Monday
May 25, 2015

Posts by Reiny


Total # Posts: 30,043

math
same thing again, plug in the straight line equation, and solve
January 26, 2015

math
You could but you don't have to recall that x = (-b ± √(b^2 - 4ac)/(2a) Judging from the type of question you have been asking, I trust you have learned the properties of the "discriminant" b^2 - 4ac I gave them to you in one of the posts.
January 26, 2015

math
Same thing as your last post Just evaluate b^2 - 4ac and decide
January 26, 2015

math
intersect the line with the parabola kx^2 - 5x + 2 = -3x + 4 kx^2 - 2x - 2 = 0 Looks like you are studying the nature of the roots, remember that if b^2 - 4ac > 0 you will have two solutions b^2 - 4ac = 0 you will have 1 solution (2 equal ones) b^2 - 4ac < 0 , there is ...
January 26, 2015

Maths
Outer dimension of the picture : 44 by 34 area whole thing including the frame = 44x34 = ... area of picture = 40x30 so area of frame = ???
January 26, 2015

Math
Perhaps I am missing something, but if we fill each of the labeled bottles just once, the big bottle can contain as little as 18 L 1 x (4L + 6L + 8L) = 18L
January 26, 2015

Math
The is a quadratic equation: sin^2 x - sinx - 2 = 0 (sinx - 2)(sinx + 1) = 0 sinx = 2 , which is not possible or sinx = -1 x = 3π/2 or x = 270° location on unit circle --- (0,-1) period --- 2π general solution x = 3π/2 + 2kπ
January 26, 2015

Add maths form 4
using the properties dealing with the nature of the roots, if there are two equal roots, then b^2 - 4ac = 0 so in hx2 _ 4kx + 9h = 0 16k^2 -4(h)(9h) = 0 16k^2 = 36h^2 4k = 6h h/k = 4/6 So h : k = 4 : 6 = 2 : 3 They should have reduced their answer to 2:3
January 26, 2015

algebra 1
Yes, your question was answered. http://www.jiskha.com/display.cgi?id=1422242533 Always check back to avoid un-necessary duplication of answers such as this. Secondly it does not help if you switch names.
January 26, 2015

Math
let the angles in order of size be x , a , b, 2x "The difference between the smallest and second smallest angles" ---> a-x "the difference between the biggest and second biggest angles" ---> 2x-b 2x - b = a - x 3x = a+b also we know x + a + b + 2x = ...
January 26, 2015

TO REINY
check our previous post for the explanation
January 25, 2015

ALGEBRA
you showed this: x+0.05<632 x<632/0.05 x<??????? following my argument, you should have had x + .05x < 632 x is a common factor x(1 + .05) < 632 x(1.05) < 632 ahhh, now you see where that 1.05 comes from, right ?
January 25, 2015

ALGEBRA
When you pay for an item with sales tax of 5% you pay the price + the sales tax = 100% + 5% = 1 + .05 = 1.05 similary a sales tax of 7% ---> you pay 1.07 etc
January 25, 2015

ALGEBRA
1.05x = 632 x = 632/1.05 = 601.90 The machine should cost less than 601.90
January 25, 2015

Calc
I agree with SJ but I would look at the backend of this thing first. Consider 1/x As x --->0 , 1/x becomes infinitely large but we are taking cos(???) and the result of cos(anything) is a number between -1 and 1 so e^(cos(1/x)) lies between e^-1 and e^1 or between 1/e and e...
January 25, 2015

algebra
let the first odd integer be n then the next even integer is n+1 3n < 4(n+1) by 11 3n = 4(n+1) - 11 3n = 4n + 4 - 11 7 = n the first odd integer is 7, then next even one is 8 check: 3 times the first = 21 4 times the second = 32 Is 21 eleven less than 32 ??, YES
January 25, 2015

calculus
how about y = 7x^2/((x-7)(x-9))
January 25, 2015

Calc 1
1. lim ( √(x+4) - 2)/x , as x-->0 =lim ( √(x+4) - 2)/x * ( √(x+4) + 2)/( √(x+4) + 2) = lim (x+4 - 4)/(x(√(x+4) + 2) = lim 1/( √(x+4) + 2) , x --> 0 = 1/(2+2) = 1/4 #2. In any limit question, the first thing I do is to sub the approach ...
January 25, 2015

Calculus
1. y = x^3 , at x = 1, y=1, so we have the point(1,1) dy/dx = 3x^2 , which is 3, when x = 1 y-1 = 3(x-1) y-1 = 3x-3 3x - y = 2 or y = 3x - 2 2. Lim sinxcos 2x/(3x) = lim sinx/x * cos 2x/3, as x ---> 0 = (1)*(1/3) = 1/3
January 25, 2015

Algebra
original price = x sale price = .85x x - .85x = 180 .15x = 180 x = 180/.15 = 1200 $1200 for a cell phone ?? check: 15% of 1200 = 180
January 25, 2015

ALGEBRA
set the 2 equations equal to each other ... 16x + 150 = -x^2 + 60x - 10 x^2 - 44x + 160 = 0 (x-40)(x-4) = 0 x = 40 or x = 4 when x = 40, y = 16(40) + 150 = 790 when x = 4 , y = 16(4) + 150 = 214 Pick out the choice that matches my solution
January 25, 2015

math
2560 m/60 sec = 2.56 km/min = 60 km/h
January 25, 2015

Quick Alegbra Help
done http://www.jiskha.com/display.cgi?id=1422231991
January 25, 2015

Math
done http://www.jiskha.com/display.cgi?id=1422231991
January 25, 2015

Math
let total distance be x bus: x/4 jog : (1/2)(3x/4) = 3x/8 walk: 800 x/4 + 3x/8 + 800 = x times 8 2x + 3x + 6400 = 8x x = 6400 total distance = 6400 ft
January 25, 2015

Algebra 2 Applications
height = -4.9t^2 when t = 3 height = 4.9(9) m = appr 44.1 m
January 25, 2015

Calculus
You must have done it correctly, since I also got x = appr 389 m Since this does not appear to make any real sense, let's investigate the other 2 cases: 1. he runs all the 300 m on the trail then at right angles through the bush 2. he runs all the way through the bush ...
January 25, 2015

Math( Attn: Reiny)
in any parabola written in the form y = a(x-p)^2 + q, the vertex is (p,q) if a is positive, q will be a minimum when x = p if a is negative, q will be a maximum when x = p if the equation is written in the form y = ax^2 + bx + c, the x of the vertex can be simply found by -b/(...
January 25, 2015

Math( Attn: Reiny)
Yes Wendy, I made the error in copying it from paper to here , should have been 36-2x Look at Kudums solution, he did it correctly using the same variable setup as mine As for #2 (#3 in your earlier post), compare Kudum's with mine and see that we just interchanged our ...
January 25, 2015

math
Using only whole numbers for lengths and widths 1 by 7 2 by 6 3 by 5 4 by 4 ---> notice that the sum is always 8 if you allow sides with fractional measurement, then there would be an infinite number of cases e.g. 2.5 by 5.5 ..... 3.412 by 4.588 ..... etc --------> ...
January 25, 2015

math
start: 22° increase for 5 min: 5(12) = 60° temp after 5 min = 22+60 = 82° decrease for next 3.5 min = 3.5(4) = 14° so temp after 8.5 minutes = 82-14 = 68°
January 25, 2015

algebric exponents
(3^x + 3^x + 1)/8 = (2(3^x) + 1)/8 = 2(3^x)/8 + 1/8 = (3^x)/4 + 1/8
January 25, 2015

Parabola Ques
Woaahhh! , that looks like a major assignment question. I will tell you what I would do if I had to actually do this. let P be (s,t) , but we know that y^2 = 4ax so t^2 = 4as s = t^2/(4a) so we can let P be (t^2/(4a) , t) from y^2 = 4ax 2y dy/dx = 4a dy/dx = 2a/y So the slope ...
January 25, 2015

law of exponents
See my reply to your other post http://www.jiskha.com/display.cgi?id=1422164761
January 25, 2015

algebra
I asked for a possible improper fraction, so I would leave it as a = 20/3
January 25, 2015

College Trigonometry
from the first: t = x/(vcosØ) from the 2nd: y = vsinØ(x/(vcosØ) - (g/2)(x^2/(v^2 cos^2 Ø) y = xtanØ - (gx^2)/(2v^2cos^2 Ø)
January 25, 2015

College Algebra and Trigonometry
Wow, 20 sheets of paper ? Since you titled your post "College Algebra & Trig" I will assume you know that both cos(π/4) and sin(π/4) = √2/2 so x = (√2/2)u - (√2/2)v and y = (√2/2)u + (√2/2)v In 5x^2 - 6xy + 5y^2 we will need...
January 25, 2015

maths
please retype we use x^2 for x squared, x^3 for x cubed etc What does ..... mean ? If you mean division, then use / for the division sign and place brackets in the correct positions
January 25, 2015

Math
The way I read it .... y = (x-8)^2 - 6 is the result if the parabola y = (x-1)^2 + 14 has been moved 7 units to the right and 20 units down, so the point (-3,30) went along for the ride, so (-3,30) ---> (4,10) check: old vertex = (1,14) new vertex = (8,-6) ---> 7 to the ...
January 25, 2015

math
let's assume you mean 2x^2 + 8x +3 = 0 since it does not factor, let's use the formula x = (-8 ± √40)/4 = (-8 ± 2√10)/4 = (-4 ± √10)/2
January 24, 2015

math
Suppose I change the question to ... "If 15 pencils cost 3 dollars, how many pencils can be bought for 90 cents?" I am sure you could do that question. Now simply replace the numbers you used with the p, d, and c and use the same operations in the same order.
January 24, 2015

Math
I think we must assume that the tower is in relatively flat plane. I don't know how well you can sketch 3-D diagrams, but mine has two right-angled triangles. One showing the first fire, has a base angle of 8° and a height of 50, so the distance of the fire from is: 50...
January 24, 2015

Math
#1 "How tall was the tree originally if the piece they chopped down was 7feet tall" ??? 7 ft tall ? #2 , x^2 = 5^2 + 3^2 = 34 x = √34 = appr 5.83 ft or 6 ft to the nearest foot
January 24, 2015

Math
I would "solve" the equation this way: 3 cot^2 x -1 = 0 cot^2 x = 1/3 tan^2 x = 3 tan x = ±√3 so x is in any of the 4 quadrants, x = 60° , 180°-60° , 180°+60° , 360°-60° = 60° , 120° , 240° or 300° in radians...
January 24, 2015

Math
A triple of numbers such as 5, 12, 13 is called a Pythagorean triple, because the satisfy the Pythagorean equation. The simplest such triple is 3, 4, 5 (3^2 + 4^2 = 5^2) and 5, 12, 13 is the next simple one. Of course any multiple of that triple would also work, e.g. 3 x (3, 4...
January 24, 2015

combination probability
Ok Let's assume that all the marbles are distinguishable , that is, I can tell any red apart from the other reds, etc Now lets "choose" 2 reds and 2 whites = C(18,2)*C(16,2) = 18360 Remember in those the order does not matter, and we can tell reds apart and ...
January 24, 2015

combination probability
Are you looking for the probability of drawing 2 reds and 2 whites when drawing any 4 marbles ? you could have 4!/(2!2!) ways or 6 ways for it to happen: RRWW WWRR RWWR RWRW WRWR WRRW prob of (RWRW) = (6/18)*(7/17)*(5/16)*(6/15) = (6*7*5*6)/73440 prob(WRRW) = (7/18)*(6/17)(*(5...
January 24, 2015

Geometry ques
We will need the equation of the tangent. y = tanx y' = sec^2 x when x = π/4 , tan π/4 = 1 so at the point (π/4,1) the slope is sec^2 (π/4) = 2 so equation is y = 2x + b at (π/4,1) 1 = 2(π/4) + b b = 1 - π/2 = (2-π)/2 tangent ...
January 24, 2015

Paarabola Ques
It has to be perpendicular to the tangent.
January 24, 2015

Probability Ques
what is whist?
January 24, 2015

Algebra
prove: (1 + 2 + 4 + . . . + 2n) + 1 = 2n+1 testing: if n = 1 , LS = (1) + 1 = 2 RS = 2(1) + 1 = 3 FAIL if n=2 , LS = (1 + 2) + 1 = 4 RS = 2(2) + 1 = 5 , FAIL again Hard to prove something which is not true check your spelling or the wording of the question. I don't know ...
January 24, 2015

Add maths form 4
done: http://www.jiskha.com/display.cgi?id=1422068863
January 23, 2015

math
Much Ado About Nothing. two ordered pairs (1950 , 2555360972) and (2000 , 6079006982) slope = (6079006982 - 2555360972)/(2000-1950) = 70472920.2 ---> m for N(t)= mt+b using the first point: 2555360972 = 70472920.2(1950) + b b = -1.348668 x 10^11 so we have N(t) = 70472920....
January 23, 2015

Add maths
recall that for ax^2 + bx + c = 0 , the sum of the roots = -b/a product of the roots = c/a we are given that the roots are r and 3r so from your equation of x^2 - 2qx + 2q+4 = 0 a = 1, b = -2q, c = 2q+4 r+3r = 2q/1 4r = 2q q = 2r r(3r) = 2q+4 3r^2 = 2(2r) + 4 3r^2 - 4r - 4 = 0...
January 23, 2015

Math (factors and products)
integral values are integer numbers, so k cannot be a fraction possible factors that end in +12: (x+1)(x+12) (x-1)(x-12) (x+2)(x+6) (x-2)(x-6)--> x^2 - 8x + 12 , so k = -8 (x+3)(x+4) (x-3)(x-4) I expanded one of them, to show one value of k You do the others
January 23, 2015

math
So we are looking for the between 3181+53 and 3181-53 or between 3234 and 3128 . best webpage for this stuff: http://davidmlane.com/hyperstat/z_table.html enter 3181 for mean enter 526 for sd click on between: enter 3128 and 3234 to get .0803
January 23, 2015

algebra
f(x)+g(x) = -5x - 4 + 6x - 7 = .....
January 23, 2015

Algebra
take out a common factor, then use grouping ... 3x^3 + 9x^2 - 3x - 9 = 3(x^3 + 3x^2 - x - 3) = 3( x^2(x + 3) - (x + 3) = 3(x+3)(x^2 - 1) = 3(x+3)(x-1)(x+1)
January 23, 2015

algebra
testing for 3 terms, (n=3) 1²/1 + (1²+2²)/2 + (1²+2²+3²)/3 = 1 + 5/2 + 14/3 = 49/6 for n = 3 a) --> (3/36)(36+45+17) = 49/6 b) --> (3/6)((4)(2) = 4 , noway! c) --> (9+9+29) = 47 , noway! suspicious it could be a) test for n = 2 sum(2) = 1...
January 23, 2015

algebra
try it yourselves, using the method I showed in your two other posts of this type
January 23, 2015

algebra
let's see if we find a pattern sum(1) = 4 sum(2) = 4+6 = 10 sum(3) = 4 + 6 + 9 = 19 sum(4) = 19+13 = 32 using a) the corresponding answers would be 4 10 19 32 mmmmhhh , looking good using b) the terms are -11/3 .... noway using c) the terms are 24 ... forget it! could it ...
January 23, 2015

Math
agree
January 23, 2015

Math
clarify if you meant it the way you typed it, or if you meant 4(1^(x/2) )^x remember that 1^anything = 1 so the way you typed it, it would simply become y = 4(1/2)^x if you meant: y = 4(1^(x/2) )^x , then we have y = 4(1)^x or simply y = 4
January 23, 2015

maths
if collinear, then their slopes must be equal (d-1)/-k = (1-1)/(1-k) = (1-d)/(1) (1-d)/k = 0/(1-k) = (1-d)/1 from the middle ratio we know that the slope = 0 and thus all numerators are 0 so 1 - d = 0 d = 1 similarly if the first and the last are equal, (1-d)/k = (1-d)/1 , ...
January 23, 2015

maths
recall that for any quadrataic in general form the sum of the roots is -b/a and the product of the roots is c/a let the roots be r and 3r so -b/a = 4r ---- b = -4ar and c/a = 3r^2 ---- c = 3ar^2 I will assume your b2/ac is supposed to be b^2/(ac) then b^2/(ac) = (16 a^2 r^2)/(...
January 23, 2015

algebra
Now = time(0) = 2 = 2^1 time(1) = 4 = 2^2 time(2) = 8 = 2^3 ... time(n) = 2^(n+1) then 2^(n+1) = 10million log both sides and use rules of logs (n+1)log2 = log 10million n+1 = log 10million/lon2 = 7/log2 = 23.25.. n = 22.25 after 23 months there will be more than 30 million
January 23, 2015

Math
It asks for miles per gallons or miles / gallons So which numbers go where?
January 22, 2015

ignore my babble - Antiderivatives
Just go with Steve's reply, ignore mine I read that -3 as an extra term
January 22, 2015

Antiderivatives
If you differentiate your answers, you certainly don't get back the original f(x), so you are clearly wrong your problem is the middle term -4x^-3 for simple single terms like this, here is how I go about it to integrate I write down the given term: -4x^-3 I then raise the...
January 22, 2015

Math
Maybe some culinary experts could enlighten me, but ... if you "double" the recipe, wouldn't you just double all the ingredients ?? Anyway, taking the wording at face value, you would need 1.3(1.5) cups of water or 1.95 cups of water
January 22, 2015

math: ratios
a) Kieran has 9 parts and Simon has 2 parts, so together they have 11 parts, So the ratio of Kieran's parts to the whole = 9parts : 11parts = 9 : 11 b) Kieran/total = 9parts/11parts = 9/11 c) Simon/total = 2/11 (notice 2/11 + 9/11 = 11/11 or the whole total) d) 9x -2x = 28...
January 22, 2015

Math please, please help
All your numbers can be changed to nice decimals 3/4 = .75 , 2 3/4 = 2.75 3 7/8 = 3.875 map1: .75 inch ---> 30 miles 1 inch -----> 30/.75 = 40 2.75 inches--> 40(2.75) or 110 miles map2: .5 inches -----> 10 miles 1 inches ------> 10/.5 = 20 miles 3.875 --------&...
January 22, 2015

math
Looking at your other post, I will assume that we are again talking about "simple interest" (in reality simple interest would not be used for any length of time greater than one year. As a matter of fact the method used above would result in a rate much higher than 6...
January 22, 2015

Quadratics
ummmh, y = 3(x+2)^2 + 5
January 22, 2015

Math-polynomials
correct expand to show that your are correct.
January 22, 2015

math
suppose we just define n to be an even number (that way I don't have to worry about the 2n idea) then the 4 consecutive even number are n , n+2, n+4, and n+6 (n+2)^2 = n(n+6) n^2 + 4n + 4 = n^2 + 6n 4 = 2n n = 2 so the 4 numbers are 2 , 4, 6, and 8
January 22, 2015

Math
term(7) = a+6d term(4) = a+3d a+6d - (a+3d) = 15 a+6d-a-3d=15 3d=15 d = 5
January 22, 2015

maths
#1: a+6d=3 #2: a+11d=-3 subtract them -5d = 6 d = -6/5 back into a+6d=3 a + 6(-6/5) = 3 a = 3 + 36/5 = 51/5 first three terms are: 51/5 , 9 , 29/5
January 22, 2015

7th grade math
First one is correct For the second, yes, you could have just subtracted the two. They actually gave you more information than was needed. Obtaining the same answer confirms that your answer is correct. The second question would have been nice had it been worded this way: If ...
January 22, 2015

algebra
4000(1.04)^n = 4800 1.04^n = 1.2 take log of both sides and use log rules n log1.04 = log 1.2 n = log 1.2/log 1.04 = appr 4.65 years
January 22, 2015

Math
correct --- x wrong ---- y , both x and y must be whole numbers x+y+2 = 20 x+y = 18 , #! 5x - 3y - 2 = 72 5x - 3y = 74 , #2 #1 times 3 --> 3x+3y=54 #2 as is -----> 5x - 3y = 74 add them 8x = 128 x = 16 back in #1 16+y=18 y = 2 a) he got 16 right, and 2 wrong, skipping 2 ...
January 22, 2015

Math
side of base of cuboid ---- x x^2 = 44 let the height be h x^2 h = 378.4 h = 378.4/44 = 8.6
January 22, 2015

math
I would pick b)
January 22, 2015

Math
#1, the key terms in each answer is the power term pick any two increasing values of x e.g. x = 2, y = 7^2 - 2 = 47 x = 3 , y = 7^3 - 2 = 341 Is there any reason for this pattern NOT to continue, so the function is INCREASING You will see the same for c) and d) Now look at b) ...
January 22, 2015

math
A good way is to take two pieces of graph paper and cut both of them into 8by8 square pieces It is easy to see that there is 1 large 8x8 square on a chessboard Now use one of the 2 pieces and cut it down to a 7x7 square template. Try placing this template on the 8x8 sheet (...
January 22, 2015

probability
The three mustaches can be used in 4 different ways, that is we could use any of the 3 of them or we could none at all in the same way the eyebrows can be used in 3 ways, the noses in 5 ways, and the set of ears in 2 ways. so the number of different makeups is 4x3x5x2 = 120 ...
January 22, 2015

. 8th grade math
2 nitro react with 3 hydro to make 2 ammo ratio: 2 : 3 : 2 we want : x : 42 : 28 2(14) : 3(14) : 2(14) so x = 28 28 molecules of nitrogen are needed check: ratio of 28:42:28 = 2:3:2
January 21, 2015

Math
#1, none are increasing http://www.wolframalpha.com/input/?i=plot+y+%3D+-2%5Ex+%2C+y+%3D+2+%281%2F2%5Ex%29+%2C+y+%3D+3+%284%5E-x%29+%2C+y+%3D+-4+%282%5Ex%29 2. for y-intercept , let x = 0 4(2^0) - 2 = 4(1) - 2 = 2 3. as x ---> +big 3^x get big , so the whole expression ...
January 21, 2015

math
simplify the situation. Suppose I compare the number 3 with the number 12 Would you agree that 12 is 4 times the number 3 ? What did I do with 12 and 3 to get 4 ? Did I subtract them? no way Did I divide them ? yeahhh so area of Canada = 1 x 10^7 and area of Mexico= 2 x 10^6 ...
January 21, 2015

Math
I would use elimination. 4x + 4y + 2z = -10 ----- 1st times 2 3x + 4y + 2z = 0 ----- #2 as is subtract them x = -10 ------ that was lucky 3x + 4y + 2z = 0 --- #2 x + 3y + 2z = 1 ----#3 subtract them 2x + y = -1 sub x = -10 into that -20 + y = -1 y = 19 back into #1 2x+2y+z = -...
January 21, 2015

Math
yes
January 21, 2015

math
arc length = rØ , where Ø is the angle in radians = 36(12) = 432 cm so in 1 second the wheel covers 432 cm so to cover 100 m or 10000cm would take 10000/432 or 23.15 seconds
January 21, 2015

Math
There are 9 things to choose from and we choose 2 of them There are C(9,2) such choices or 36 choices, which must match the number of children
January 21, 2015

Precalc/Trig
make a sketch and place (2,-3) into the fourth quadrant. Complete the right-angled triangle the hypotenuse will be √13 , x - 2, y = -3 let the angle be Ø tanØ = -3/2 Ø = 2π - .98279.. = 5.3 so one point is (√13, 5.3) which is what you have...
January 21, 2015

Math
find the vertex to find the maximum height let 0 = 15 + 110t - 16t^2 and solve for t to get the time it hits the ground. One of your answers will be negative, you will ignore that one
January 21, 2015

math
since area = lw x^2 + x - 12 = (x+4)( ......) clearly ( ..... ) must be (x - 3) check: expand (x-3)(x+4)
January 21, 2015

Math
Is there a question? Also, which is it, 35402.06 or 35403.06 ?
January 21, 2015

Algebra please help
mmh, let her try x = 3 and to really confuse her, let her try x =
January 21, 2015

12 Math
f(1) = 2 + 5 - 1 - 3 + 1 = 4 f(3) = 162 + 135 - 9 - 9 + 1 = 280 for between the points (1,4) and (3,280) slope = (280-4)/(3-1) = 138 f'(x) = 8x^3 + 15x^2 - 2x - 3 f ' (1) = 8+15 - 2 - 3 = 18 at (1,4) the real slope is 18 f ' (3) = 216 + 135 - 6 - 3 = 342 at (3,280...
January 21, 2015

math
Re-wording your problem: find the vertex of the parabola h = -4.9t^2 + 16t + .5 the t of the vertex is -16/(2(-4.9)) = 80/49 the h = -4.9(80/49) + 16(80/49) + .5 = appr 13.56 m
January 21, 2015

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