sketch slope BC = (5-2)/(4-6) = 3/-2 = - 3/2 slope AD = (5-(-1))/)-2-2) = 6/-4 = -3/2 Yup, it is I didn't check for the other pair I could see that AB is horizontal, since both points have the same y value, whi...

Algebra 1 Answer Check (Reiny or Kuai)
#5. no, it is not a rectangle. angle P = 90° angle S = 90° but since slope PQ = 2 and slope of QR = -3/5 we don't have a right angle at Q no need to go further.

Algebra 1 Answer Check (Reiny or Kuai)
1. y=6 and y=-8 are parallel, they are both horizontal y=6x + 5 and y = 6x-7 are parallel, they both have a slope of 6 2. the first and third are parallel, you had that but also the 2nd and last line are parallel, both have a slope of -2 3. the 1st and 2nd lines are perpendicu...

math
Did you mean 7 is added to the result after dividing by 6 ? Else how can you add 7 to the divisor if the division has been done? The wording is very odd. According to my interpretation: x/6 + 7 = 4 x/6 = -3 x = -18

Math
1 inch ---> 6 inches 2 inches ----> 1 foot 32 inches ----> 16 feet

math
type it this way: f(x) = x^5 - 6x^4 + 7x^3 - 10x^2 since complex number zeros always come in conjugate pairs, there is another zero of 1-i so (x -(1+i)) and (1 - (1-i)) are factors expanded gives us: (x-1-i)(x-1+i) = x^2 - x + ix - x + 1 - i - ix + i - i^2 , but i^2 = -1 = x^2...

math
I found f(3) = 0 , x-3 is a factor then found f(-2) = 0 , so x+2 is a factor divided both of those and got -(2x^2-7x+3) which factored further to -(x-3)(2x-1) so f(x) = -(x-3)^2 (x+2)(2x-1) with zeros at x= -2, 1/2 and 3 , 3 being a double root

2nd question - calculus area between three curves
nice symmetry, should be easy to see that the x-intercepts are (c,0) and (-c,0) for both so just double the area from 0 to c area = 2∫(c^2 - x^2 - (x^2 - c^2)) dx from 0 to c = 2∫(2c^2 - 2x^2) dx from 0 to c = 2[2c^2 x - (2/3)x^3] from 0 to c = 2(c^3 - (2/3)c^3] = ...

calculus area between three curves
3 graphs: y = 2√x y = 3 y = (-3/2)x + 7 see: http://www.wolframalpha.com/input/?i=plot++y+%3D+2√x+%2C+y+%3D+3+%2C+y+%3D+%28-3%2F2%29x+%2B+7+%2C+2%3Cx%3C3 intersection of y = (-3/2)x+7 and y = 2√x is aprr A(2.54, 3.188) intersection of y = 2√x and y = 3 ...

calc
Ok, let's do it their way, (and get the same answer as I got before) Let the number of actual trees planted be k (I will now switch my original definitions to this new definition) number of trees = k , I had x+30 so k= x+30 and x = k-30 yield per acre: I had 150-3x = 150 -...

calc
Looks like you defined x as the number of extra trees to be planted, which is what I did as well They defined x as the actual number of trees planted. When you differentiate their equation , set it equal to zero and solve you get x = 40 the total number of trees is 40 Notice t...

calc
Let x be the number of additional trees planted per acre Number of trees per acre = 30+x yield per tree = 150 - 3x total = (30+x)(150-3x) = 4500 + 60x - 3x^2 d(total)/dx = 60 -6x =0 for a max total 6x=60 x = 10 So the max yield is obtained with 40 trees per acre. BUT, your con...

Math
first derivative: 2x = -2y dy/dx at (3,4) dy/dx = -3/4 2nd derivative: 2 = -2y( d^2y/d^2x) + (-2)(dy/dx) at the given point (3,4) 2 = -8(d^2 y/d^2 x) - 2(-3/4) 8 (d^2 y/d^2 x ) = 3/2 - 2 = -1/2 d^2 y/d^2 x = -1/16

Geometry
make a sketch drawing both diagonals Look at one of the triangles containing the 60° angle. Since the diagonals bisect each other, each side containing the 60° angle must be 12 inches long. The triangle must be isosceles, so each of the other angles is also 60°, an...

Math
I do not follow your order of exponents You will have to be much more specific by using brackets e.g. 2^3^4 done on my calculator by punching it in that way gives me 4096 (The calculator appears to evaluate from left to right and simply does (2^3)^4 = 2^12= 4096 But, what abou...

Math Probability *Repost*
yes if the prob of winning by buying 1 ticket is 1/38760 then the prob of winning with 1000 tickets is = 1000(1/38760) = 25/969

Math Probability *Repost*
As I stated in my previous reply to the same post .... Number of ways to draw 6 numbers from 20 is C(20,6) = 20!/(6!14!) = 38760 so prob(winner) = 1/38760

Algebra
width = x length > 2x Area > 2x^2

Math
first number --- x 2nd number --- y 2x - y = -1 or y = 2x+1 2y + 3x = 9 2(2x+1) + 3x = 9 4x + 2 + 3x = 9 7x = 7 x = 1 then y = 3 The first number is 1, and the second number is 3 check: twice the first - second = 2 - 3 = -1 , check! twice the second added to three times the fi...

algebra
one cut makes 2 pieces two cuts make 3 pieces ... ? cuts make 12 pieces ?

Math Probability
Done here http://www.jiskha.com/display.cgi?id=1385948148 Why are you switching names?

Math
Once again, the same kind of question as before. step1: find slope (you did that correctly and got m = -2) step2: use y-y1 = m(x-x1) , where (x1, y1) is either of the given points using (2,4) y-4 = -2(x-2) y-4 = -2x + 4 standard form has both x and y terms on the left, the con...

Math Probability
Joe has assumed that the same number could be drawn more than once. However,in most of these lotteries, some kind of drawing method is used, such as 20 different-numbered pingpong balls, and the order that they are drawn does not matter. Number of ways to draw 6 numbers from 2...

MATH
Henry had done this same question for you here http://www.jiskha.com/display.cgi?id=1385944773 why did you repost it?

PreCal
notice the following pattern 2^0 = 1 2^0 + 2^1 = 3 = 2^2 - 1 2^0 + 2^1 + 2^2 = 7 = 2^3 - 1 , 3 terms in sum 2^0 + 2^1 + 2^2 + 2^3 = 15 = 2^4 - 1 , 4 terms in sum ... 2^0 + 2^1 + ... + 2^9 = 1023 = 2^10 - 1 (the sum of n powers of 2 starting with 2^0 or 1, will be 2^(n+1) - 1 s...

Calculus Please Help!!
I assume you mean the triangle that the ladder makes with the ground and the wall. Area = (1/2)ab d(Area)/dt = (1/2)a db/dt + (1/2)b da/dt so when a= 5, b=12 , db/dt = 6, da/dt = -72/5 d(Area)/dt = (1/2)(5)(6) +(1/2)(12)(-72/5) = 15 - 86.4 = -71.4

Maths
or 3x9^x=81 , divide both sides by 3 9^x= 27 (3^2)^x = 3^3 3^(2x) = 3^3 2x = 3 x = 3/2 = 1.5

MATH
Hannah, you have had several related questions, and should be able to do these by now. Once more .... you slope is correct. Here is a method that should work for you all the time if you know the slope and a point ( let's pick the point (3,8) with slope 4/3 then (y-8)/(x-3)...

MATH HELP
a^(2t/3)

Math
Perpendicular to which line ? Did you just want a vertical line ? Try to sketch a vertical line which "cuts" across the y-axis , pretty tricky eh? So what do you think?

Math - Algebra 2
let y = ax^2 + bx + c for (0,-5) -5 = 0 + 0 + c, so c = -5 for (3,-6) -6 = 9a + 3b - 5 9a + 3b = -1 , #1 for (-3,-7) 9a -3b -5 = -7 9a - 3b = -2 , #2 add #1 and #2 18a = -2 a = -1/+ sub into #1 9(-1/6) + 3b = -1 -3/2 + 3b = -1 -3 + 6b = -2 6b = 1 b = 1/6 so f(x) = (-1/6)x^2 + ...

Maths
The first one contains a typo and makes no sense 2nd: I bet you mean: 27^(x+5) = 9^(2x-1) then ... (3^3)^(x+5) = (3^2)^(2x-1) 3^(3x+15) = 3^(4x-2) 3x + 15 = 4x - 2 -x = -17 x = 17 3rd: 8(16^(x-1) = 4^(3x) (2^3)(2^(4x-4) = 2(6x) 2^(4x-1) = 2^(6x) 4x-1 = 6x -2x = 1 x = -1/2

Math
y = |x^4 - 5x^2 + 4| = | (x^2 - 4)(x^2 - 1) | = | (x+2)(x-2)(x+1)(x-1) | I graphed it on Wolfram http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx%5E4+-5x%5E2+%2B4%7C%2C+-3%3C+x+%3C+3 Notice that there are cusps at the zeros of the corresponding non-absolute function At a c...

Trigonometry
And I had already done this for you here http://www.jiskha.com/display.cgi?id=1385827548 This is the third time you have posted this question. Always check your previous post before re-posting

Trigonometry
And I had already done this for you here http://www.jiskha.com/display.cgi?id=1385827548 This is the third time you have posted this question. Always check your previous post before re-posting

algebra 1
slope = (4-3)/(-2-0) = -1/2 since (0,3) is the y-intercept y = (-1/2)x + 3 ...... all done

MATHS
I suggest you Google something like "Chinese Remainder Theorem" and I assume you know about modular arithmetic since I will be using properties of modular arithmetic so we have z = 1 mod 6 z = 1 mod 7 z = 7 mod 8 z = 7 mod 11 But, in the Chinese Remainder Therorem we...

math
I find it hard to see why this is difficult. Since there is no interest Just subtract the rebate, then divide that answer by 60.

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