Wednesday
April 23, 2014

Posts by Reiny


Total # Posts: 26,103

cal
f(x) = x^-2 - 2x - 8 f ' (x) = -2x^-3 - 2 f '' (x) = 6x^-4 extrema: -2/x^3 = 2 x^3 = -1 x = -1, f(-1) = 1 - 2(-1) - 8 = -5 at x = -1, f ''(-1) is > 0, so (-1,-5) is a minimum my answer confirmed by http://www.wolframalpha.com/input/?i=plot++y+%3D+1%2Fx%5...

check: Algebra 1
I assumed your constant would have been correct, wrong assumption. go with kuai's solution, but write it as x- 2y = -7

Algebra 1
It is considered "poor form" to have the equation in standard form start with a negative x or containing fractions. so the 1st one I would write as x - y = -8 the last one: firs of all it should have been (-1/2)x + y = 23/2 multiply each term by -2 x - 2y = -23

geometry
correct

geometry
dodecagon --- 12 sides It must be regualar, that is, all sides must be equal and all 12 interior angles are equal. sum = 180(n-2) so each angle = 180(n-2)/n for 12 sides: each angle = 180(12-2)/12 = 150° you do the one with 20sides

6th grade math
nope http://www.wolframalpha.com/input/?i=plot+%281%2C5%29%2C+%282%2C5%29%2C+%283%2C5%29%2C+%284%2C5%29 notice all their y values are the same, y = 5 so it is a horizontal line

math
Your question makes no sense to me What is $150 ? Is the 8% rate compounded monthly? What is the $12.87 supposed to represent? You did not define m, r and t

algebra
Is what answer true or false ?? 8x-2 = -9+7x x = -7

LOL @ Steve --
Hilarious Captain: What happen ? Mechanic: Somebody set up us the bomb. Operator: We get signal. Captain: What ! Operator: Main screen turn on. Captain: It’s you !! CATS: How are you gentlemen !! CATS: All your base are belong to us.

MATH
Great read: Outliers by Malcolm Gladwell

College Algebra
your equation only has one variable. 5x + 3y = 60 3y = -5x + 60 y = (-5/3)x + 20 the y intercept of 20 ( or y = 20) gives you the number of gumballs (y) you can buy for 60 cents if you buy zero mints.

cal
f'(x) = 6x^2 - 6x - 12 = 0 for a max/min (critical value) divide by 6 x^2 - x - 2 = 0 (x-2)(x+1) = 0 x = 2 or x = -1 so, yes, x=2 is a critical number, (the other is x = -1) f '' (x) = 12x-6 f(2) = 2(2^3) - 3(2^2) - 12(2) + 18 = -2 f '' (2) = 24-6 > 0 si...

clarification - math(help)
Just because one of the numbers is a prime, does not mean the fraction is in lowest terms. e.g. 13/26 = 1/2 21/7 = 3 the numerator and denominator have to be "relatively prime", that is, no whole number exists that divides into both of them

math(help)
Why didn't they just ask, " Is 138435 evenly divisible by 3 ? " yes it is. is 38/53 in lowest terms? yes it is, since no whole number divides into both 38 and 53 here is a little-known trick: find a key a b/c on your calculator enter: 38 a b/c 53 = you will g...

Maths
I will assume that the building with side BC is on top of the cliff and A is at the bottom of the cliff. step1: tan44= AB/200 AB = 200tan44 so AC = 80 + 200tan44 let angle CPA = Ø tanØ = AC/200 = (80 + 200tan44)/200 tanØ = 1.365 Ø = 53.79°

cal
I will assume that you meant f(x) = 2x^(3/2) - 6x^(1/2) (or else we could just divide out the 2's in the first term) f ' (x) = 3x^(1/2) - 3x^(-1/2) f '' (x) = (3/2)x^(-1/2) + (3/2)x^(-3/2) or (3/2)( 1/√x + 1/(x√x) )

6th grade math
1. all three are correct 2. "they ate 1/5 of the bag" is not clear Did they eat 1/5 of a full bag, or Did they eat 1/5 of what was in the bag when she arrived?

Algebra 1
y+4 = x-2 y = x - 6 ---> usually called the y intercept - slope form or x - y = 6 ---> some texts call this standard form and this x-y - 6 = 0 ---> general form

Algebra, URGENT!!!
1. x^2 + (x+6)^2 = 8^2 x^2 + x^2 + 12x + 36 - 64 = 0 2x^2 + 12x - 28=0 x^2 + 6x - 14 = 0 x^2 + 6x = 14 , completing the square .... x^2 + 6x + 9 = 14+9 (x+3)^2 = 23 x+3 = ± √23 x = -3 ± √23 but x has to be positive so x = √23 - 3 so one leg is &...

College Algebra
A = 25000 e^(.06(5)) A = 25000 e^.3

home school
let the numbers be x and y x+y = 42 ---> y = 42-x xy = 185 --->x(42-x) = 185 42x - x^2 - 185 = 0 x^2 - 42x + 185 = 0 (x-37)(x - 5) 0 x = 37 or x = 5 then y = 42-37 or y = 42-5 y = 5 or y = 37 (symmetric solution) the two numbers are 5 and 37

Algebra NEED HELP ASAP!!!!!!
T = 4h + 72 , 0 < h < 12, where h is the number of hours at noon , h = 6 T = 72 + 4(6) = 96

cal
did you mean it the way you typed it, or did you mean f(x) = √(x+2) ? I will assume f(x) = √(x + 2) judging by the values of the interval first take the definite integral of the function = ∫(x+2)^(1/2) dx from 1 to 7 = (2/3)(x+2)^(3/2) | from 1 to 7 = (2/3)9^...

Math Properites
= (3.4)(3.8)(10^5)(10^-9) = 12.92(10^-4) = 12.92/10000 = .001292

TRIANGLE SIMILARITIES RATIOS AND PROPORTIONS
The key to this question is to realize that all the right -angled triangles are similar, and have the ratio of 3:4:5 in the length of their sides. Mark the two angles in triangle BCD with o and x ( you should be able to see that since XD | BC , so you can mark XDC as o and DCX...

Pre-Calculus
did you notice that f(x) = (x-9)(x-2)/(x-9) ?? = x-2, x ≠ 9 So for all values of x except x=9 the given function reduces to f(x) = x-2 which is a straight line. when x = 9, the original gives you 0/0 which is indeterminate, while the reduced function gives you (9,7) So t...

algebra 2
Prob(cheese, then turkey) = (6/15)(5/14)= = 30/210 = 1/7

MATHS
all multiples of 7 are $1 7, 14, 21 ------- $3.00 all multiples of 6 are .50 6,12,18,24,------- 4(.50) = $2.00 all multiples of 5 are .20 5,10,15,20 ---- 4(.20) = $.80 all multiples of 4 are .10 4,8,12,16,20,24 but the 12, 20 and 24 have been changed, so only the 4,8, and 16 c...

Advanced Funtions
if either x or y , or both = 0

Advanced Functions
They were the most obvious ones.

Advanced Functions
sin 60° = √3/2 cos 30° = √3/2 sin 120° = √3/2

PRECALCULUS
solve both as quadratics that factor 1. 2cos^2 x - 5cosx + 2 = 0 (2cosx - 1)(cosx - 2) = 0 cosx = 1/2 or cosx = 2 but cosx = 2 is not possible, since -1 ≤ cosx ≤ +1 for cosx = 1/2, since it is positive, x could be in I or IV x = 60° or x = 360-60 = 300° 2. ...

Advanced Functions
if cosx = 5/13, (recognize the 5,12,13 triangle ?) sinx = 12/13 tanx = 12/5 if cosy = -5/13 and y is in III siny = -12/13 tany = 12/5 2sinx+2siny+2cosx-2tanx+tany+2cosy = 2(12/13) + 2(-12/13) + 2(5/13) -2(12/5) + (12/5) + 2(-5/13) = - 12/5 or -2.4

Trig - Law of sines and cosines
I started with AB, the vertical diagonal of the square. I then drew square ALMN At M, I drew the base BC of the equilateral triangle perpendicular to AM, letting BM = MC = 2 Joi AB and AC for the triangle. Let the intersection of ML and AB be P, and the intersection of MN and ...

algebra 2
What is your question? What does "3/4 Six lots" mean?

algebra
BTW, Steve answered you yesterday when you posted it then. Did you not look at his answer?

algebra
prob(rain on Sat and Sun) = (10/100(30/100) = (1/10)(3/10) = 3/100 or 3%

Algebra
multiply each term by ab, the LCD bx - ab = ay y = (bx - ab)/a or just multiply both sides by b bx/a - b = y , which is the same as my first result

algebra
let the amount invested at 11% be x so .11x + .12(x+4000) = 940 .11x + .12x + 480 = 940 .23x = 460 x = 2000 So originally you had $2000 in the 11% account and $6000 in the 12% account at the end you had 2220 and 6720 respectively check: 2220+6720-8000 = 940

Geometry (math)
True No need to draw a figure, just look at the screen on your computer. let s be the top of the screen let q be perpendicular of your screen, how about the left side? let p be the bottom of your screen Is the top of your computer screen not parallel to its bottom?

Math
geesh, forgot to put D) in front D) which means that for every increase of 1800 feet, the temperature would decrease by 1° or for every decrease of 1800 ft , the temperature would rise by 1° F B) so how did Tessa get +.9/-.5 ? look at the bottom number of -.5. where di...

Math
clearly Gemma used the first two pairs, just check the calculations. B) which difference in the first elements would give you -.5 ?? c) no matter which pair you take you get a slope of -1.8 or -1.8 : 1 or -1800 ft : 1° F which means that for every increase of 1800 feet, th...

math
prob(yellow) = x/(20+x) but we know this is 1/6 x/(20+x) = 1/6 6x = 20+x x = 4 so there are 24 balls, of which 9 are blue so Prob(blue) = 9/24 = 3/8

Math questions
think of 8 as the slope and (12,240) as an ordered pair for this relation y = -8x + c at (12,240) 240 = -8(12) + c c = 336 y = -8x + 336 so when x = 0, y = 336 Where was he when x = 0 ???? at ground, y = 0 solve 0 = -8x+240 8x = 240 etc ....

algebra
What do you think? I don't see your choice of answer for any of them.

Pre-Calculus
since the line is perpendicular, their slopes are negative reciprocals of each other, that means, they must be OPPOSITE in sign so first slope = -3/2 2nd slope = +2/3 y-2 = (2/3)(x-4) 3y-6 = 2x-8 3y = 2x - 2 y = (2/3)x - 2/3

Math Help
#2 is correct #3 solving your 2 equations: 1st times 2: 8b+6n=47 2nd times 3: 15b+6n=64.5 subtract them: 7b = 17.5 b = 2.5 sub back in ----> n = 4.5 necklace costs $4.50 and bracelet costs $2.50 so buying just one each = $7.00

Math Help
first one: your equation: B = 22 +11.5w , where B is the balance, and w is the number of weeks or y = 22+11.5x to make it fit your x = 8 your friend: y = 218-13x if x = 8, you will have 22+11.5(8) = 114 your friend has 218-13(8) = 114 What do you think? Give the other two a sh...

Math
number of small posters x number of large posters y cost of small posters 240/48 = 5 cost of larger posters 240/30 = 8 5x+8y=240 to graph it, I would use intercepts let x = 0, y = 30 --->(0,30) let y = 0 , x = 48 ---> (48,0) slope = (0-30)/(48-0) = -5/8 For each reductio...

Geometry
Use the results of the ratio properties I gave you in your previous post

geometry
For the question to be "workable", AF is probably the median, with F on BC remember the centroid cuts the median in the ratio of 2:1, or AG:GF = 2:1 then FG:AF = 1:3 (x+8)/(9x-6) = 1/3 9x - 6 = 3x + 24 6x = 30 x = 5

My fuzzy thinking - math
Forget my previous post, r could be 1.5 my program line 60 should say: 60 if (b*c*d)^2 = (a*b*c^2*d*e) then print a;b;c;d;e and I got 64 96 144 216 324 80 120 180 270 405 96 144 216 324 486

math
I think I missed the obvious Since a,b,c,d,e are integers in GS, the smallest value of r is 2 a - b - c - d - e 51 102 204 408 816 52 104 ... 53 .... infinite number of choices for a so... still a silly question

For Steve - math
Crazy question. Agree with you, there has to be more As it stands: b/a = c/b and c/b = d/c and d/c = e/d b^2 = ac , c^2 = bd , d^2 = ed then b^2 c^2 d^2 = abcde I then ran this "primitive" BASIC program 10 for a = 50 to 100 20 for b = 51 to 100 30 for c = 52 to 100 4...

Calculus
Write it as f(x) = 7x^-2 - 6x^-6 F(x)= -7x^-1 + (6/5)x^-5 + c F(2) = -7/2 + (6/5)/2^5 + c = ......

Calculus
let the side of the square be x let the side of the triangle be y 4x + 3y = 40 x = (40-3y)/4 height of triangle from the 30-60-90 triangle ratio = √3/2 y area of triangle = (1/2)(y)(√3/2 y) = (√3/4)y^2 area of square = [(40-3y)/4]^2 = (1600 - 240y + 9y^2)/16 ...

TO ANY MATH HELPERS
1. from the 1st equation: x = 3y+1 into the 2nd: 3(3y+1) - y +1 = 0 9y + 3 - y +1 = 0 8y = -4 y = -1/2 sub into 2nd: 3x - (-1/2) + 1 = 0 3x = -3/2 x = -1/2 Do #2 the same way from the 2nd: y = 2x+4 etc (Just stating the answers is not acceptable and serves no purpose)

math and physics
asks for login and password

math
just did it http://www.jiskha.com/display.cgi?id=1384818273

math
36 = 1x36 = 2x18 = 3x12 = 4x9 = 6x6 = 9x4 = ....

Math
1 more than half of x should be x/2 + 1

math
To add/subtract something, they must be in the same units e.g 5 apples + 8 oranges = 13 appleoranges? so 2 hrs, 45 minutes = 2 + 45/60 = 2.75 hrs 3hrs, 57 minutes = 3 + 57/60 = 3.95 hrs now you can add them: 2.75+3.95 = 6.7 hrs = 6 hrs + (7/10)(60) minutes = 6 hrs, 42 minutes ...

math
As an after-thought ..... Tn = T(n-1) + 4 , T1 = -40 , n > 1 In the recursive notation, the initial value has to be included or else you can't begin your sequence.

Precalculus
tanØ secØ = tanØ tanØ secØ - tanØ = 0 tanØ(secØ - 1) = 0 tanØ = 0 or secØ = 1 if tanØ = 0 Ø = 0, 180°, 360° ... , 180k° , where k is an integer if secØ - 1 then cosØ =...

Precalculus
sec(Ø + 81) = 2 cos(Ø + 81) = 1/2 I know cos 60° = 1/2 so Ø+81 = 60 or Ø+81 = 300° Ø = 60-81 = -21° or Ø = 219° now the period of cos(Ø+81) = 360° so adding 360 will give me another answer so Ø = -21 +...

math
lots of missing information What was the rate of interest? Did he make any monthly payments? Did he make not payments except the one at the end of 31 months?

Math-Algebra
A direct square variation is a quadratic Given any 3 points , I can find that quadratic, but we can't "force" a fourth point on it. e.g A = 20.115r^2 - 101.835r + 135.78 produces the first 3 points , but not the last one

Math-Algebra
What is the topic for this question? Are you learning about "curve fitting" ?

Math-Algebra
Not enough data to see a pattern http://www.wolframalpha.com/input/?i=plot+%282%2C12.57%29%2C+%283%2C11.31%29+%2C+%284%2C50.28%29%2C+%285%2C78.56%29

math
x(1.07)^1 = 6100 x =6100/1.07 = $5700.93

stats
Play around with this website, it is great http://davidmlane.com/hyperstat/z_table.html click on "value from an area" enter 1 - .011 or .989 in "area" click on "below" and recalculate

Question About Math
correct for #1, wrong for #2 #2 If x is cost of buritos, y is cost of tacos "3 burritos and 4 tacos costs $11.33" --->3x+4y = 11.33 "9 burritos and 5 tacos costs $23.56" ----> 9x + 5y = 23.56 B !!!! Now , how easy was that? Notice how I just translate...

Question About Math
#1 should be obvious since d is "dime", it has to be multiplied by 10 (10 cents in a dime) and n is "nickels" it has to be multiplied by 5 So what do you think? #2, Once you define what x and y represent, the answer should be obvious as well. I would have u...

Math
I assume you made a diagram showing the highway and the road at 90° and the cop at 225 ft from the highway. let the moving car's position be x ft from the intersection, and Ø be the angle. then x/225 = tanØ x = 225tanØ 1 = 225 sec^2Ø d&Oslas...

Finance
80% of2800000 = 2240000 2240000 = 22000( 1 - (1+i)^-360)/i 101.81818.. = ( 1 - (1+i)^-360)/i 101.818182i = 1 - (1+i)^-360 (1+i)^-360 = 1 - 101.818182 i Now that is tough equation to solve. In the "olden days" we used interpolation. Even Wolfram, at least in its simpl...

Math
now, end of 0 months :2 at the end of 1 month :4 at the end of 2 months = 8 or 2^3 ... at the end of 6 months = 2^5 = 32 rabbits, or 16 pairs

Algebra 1 Problem
1. -26 < 4k-2 -13 < 2k-1 so now you have -13 < 2k-1 and 2k-1 < 5 which can be written as -13 < 2k-1 < 5 solving: add 1 -12 < 2k < 6 divide by 2 -6 < k < 3 since both "ends" are < draw an open circle at -6 and 3, join them with a solid...

Math:)
For Brandon's car to have m = 12000 100w + 10000 = 12000 100w + 10000 - 10000 = 12000 - 10000 100w = 2000 100w/100 = 2000/100 w = 20 part 2: obviously there has to be a second equation, which you did not include. Anyway, just set the two equations equal to each other and s...

math
prob of landing on blue = 2/7

math
Just use Pythagoras ... x^2 = 30^2+30^2 = 1800 x = √1800 = 30√2 or the 30-3--x triangle is similar to the 1-1-√2 right-angled triangle so x = 30√2

finance
PV = 50000(1.04)^-30 = $15,415.93

math
This is just like find the LCM of 8 and 10 which would be 40 must buy 40/8 or 5 packages of buns ---> 40 buns and 40/10 or 4 packages of hotdogs ----> 40 hotdogs

math
time = 8 years , 155 days = 8 + 155/365 = 8.42466 x e^(8.4266(.0895)) = 225500 x = $106092.70

Math
varies directly with the cube of their scale factor e.g if the scale factor is 1: 12 ( 1 inch = 1 foot) and a tiny table weighs 20 g then the full size table would weigh 12^3(20 g) or 34560 g which would be 34.56 kg

Math
10259 ft = 3419.67 yds correct to 2 decimal places as required.

staistics, is it right?
see http://www.jiskha.com/display.cgi?id=1384488019

Math
greens ---- x reds ------ 4x x + 4x = 50 take over.

algebra please help!!!!
multiply both sides by -11/20 (-11/20)(-20/11)y < (-9/17)(-11/20) y < 99/340 notice I reversed the inequality sign, since I multiplied by a negative.

Math
see http://www.jiskha.com/display.cgi?id=1384486281

statistics
to get the mean, add them up , then divide by 7 I get 168/7 = 24 (how can the average of your numbers possibly be 335 ??? The average must always lie between the smallest and the largest) your median and mode are correct

Algebra 1 (Reiny or Kuai)
not sure what you mean by "any lines of the graph", are you talking about the x or y axes ? if a line is horizontal, then it must cross the y-axis and all horizontal lines are functions if a line is vertical, then it must cross the x-axis, it is NOT a function any ot...

Algebra
I assume you are learning about Markov's chains in the study of matrices end of year 1: [4200 4800] x .88 .12 .72 .28 = [7152 1848] end of year 2 [7152 1848] .88 .12 .72 .28 = [7624.32 1375.68] I am not absolutely sure if I have the correct order, haven't done this kin...

pre-alg Answer Check
If this is supposed to be the equation x/2 = 9/4 , then 4x = 18 x = 4.5

statistics
z-score = (88 - 75)/10 = ....

math
What is 7! ?

math
what is 5000(1 + .06/12)^60 ?

math
Lexi's amount --- x Maria's amount --- 250-x Lexi spent 2/5 of x, so she has 3x/5 left Maria spends 40, so she has 250-x-40 or 210-x left 3x/5 = 210-x times 5 to get rid of fractions 3x = 1050 - 5x 8x = 1050 x =131.25 So Lexi had $131.25 and Maria had 118.75 check: Lex...

Pre calculus
cos(Ø - 42°) = -1 I know cos 180° = -1 Ø - 42 = 180 Ø = 222° , only one solution between 0° and 360° (look at the graph of cos Ø ) The period of cos(Ø-42) is 360° so a general solution is Ø = 222° + 360k°...

math
I did this for you on Tuesday. http://www.jiskha.com/display.cgi?id=1384305313 What part of my solution did you not like ?

interest math
How are you getting your answers ??? a) interest = 5000(.09)(80/365) = 98.63 b) value = 5000 + 98.63 = $5098.63 c) look at a calendar, count 80 days starting April 13 as one, april 14 as 2 , etc

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