Tuesday
July 22, 2014

Posts by Reiny


Total # Posts: 26,851

Algebra 1--Please, help me!
show that slope AB = slope DC and slope AD = slope BC I will do the first pair, you do the second slope AB = (5-5)/6+2) = 0/8 = 0 slope DC = (-3+3)/(-4-4) = 0/-8 = 0 so AB || DC test if AD || BC if so, then by definition, it is a parallogram.

Geometry
Strange wording. How high is the lighthouse above the sea level ?

Algebra 1--Step-by-Step
3 and 4 are correct #2 14q^2 - 21q + 6 - 4q = 7q(2q - 3) + 2(3-2q) = 7q(2q-3) - 2(2q-3) = (2q-3)(7q-2)

Algebra 1--Step-by-Step
look at my answer ... (r-3)(2r-4) = (r-3)(2)(r-2) = 2(r-3)(r-2)

Algebra 1--Step-by-Step
Surely you could see that 2 was an additional common factor contained in my (2r-4) factor.

Algebra 1--Step-by-Step
1. 2r(r - 3) + 4(3 - r) , ahhh, did you notice that the brackets are opposite? , so .. = 2r(r-3) - 4(r - 3) = (r-3)(2r-4) Use the same "trick" on the others if you have to.

algebra
sub the first into the 2nd ... 3x - 18y = 4 3(6y+2) - 18y = 4 18y + 6 - 18y = 4 6 = 4 , which of course is nonsese, so .. there is no solution (You have two parallel lines)

algebra
number of people---- x cost = 20x + 35 20x + 35 ≤ 350 20 x ≤ 315 x ≤ 315/20 ≤ 15.75 So he can invite 15 people maximum test: if he invites 15 cost = 20(15) + 35 = 335 , within his budget if he invites 16 cost = 20(16) + 35 = 355 , above budget.

algebra
Does the fence run on 4 sides or on 3 sides ?

Math
|2x-7|=11 2x-7 = 11 OR -2x+7 = 11 2x = 18 OR -2x = 4 x = 9 OR x = -2 so the sum of the solutions is 9-2 = 7

Algebra
I = k(1/R), where I current, R is resistance and k is a constant given: I = 5, R = 20 5 = k(1/20) k = 100 I = 100(1/R) so when R = 25 I = 100(1/25) = 4

Trigonometry
from last night at 10:06 pm RS = (1-sinØ)/(1+ sinØ) = (1-sinØ)/(1+ sinØ) * (1-sinØ)/(1- sinØ) = (1 - 2sinØ + sin^2 Ø)/(1 - sin^2 Ø) = (1 - 2sinØ + sin^2 Ø)/cos^2 Ø = 1/cos^2 Ø - 2sin&Osl...

Trigonometry
ok I usually start with the more complicated looking side and try to change it to the more simplified LS = cosØ/(sinØ - 1) + cosØ(sinØ + 1) , note it didn't matter to change the order of that last denominator common denominator of (sinØ-1...

Trigonometry
I see no equal signs What are we verifying ?

MATH
5√8 - 3√18 + √3 in general to change √k to a mixed radical, look for factors of k which are perfect squares e.g. 18 = (3)(6) or 2(9) the choice of (3)(6) does not do us any good, since neither factor is a perfect square so your problem can be written as...

MATH
4√2 + 6√4 = 4√2 + 6(2) = 4√2 + 12

Probability
let S be the event of being dealt a spade, x the event of a non-spade One such 5 spade hand could be SSSSSXXXXXXXX The prob of that is (13/52*12/51*11/50*10/49*9/48)(39/47*38/46*37/45*36/44*35/43*34/33*33/32*32/31) a quicker way would be to say prob(exactly 5 spades) = ( C(13,...

Trig
That's a better job of typing it. I did the first of these in your previous post.. the 2nd: LS = (1-sinØ)/(1+ sinØ) = (1-sinØ)/(1+ sinØ) * (1-sinØ)/(1- sinØ) = (1 - 2sinØ + sin^2 Ø)/(1 - sin^2 Ø) = (1 - 2sin&Os...

Math
how about just treating it like 2 ordered pairs (1991, 4.25) and (1997, 5.15) ? rate of change = (5.15-4.25)/(1997-1991) = .15

Trig
Don't try to build up fractional equations using your method, the spacing will not work out instead do something like this: 1/(tanØ - secØ) + 1/(tanØ + secØ) = -2tanØ LS = (tanØ + secØ + tanØ - secØ)/(tan2 &Osl...

Pre-Calculus
we know x =rcosØ and y = rsinØ -3rcosØ + (1/2)rsinØ = 2 -6rcosØ + rsinØ = 2 r(sinØ - 6cosØ) = 2 or r = 2/(sinØ - 6cosØ) looks good: http://www.wolframalpha.com/input/?i=polar+r+%3D+2%2F%28sinx+-+6cosx%29

Calculus Please help!
dy/dx = 3(x^2 + 6)^2 dy = 3(x^2 + 6)^2 dx when x = 2 and dx = .05 dy = ...... just plug in the above values.

Probability
#1 is correct, in effect what you are doing is C(60,60) (.99^60 (.01)^0 = .547 #2, you want to have 59 correct and one wrong = C(60,59) (.99)^59 (.01)^1 = 60(.55268..)(.01) = .33161 #3 , same way, 58 correct, 2 wrong prob = C(60,58) (.99)^58 (.01)^2 = .09881 #4 , at least 2 mi...

Probability
at least 4 means 4 or 5 or 6 or ... or 20 are colourblind so exclude cases of none, 1 , 2, and 3 colourblind = .05 not colourblind = .95 None: C(20,0) (.05)^0 (.95)^20 = .358486 one: C(20,1) (.05) (.95)^19 = .37735.. two: C(20,2) (.05)^2 (.95)^18 = .1886768 three: C(20,3)(.05)...

Math:Probability
1. could be 1 in math or 1 in history or 1 in Spanish that is (math)(no history)(no Spanish) + .... prob = .9(.4)(.25) + .6(.1)(.25) + .25(.1)(.4) = .115 Exclude the case of no homework in any which is (.1)(.4)(.25) = .01 prob(homework in at least 1 class) 1 - .01 = .99

Math (Statistics)
Perfect data, one standard of devation below and above. so appr 68% or prob of .68 confirmed by David's webpage http://davidmlane.com/hyperstat/z_table.html fill in the data to see and get .6827

Calculus Please help!
Let the radius be r, so the diameter is 2r then the height is 2r V = (1/3)π r^2 h = (1/3) π r^2 (2r) = (2/3)π r^3 dV/dt = 2π r^2 dr/dt when h = 24 2r = 24 r = 12 and dV/dt = 30 30 = 2π (144) dr/dt dr/dt = 30/(288π) = 5/(48π) ft/min or appr .0...

Calculus Please help!
darn them brackets 23t^2 vs (23t)^2

Calculus Please help!
let the time be t hours past noon. I see a right-angled triangle , with sides 23t and 50 + 18t, with D as the distance between them D^2 = (23t)^2 + (50+18t)^2 D^2 = 529t^2 + 2500 + 1800t + 324t^2 = 853t^2 + 1800t + 2500 2D dD/dt = 1706t + 1800 dD/t = (853t + 900)/D , #1 at 3:0...

Algebra 2 Help!
No, since the disc I negative, you will have 2 complex roots

Algebra 2 Help!
f(x) = 5x^2 - 10x + 3 , notice how we use exponents in this format = 5(x^2 - 2x + 1 - 1) + 3 = 5 ( (x-1)^2 - 1) + 3 = 5(x-1)^2 - 5 - 3 = 5(x-1)^2 - 8 6= 4x - 5x^2 5x^2 - 4x + 6 = 0 b^2 - 4ac = 16 - 4(5)(6) = -104 What do you think ?

Algebra 2 Help!
[sqrt3 + 2i][sqrt3 - 2i] = 3 - 2i√3 + 2i√3 - 4i^2 = 3 - 4(-1) = 7 (y - 4)^2 = -18 y - 4 = ± √18 y = 4 ± 3√-2 = 4± 3√2 i

math
36 hrs, 12 minutes <---> 1 day + 12 hrs , 12 min 6:12 pm + 12:12 = 6:24 am (wouldn't it be nice it time was metric ??)

Math
pigs--- x horses --- 2x cows--- 4(2x) or 8x 8x + 2x + x = 99 11x = 99 x = 9 9 pigs, 18 horses, and 72 cows

math --- can someone help me pls?
I assume you mean the diameter of the circular base of the cone, so the radius is 4 slant-height^2 = 9^2 + 4^2 = 97 slant-height = √97 = appr 9.85 your second question is correct

Math
Pablo --- x yrs old Chita ---- x- 15/4 4(x -15/4) = 43 4x- 15= 43 4x = 58 x = 14 1/2 years old

algebra
The corresponding sides of a regular polygon are in the same ratio, so 8/2 = 29/x 8x = 58 x = 58/8 = 29/4

Algebra
You should be familiar with the vertex form of a parabola as y = a(x-p)^2 + q , where (p,q) is the vertex, so we have: y = a(x-4)^2 - 4 using any of the other given points will give us the a let's use the easiest, (2,0) 0 = a(2-4)^2 - 4 0 = 4a - 4 a= 1 y = (x-4)^2 - 4 is y...

Ethiopia(AAU)
A) f(x) = x^2 e^x , notice how I indicated exponents? f ' (x) = x^2 e^x + 2x e^x = e^x(x^2 + 2x) f'' (x) = x^2 e^x + 2x e^x + 2x e^x + 2 e^x = e^x (x^2+ 4x + 2) here is a graph of your first function http://www.wolframalpha.com/input/?i=y+%3D+x%5E2+e%5Ex type in yo...

math
number of men ---- x number of boys ---- 20-x solve for x 60x + 35(20-x) = 900 You should get 8 men .... etc

Math
That was a coincidence and only happens when r = 4 When r = 2, the area and the circumference just happen to be equal, again a coincidence.

math
I like that equation. What about it ?

Algebra
5x^2 - 526 = -651 5x^2 = -125 x^2 = -25 Unless you have another typo, there is no real number solution, since we cannot take the square root of a negative. If you equation was supposed to be 5x^2 - 526x= -651 5x^2 - 526x + 651 = 0 x = (526 ± √263656)/10 = appr 103...

Math
If my middle term is even and it starts with x^2, I always complete the square. x^2 + 14x + 49 = -4 + 49 (x+7)^2 = 40 x+7 = ± √40 = ± 2√10 x = -7 ± 2√10

Math
Use the formula exact values: x = (5 ± √13)/2 Use your calculator to find appr. values

Finance
PV = 235 (1 - 1.006458333..^-48)/.006458333 = $ 9672.48

Maths
A - B = 51 ---> A = B+51 A - C = 108 subtract them -C + B = 57 B = C + 57 C = (15/100)(A+B+C) C = (3A + 3B + 3C)/20 20C = 3A + 3B + 3C 17C = 3A+ 3B 17C = 3(B+51) + 3(C+57) 17C = 3B + 153 + 3C + 171 17C = 3(C+57) + 153 + 3C + 171 17C = 3C + 171 + 153 + 3C + 171 11C = 495 C =...

Geometry A
The line y+4 = 3(x+6) does expand and simplify it if you have to

algebra
8| x+3/4|< 2 | x+3/4| < 1/4 x+3/4 < 1/4 AND -x-3/4 < 1/4 x < -1/2 AND -x < 1 x < -1/2 AND x > -1 which matches: -1 < x < -1/2

algebra
2|3 x-5|-8=8 2|3 x-5| = 16 |3 x-5| = 8 3x-5 = 8 or -3x+5 = 8 3x = 13 or -3x = 3 x = 13/3 OR x = -1 choose your matching answer, it is there.

Math
welcome

Math
distance = √( (5-1)^2 + (-4+2)^2 ) = √(16 + 4) = √20 = appr 4.47 I would leave it in exact form of √20 or 2√5

algebra
2(8x-4)-2 x<14x+12 16x - 8 - 2x < 14x + 12 -8 < 12 which is a true statement, thus your inequation is true for all values of x so always

algebra
solve it to see which choice is correct

algebra
2(8 x-4)-<14 x+12 16 x - 8 ≤ 14x + 12 2x ≤ 20 x ≤ 10 what do you think?

algebra 1
let the number of 4-people cars be x then the number of 6-person cars is 15-x 4x + 6(15-x) = 72 4x + 90 - 6x = 72 -2x = -18 x = 9 9 of the 4-person cars and 6 of the 6-person cars

Math
These non-metric units always confuse me, so since I use metric most of the time, I will convert to decimals consider 1 board + 1 gap to be one unit so we have 6.5 + .1875 = 6.6875 inches 6.5 = .25 = 6.75 6.5 + .375 = 6.875 now... 18 feet = 216 216/6.6875 = 2.6932.299.. 216/6....

Math
arggh, just a lot of arithmetic..... time per day open for rides: 6.5 hours = 390 minutes time available per year = 390(365) = 142350 minutes time needed to complete one ride = 3 + 4 + 3 = 10 minutes. (so they can complete 39 rides per day) number of rides per year = 142350/10...

Math
look at the pattern 1 line --- 0 intersection 2 ines --- 1 intersection 3 lines ---- 3 intersections 4 lines ---- 6 intersections 5 lines --- 10 intersections 6 lines ---- 15 intersections ..... the numbers of the sequence 1 3 6 10 15 .... are called the "triangular numbe...

maths
2nd term = a+d 6th term = a + 5d "the 6th term is 3 times the second term" --> a+5d = 3(a+d) a+5d = 3a + 3d 2d = 2a a = d "the 5th term is 15" ---> a+4d = 15 but a = d 5d = 15 d = 3 then a = 3 "the 4th term is 4 times the first term" --> ...

Algebra
or 100x/(x+314) = 42 cross-multiply ... 100x = 42x = 13188 58x = 13188 x = 13188/58 = 6594/29 or appr 227.38 I took your * to mean multiplication, the common symbol for multiplication If, somehow, you meant it to be an exponent, that is [x/(x+314)]^100 = 42 then take the 100th...

German Help Please....
#1 , ok #2, should be Sie haben den Film lieber. You need the plural, your choice would say "She prefers the film" , which would be singular #3 choice D, yours sounds like a Google translation #4 ok #5 A, B, and C are definitely out, C sounds very clumsy, I would say...

Math
cost = 50 + 2n, where n is the number of pages if n = 75 Cost = 50 + 2(75) = ....

Calculus
Just about every Calculus book I have ever seen uses this question as an introductory example of "rate of change" problem. At a time of t seconds, let the foot of the ladder be x ft from the wall, and the top of the ladder by y ft above the ground> then, x^2 + y^2...

math
sorry about the typo, but I am sure you were able to make sense out of it.

math
I am assumungthere are 26 lower case, 26 upper case and 10 digits that can fill any position number of all possible cases = 62^6 = 5.68 x 10^10 (huge) number without any digits = 52^6 = 1.977 x 10^10 (still huge) so the number of possible cases with at least 1 digit = number u...

math
lower end speed: so far --- time = 70/50 = 1.4 hrs total trip -- time = 154/50 = 3.08 hrs top end speed: so far --- time = 70/57 = 1.23 hrs total trip -- time = 154/57 = 2.701 hrs I don't see a " which of the following" part , so use my results above to match wit...

math
to go from 1: 15 to 1:16 the minute hand has moved (1/60)(360)° or 6° but the hour hand has also moved (1/60)(1/60)(360)° or 1/10 ° so the change in angle is 6 - 1/10 ° or 59/10 ° or 5.9°

algebra
On my screen the - was on one line and the 2(.... on the next, so I read it as shown if your statement was -2(2x+9) > -4x + 9 your x's would drop out and you have the situation when you posted as "Lucky". Draw your conclusion.

algebra
4x + 18 > -4x + 9 8x > -9 x > -9/8 which of your answers matches this ?

algebra
26+6b > 2(3b+4) 26 + 6b > 6b + 8 26 > 8 , which is true so it is true for all real values of b

math
Did you notice one parabola opens up, the other one down To have only one point of intersection, they must have a common tangent, that is the slope of one equals the slope of the other for the 1st: dy/dx = 2x+6 for the 2nd dy/dx = -2x - 6 2x + 16 = -2x -6 4x = 12 x = 3 when x ...

algebra
What is 5(-6) + 5(-5) ?

math
mmmh, they gave you the equation y = kx^2 when y = 50, x = 10 , so.... 50 = k(100) k = 1/2 your equation is y = (1/2)x^2 now just plug in x = 30 in your head you can do y = 900/2 or 450

math
complete the square to find the centre x^2 -10x + 25 + y^2 = k + 25 (x-5)^2 + y^2= k+25 so the centre must be (5,0), which lies on the x-axis to be tangent to the y-axis it must pass through (0.0) and its radius must be 5 so the equation must be (x-5)^2 + y^2 = 25 and k+25 mus...

Math
isn't profit = revenue - cost ? plug in those values, simplify, then use either of the methods I just showed you in your previous post

Math
So in effect you are finding the vertex of the downwards opening parabola shortest way: the x of the vertex is -b/(2a) = -8/-.8 = 10 when x = 10 N(10) = -.4(100) + 8(10)+11 = 51 The ticket sales will peak at day 10 and on that day 51 tickets are sold method 2: complete the squ...

business finance
so you are financing 55000 - 15000, or 40000 so let the monthly rate be i 1050(1 - (1+i)^-60)/i = 40000 payment = 40000/( 1 - (1+i)^-60)/i checking for some interest rates let i = 0, (no interest) payment = 40000/60 = 666.67 let i = .005 , (6% interest) payment = 40000/ (1 - 1...

maths
Ohh dear! midpoint is a "point" so it must look like ( ? , ? ) your method should be the x of the midpoint is (6+0)/2= 3 the y of the midpoint is (6-2)/2 = 2 so the midpoint is (3,2) (notice that in effect we are taking the average of the x's and the average of t...

maths
gradient = slope = (6-(-2))/(6-0) = 8/6 = 4/3 since (0,-2) is the y-intercept or the b of the y = mx + b notation, we can simply write y = (4/3) - 2 surely you have 2 little formulas in your text or your notebook to find the midpoint and the length. Let me know what you get.

Math
y = 4x^2 + 1 dy/dt = 8x dx/dt when x = 2, dy/dt = 1/2 sub that in.... 1/2 = 16 dx/dt dx/dt = 1/32

Precalculus
I was the one that answered you before when you had the typo (you had S instead of A for the short-tailed mice) and I actually found my scrap piece of paper where I made my Venn diagram. so.... My Venns agree with your data, and n(M' union S) = n(non male) + n(short tailed...

Math
I am going to assume that the kitchen and the dining room have the same width. so the length of large rectangle is x+12 and the width is x so x(x+12) = 589 x^2 + 12x = 589 x^2 + 12x + 36 = 589+36 (x+6)^2 = 625 x+6 = ± √625 = ± 25 x = -6 + 25 or -6-25 , the ...

math
put the decimal between the 1 and 4, then count the number of decimals it was moved from the end of the big number = 1.406 x 10^?? , you do the counting.

math class
f '(3) = 4 says that the slope is 4 when x = 3 f)3) = 9 means that you are dealing with the point (3,9) So they have given you the slope of the line and a point on it. I am sure you can take it from there.

calculus
What about it ?

Math
let x^2 - 18x - 4 = 0 best done by completing the square x^2 - 18x + 91 = 4 + 81 (x-9)^2= 85 x - 9 = √85 x = 9 ± √85 Your question should have said "What are the zeros of ...." , since there are two of them.

math class
The derivative should have been dy/dx = -3x^-4 = -3/x^4 when x = .5 or 1/2 dy/dx = -3/(1/2)^4 = -3/(1/16 = -3(16) = -48

math
first day he ran 1.5 2nd day he ran 1.5(1.1) 3rd day he ran 1.5(1.1)(1.1) = 1.5(1.1)^2 .. on the 7th day he ran 1.5(1.1)^6 so we have: 1.5 + 1.5(1.1)+ 1.5(1.1^2 + ... + 1.5(1.1)^6 which is a geometric series whose sum is 1.5( 1.1^7 - 1)/(1.1 - 1) = 1.5(.9487171)/.1 = 14.230756...

Pre-calculus
your equation "falls apart" when p = 100 because you would be dividing by zero So mathematically, the cost would be infinitely large (that is, it is not possible) look at this graph and see what happens at p = 100 http://www.wolframalpha.com/input/?i=plot+C%3D80%2C00...

not Calculus Please help!
B) compounded quarterly ----> i = .07/4 or .0175, and n = 6(4) or 24 amount = 7000(1.0175)^24 = $ 10,615.10 Do A and C the same way D amount = 7000 e^(6(.07)) = $ 10,653.73

Calculus Please help!
-8x + 4x dy/dx + 4y - 6y^2 dy/dx = 0 dy/dx(4x - 6y^2) = 8x - 4y dy/dx = (4x - 2y)/(2x - 3y^2) plug in x = 1 and y = 3 to find the slope

Math
Let the dimensions of the box by x by y by z xyz = 80 z = 80/(xy) "least amount of plasic" implies least surface area SA = 2xy + 2xz + 2yz = 2xy + 2x(80/(xy)) + 2y(80/(xy)) = 2xy + 160/y + 160/x now we know that xyz = 80 and 80 = (2)(2)(2)(2)(5) combinations of x y z...

Math
For simplicity sake, let's assume that the temperature increase is a linear function, (which it isn't), we would solve 2t + 20 = 98 2t = 78 t = 39 seconds

Math! HELP!
(3/2b^4)^3 = (27/8)b^12 (3/5y^4)^-2 = 1/(3/5y^4)^2 = 1/( (9/25)y^8 = 25/(9y^8) or (25/9)y^-8

Algebra 1
5x^2 + 2x^2 = 7x^2 (5 apples + 2 apples = 7 apples) Steve had a typo, happens even to the best of us

Algebra 1
Your question was answered , go back and check

Intermediate algebra
let number of AC adapters be x let number of flashlights be y 7x + 2y = 86 3x + 4y = 84 double the first equation 14x + 4y = 172 3x + 4y = 84 subtract them 11x = 88 x = 8 sub back into 1st: 7(8) + 2y = 86 2y = 30 y = 15 so 8 adapters and 15 flashlights. Check my answer to see ...

Algebra 1 Answer Check
1. correct if you meant 49^(3/2) The way you typed it --- 117649/2 2. can't read the question 3. the leading term in standard notation would be 8x^2 so leading coefficient is 8 4. correct 5. the x is undefined in your problem 6. 7x^2 - 2x + 5, the exponent is not affected ...

algebra
Steve is right, go with x-8 ≥ 20

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