Wednesday
August 27, 2014

Posts by Reiny


Total # Posts: 26,978

trigonometry
For any quadratic equation, if you have irrational or complex roots, they will always come as conjugate pairs, just like your given roots method one: use the fact that if x=a is a root, then x-a will be a factor of your equation, so 1. (x - (2+√5))(x - (2-√5) = 0 (...
August 27, 2014

Check my math please ASAP
#1 is incorrect it should be C think of the number line, -4 is to the right of -9 so -9 < -4 , not > The other three are correct
August 26, 2014

Math
follow the same steps I just showed you in your previous question of this type of problem. Let me know what you get
August 26, 2014

Math 114
Without even checking the answer by substitution, it sound unreasonable right from the start. Since the 588 kg sells for $12 and was mixed from a $11 and a $13 source, we would expect the split to be about half way. 11x + 7644 - 13x = 7056 -2x = -588 x = 294 well, what a ...
August 26, 2014

Math 114
amount of Kenyan coffee --- x amount of Turkish coffee --- 588 11x + 13(588-x) = 12(588) solve for x and you got it
August 26, 2014

Math
let their current salaries be 2x : 3x : 5x new ratios are 2x(1.15) : 3x(1.1) : 5x(1.2) = 2.3x : 3.3x : 6x = 23 : 33 : 60
August 26, 2014

MA
well, let's try it ... a/b = (a+b)/b times b, if b ≠0 a = a+b then b = 0 but now we have a contraction, so ..... or cross - multiply ab = ab + b^2 b^2 = 0 b = 0 , but that would make a/b undefined, so what do you think?
August 25, 2014

math
Don't know what you mean by "work this" The way you typed it, there is no useful simplification. If you meant (6x^2 + 7)/(3x^2 + 1) , there is no useful simplification After a long division you could state the answer as 2 + 5/(3x^2 + 1) , but certainly not what ...
August 25, 2014

Math
don't switch names, I responded you you before http://www.jiskha.com/display.cgi?id=1408984634 The way you have it, the sum is 206 Why is this a difficult question for you, why not just add them up ??
August 25, 2014

Math
I will assume you meant ... x^(log10 x = 100 then by definition: logx 100 = log10x changing to a common base of the log ... log10 100/logx = logx/log1010 2/log10x = log10 x/1 (log10 x)^2 = 2 log10 x =√2 using my calculator x = appr 25.9546 or x = appr .03853 (both ...
August 25, 2014

check (math)
Yup !
August 25, 2014

Math
Is there a typo ? Your first term does not fit the pattern
August 25, 2014

Math
radius of larger circle --- r radius of smaller circle --- r-1 circumf of large ---- 2πr circumf of smaller = 2π(r-10 but 2πr = 4(2π(r-1)) 2πr = 8πr - 8π divide each term by π and rearrange equation -6r = -8 r = 8/6 = 4/3 larger has ...
August 19, 2014

Math
original radius --- r new radius ------ r+1 original area = πr^2 new area = π(r+1)^2 π(r+1)^2 - πr^2 = 16π divide by π and expand ... r^2 + 2r + 1 - r^2 = 16 2r = 15 r = 7/5 units check: old area = π(7.5)^2 = 56.25π new area = π(8.5...
August 19, 2014

math
None of your "following points" are showing up Point with integer values on the circle are (5,0), (-5,0), (0, 5) , (0, -5) (3,4) ,(-3,4) , (3, -4), and (-3,-4) Jodie's point of (0,-4) does not lie on the circle the equation would be x^2 + y^2 = 25 so sub in your ...
August 19, 2014

math
x^2-3x-8=0 x^2 - 3x = 8 x^2 - 3x + 9/4 = 8 + 9/4 (x - 3/2)^2 = 41/4 x - 3/2 = ±√41/2 x = 3/2 ± √41/2 = (3 ±√41)/2 to find the term to be added to each side, take 1/2 the coefficient of the x term , then square it that is, 1/2 of 3 is 3/2...
August 19, 2014

Volume
Let the volume be V at a rate of 125 L/h, time would be V/125 hrs at a rate of 150 L/h, time would be V/150 hrs V/125 - V/150 = 1 1/3 = 4/3 times 750 6V - 5V = 1000 V = 1000
August 19, 2014

Year 11 Maths
midpoint M is ( (-1+6)/2 , (-2+2)/2 ) = ( 5/2 , 0) midpoint N is ( (-1+4)/2 , (-2+6)/2 ) = ( 3/2 , 2) slope BC = (6-2)/(4-6) = 4/-2 = -2 slope of MN - (0-2)/(5/2 - 3/2) = -2 So BC is || to MN length of BC = √( (6-2)^2 + (4-6)^2) = √(16+4) = √20 = 2√5 ...
August 19, 2014

MAth
Yessss!!! Looks like you got it
August 18, 2014

small typo - MAth
the second line of the solution should say : = 30/10 + |5|/5x8 has no effect on the rest
August 18, 2014

MAth
as it applies to your previous problem |30|/|10| + |-2+7|/5 x 8 = 30/10 3 + |5|/5x8 = 3 + 5/5*8 = 3 + 1*8 = 3+8 = 11
August 18, 2014

MAth
Do all calculations inside the bars following the usual rules of arithmetic. If your answer is positive, make that your answer. If your answer is negative, ignore the negative sign, and state the positive result. That is | anything in here | will always produce a positive (or ...
August 18, 2014

MAth
no, |30|/|10| + |-2+7|/5 x 8 = 3 + 5/5*8 = 3 + 1*8 = 3+8 = 11 How did you get 17.4 ???
August 18, 2014

statistics
Perfectly suited for David Lane's great stats calculator Just enter the values from your problem http://davidmlane.com/hyperstat/z_table.html I get 84.15% If you must use your tables, z-score for 10 = (10-7)/1.7 = 1.7647 z-score for 5 = (5-7)/1.7 = -1.17647 look up ...
August 18, 2014

maths
gold coins --- x silver coins -- (1/3)x x + (1/3)x = 88 times 3 3x + x = 264 x = 66 there are 66 gold coins and (1/3)(66) or 22 silver coins
August 18, 2014

math
Let's just use an intuitive approach. We know that if x -->0 , 1/x becomes infinitely large. But cos(anything) is always a number between -1 and +1, no matter how large 1/x becomes So we are then multiplying this by "almost zero" , so the answer will be zero.
August 17, 2014

math
depends what your expression is supposed to represent Suppose you want to know the depth after t minutes rate = 150/30 ft/min or 5 ft/min so depth = 210 + 5t Your answer is perfectly correct, since it also shows the position relative to the ocean floor, mine shows the ...
August 17, 2014

math
breath --- x length --- (5/3)x 2x + 2(5/3)x = 64 times 3 6x + 10x = 192 x = 12 area = x(5/3)x = (5/3)(144) = 240 cm^2
August 17, 2014

math
Being familiar with this type of optimization problem, I was expecting to be given the rate at which he can run or walk along the beach. If the rate along the beach is faster than his swimming rate, then the hypotenuse that Henry found will not give him the minimum time. he ...
August 17, 2014

math
SIN(90*-0)COT(90*-0)/SIN0+COS(90-0)=1/2 What is that supposed to be ? The first thing I noticed is that you are dividing by sin0, which is division by zero! That makes everything else I see useless. Is 0 supposed to stand for Ø ??? If so, then the following properties ...
August 17, 2014

Math
width --- x length -- 3x + 6 x(3x+6) = 57 3x^2 + 6x - 57 = 0 x^2 + 2x - 19 = 0 I am going to complete the square, easier in this case than the formula x^2 + 2x + 1 = 19+1 (x+1)^2 = 20 x+1 = ± √20 x = -1 ± √20 = appr 3.472 or a negative width = 3.472...
August 17, 2014

Maths
let O be over average, A be average, and B be below average, F for fail and P for pass prob(O) = 15/75 = 1/5 prob(A) = 45/75 = 3/5 prob(B) = 15/45 = 1/5 prob(P) = x prob(F) = 1-x , not really needed so we have AF = .05 AP = (3/5)x OF = .005 OP = (1/5)x BF = .15 BP = (1/5)x .05...
August 17, 2014

Maths
What makes this question messy is the fact that the bags contain different number of balls, so we have to take all cases BagA: WW - 2/6 * 1/5 = 2/30 = 1/15 WB - 2/6 * 1/5 * 2 = 4/30 = 2/15 , times 2 since it could be BW WR - 2/6 * 3/5 * 2 = 12/30 =6/15 BR - 1/6 * 3/5 * 2 = 6/...
August 17, 2014

Math
Poor wording Is the payment made monthly? Was the first payment made one month after the loan was taken out? Is the interest compounded monthly? I will assume those three important facts i = .07/12 = .00583333... amount owing after 19 months = 26400(1.0058333)^19 - 300( 1....
August 16, 2014

contemporary math
Just good ol' Pythagoras here ... x^2 + (x-2)^2 = 10^2 x^2 + x^2 - 4x + 4 - 100 = 0 2x^2 - 4x - 96 = 0 x^2 - 2x - 48 = 0 (x - 8)(x + 6) = 0 x = 8 or x = -6, but we can't have a negative side so the triangle is 8 by 6 by 10 (which you might recognize as double the well-...
August 16, 2014

Math
Mark --- x Cindy --- 2x+4 Juan --- (1/2)(2x+4 = x+2 comparing x with (x+2) ..... so Juan is 2 years older than Mark this will be true for any age of Mark you pick: e.g. let Juan's age be 10 then Cindy is 24 and Mark will be 12, which is 2 years more than Juan
August 16, 2014

math
width-- x length -- x+7 2x + 2(x+7) = 74 solve for x to width the width and length Area = width x length
August 16, 2014

Pure Maths
make a sketch to see that by ratios, r = h/2 , like bobpursely noted The sneaky part of the question is that when the cone is 1/8 full , the water is NOT 1/8 of the way up Full volume = (1/3) π (1^2)(2) = 2π/3 m^3 we want r and h when volume = (1/8)(2π/3) or &#...
August 16, 2014

Algebra
1. -6.8^2 , the way you typed it is -46.24 If you meant (-6.8)^2 , the you get 46.24 2. ok , if your answer is -14 3 ok 4. -7/3 is reduced to lowest terms or as a mixed fraction = -2 1/3
August 15, 2014

math
Either two blues or two greens prob of 2 blues = (4/6)(3/5) = 2/5 prob of 2 grees = (2/6)(1/5) = 1/15 , this is where PsyDAG slipped up so prob of 2 of same colour = 2/5 + 1/15 = 7/15
August 15, 2014

math
side of square = 2 so perimeter of square = 4s circumference of circle with radius r is 2πr so ... 2πr = 4s πr = 2s r/s = 2/π
August 15, 2014

math
n rotations = f/π ft 1 rotation = fπ/n ft 2πr = fπ/n r = f/(2n) ft diameter = 2r = f/n ft
August 15, 2014

math
I usually start with the smallest quantity, which here is Carl's age let Carl's age be x then Bill is 2x and Al is 4x in 10 years: Carl --- x+10 Bill --- 2x+10 Al ---- 4x + 10 so 4x+10 = 2(x+10) 4x + 10 = 2x + 20 2x = 10 x = 5 So now Al is 4(5) = 20 check: present ages...
August 15, 2014

Maths Help!!
06 kg of red + 250 g of blue = 1100 g of mixed sand 1/2 of that is 550g she adds 500 g of white to that, so total stuff with white sand in it is 1050 g or 1.05 kg
August 15, 2014

hard to read - algebra
Kathy, I find it hard to figure out what your equation is (same for your previous post) Since you labeled it "radicand" , I expected some kind of square root or root we use the ^ symbol to show exponents, e.g. x^2 ---- x squared x^(1/2) = √x = square root of x ...
August 13, 2014

Math
You are welcome
August 13, 2014

Math
You are just finding the radius of circle with a circumference of 27 inches 2πr = 27 r = 27/(2π) = appr 4.30
August 13, 2014

math
so you want to set the area equal to the circumference .. πr^2 = 2πr r^2 - 2r = 0 r(r-2) = 0 r = 0 , the trivial case or r = 2 so the diameter is 4 inches
August 13, 2014

math
A = (5/4)B 4A = 5B B = (4/5)A B = 80% of A looks like B is 20% less than A
August 13, 2014

Math
You keep repeating the same question, which I answered for you, and which does not make sense.
August 13, 2014

mathematics
Artem! The bell will ring at 0:00 , 0:02 , 0:04 , 0:06 , 0:08, ... The bird will chirp at 0:00 , 0:03 : 0: 06 < 0:09 , ... Can you not see that your choices of answers make no sense ? I don't know of any way to make it more obvious.
August 13, 2014

mathematics
Something wrong with your problem As you stated it, they will occur together in 6 seconds
August 13, 2014

fractions/math / Help!
8 3/7-2 1/2 = 59/7 - 5/2 = 118/14 - 35/14 = 83/14 or 5 13/14 93 = 3x31 524 = 2x2x131 both 31 and 131 are primes
August 12, 2014

Algebra
let the smaller be x then the larger is 9-x " Four times the larger number plus three times the smaller number is 48" ---> 4(9-x) + 3x = 48 36 - 4x + 3x = 48 -x = 12 x = -12 The smaller is -12 and the 21 check: -12 + 21 = 9 , check! 4(21) + 3(-12) = 48 , check!
August 12, 2014

Math
-2/5+(-1/10) = -2/5 - 1/10 = -4/10 - 1/10 = -5/10 = -1/2
August 12, 2014

algebra
For a polygon of n sides, the sum of the interior angles = 180(n-2)°
August 12, 2014

algebra
probably: 1/3 + 5/(s-4) = 2 time 3(s-4) 1(s-4) + 5(3) = 2(3)(s-4) s-4 + 15 = 6s - 24 35 = 5s s = 7
August 12, 2014

algebra
I assume from your 2nd line that your 1st line should have been n/4=(n+1)/(3n) 3n^2 = 4n+4 3n^-4n-4=0 (3n + 2)(n - 2) = 0 n = -2/3 or x = 2
August 12, 2014

algebra
Is your first line, 20/(x^2 + 4x) = 3/(x+4) + 1/x ?? I will assume that, then 20/(x(x+4)) = 3(x+4) + 1/x your LCD is x(x+4) , so let's multiply each term by that ... 20 = 3x + x+4 16 = 4x x = 16/4 = 4 The rest of your post has no relation to your first equation. If it is a...
August 12, 2014

Math
So we need 2 widths and 1 length let the width be x and the length be y 2x + y = 2400 y = 2400-2x Area = A = xy = x(2400-2x) = 2400x - 2x^2 dA/dx = 2400 - 4x = 0 for a max of A 4x = 2400 x = 600 then y = 2400-1200 = 1200 field is 600 ft by 1200 ft
August 12, 2014

math
let the width of the base be x let the length of the base by y 2x + 2y = 50 x + y = 25 ---> y = 25-x volume = V = 5xy = 5x(25-x) = 125x - 5x^2 dV/dx = 125 - 10x = 0 for a max of V 10x = 125 x = 12.5 y = 12.5 the box is 12.5 by 12.5 by 5 cm
August 12, 2014

math
"..having all the digits odd except 9.." but 9 is odd Typo?
August 12, 2014

maths
number of selections without conditions = C(15,6) number of selections as stated = C(6,2) x C(9,3) Problem with your question ..... 2 men and 3 women adds up to only 5 people chosen, but you are choosing 6. Fix your problem and I will continue
August 12, 2014

ramjas
in the original number let the unit digit by x and the tens digit be y the number is 10y+x x+y = 13 then the number reversed is 10x + y 10x + y - (10y + x) = 27 9x - 9y = 27 x-y = 3 add the two equations: 2x = 16 x = 8 then y = 13-8 = 5 the number is 58 check: 85-58 = 27 , all...
August 12, 2014

2nd: Algebra
sale price = 40 - .25(40) = 30 or sale price = .75(40) = 30 (your statement of s = p - .25 makes no sense)
August 12, 2014

Algebra
1st question: not sure if you mean: 5^2 - 4/5 + 2 or (5^2 - 4)/5 + 2 or .... can you see why you might want to use brackets to establish the correct order of operation so, if 5^2 - 4/5 + 2 then 25 - 4/5 + 2 = 27-4/5 = 131/5 if (5^2 - 4)/5 + 2 then (25-4)/5 + 2 = 21/5 + 2 = 31/5
August 12, 2014

mathhhhhhh!
Since it asked for substitution, why not just sub the 2nd into the 1st 5x = 4x - 4 x = -4 now back into the 2nd: y = 5x= 5(-4) = -20 so the intersection point is (-4,-20)
August 11, 2014

Algebra
1. width --- w length -- w+14 w(w+14) = 1632 w^2 + 14w = 1632 w^2 + 14w + 49 = 1632 + 49 I completed the square (w+7)^2 = 1681 w+7 =±41 w = -7 ± 41 = 34 or a negative the width is 34 ft and the length is 48 ft or it factors to (x-34)(x+48) = 0 x = 34 or x = -48 2...
August 11, 2014

math
x^4 - 13x^2 + 36 = 0 (x^2 - 4)(x^2 - 9) = 0 (x - 2)(x + 2)(x - 3)(x + 3) = 0 so x = ±2, ±3 or x = -3, -2, 2 3
August 11, 2014

math
let the load be x N 10x = 5(200) + 2(300) 10x = 1600 x = 160 N
August 11, 2014

Precalculus
First of all I will assume that your equation is in polar form, so it should have been r = 4/(2 - cosØ) converting: r = 4/(2 - x/r) 2r - x = 4 2r = x+4 square both sides 4r^2 = x^2 + 8x + 16 4(x^2 + y^2) = x^2 + 8x + 16 3x^2 - 8x + 4y^2 = 16 3(x^2 - (8/3)x + 16/9) + 4y^...
August 9, 2014

math
so πr^2 = 2πr divide by π and bring the 2r over r^2 - 2r = 0 r(r - 2) r = 0 or r = 2 r = 0 would be no circle r = 2, then diameter is 4
August 9, 2014

co-ordinate geometry
slope between the points (2,4) and 2,-1) = (-1-4)/(3-2) =-5 / 1 so the other line must have slope 1/5 (3k-0)/(2-k) = 1/5 15k = 2-k 16k = 2 k = 1/8
August 9, 2014

math
2nd term is 81 ---- ar = 81 4th term is 9 ----- ar^3 = 9 divide second equation by the first r^2 = 9/81 = 1/9 r = ± 1/3 so ar = 81 a(1/3) = 81 a = 243 ii) you have a type, but now that you have a and r, whatever the question should be simple iii) sum of infinite =a/(1-r...
August 9, 2014

math
There is an infinite number of these, as long as they look like y = (-3/2)x + b , where b is any constant, it would be perpendicular to your given line notice I made my new slope the negative reciprocal of the given one. e.g. y = (-3/2)x + 56 would do
August 8, 2014

Maths - Optimisation
since we had y^2 subbing in 2x for y would give us (2x)^2 = (2x)(2x) = 4x^2 notice it was 4x^2 and not 4x like you stated
August 8, 2014

Maths - Optimisation
Let's put the rectangle on the x-y grid so that A is (0,0) and B is (3,6) the equation of the line from A to B is clearly y = 2x d = √(x^2 + y^2) = (x^2 + 4x^2)^(1/2) = √(5x^2) = (√5)x dd/dx = √5 So for each unit of x, the length changes by √5...
August 8, 2014

Math
-3x^2 – x = 10 3x^2 + x + 10=0 the discriminant is b^2 - 4ac = 1 - 4(3)(1) which is negative, so there are two complex solutions, and the statement is false 2. again it is false, it would be true if the right side = 0 and not 8 or take one the answers, x+5 = 8 x = 3 sub ...
August 8, 2014

Algebra
They double in number every 2 hours 8:00 -- 100 10:00 -- 200 12:00 -- 400 2:00pm -- 800 4:00 pm -- 1600 6:00pm -- 3200
August 7, 2014

ogive-maths
I did not know what ogives are, so I googled it. I can't see why you could not do likewise.
August 7, 2014

geo
slope of the line going through the first two points = (-7-9)/(-12-8) = -16/-20 = 4/5 so going through new point (-5,-15) with the same slope y+15 = (4/5)(x+5) do whatever you have to do further, but that is in point-slope form
August 7, 2014

Maths
5 kg cost 65 1 kg cost 13 500 g or 1/2 kg cost 6.50 ahh , the simplicity of metric!
August 7, 2014

math
Let P be the foot of the tower, and h be the height of the tower let AP = x , then BP = 80-x I see two right-angled triangles tan21 = h/x ---> h = xtan21 tan46 = h/(80-x) --> h = (80-x)tan46 xtan21 = (80-x)tan46 xtan21 = 80tan46 - xtan46 xtan21 + xtan46 = 80tan46 x(tan21...
August 7, 2014

trigonometry
1 km = appr 3280.84 feet 2 km/h = 2(3280.84/3600) ft/s = 1.82269 ft/s let r be the resultant velocity r^2 = 2^2 + 1.82269^2 r = √7.32219.. = appr 2.7 ft/s tanØ = 1.82269/2 , where Ø is in my right-angled triangle Ø = appr 42.34° his direction is ...
August 7, 2014

Maths
my little BASIC program gave the following: Chipmunk BASIC v3.6.5(b3) 4 possible cases: 135 175 518 598 testing for 518 518 ---> 5 + 1^2 + 8^3 = 5+1+512 = 518 YUP! I ran the following little program Chipmunk BASIC v3.6.5(b3) >10 for a = 1 to 9 >20 for b = 0 to 9 >...
August 7, 2014

MATH
The following site takes the place of tables in a textbook http://davidmlane.com/hyperstat/z_table.html click on: Value from an area enter: area 0.7 mean 2.9 sd .6 click on 'below' to get3.214
August 7, 2014

math
mmmmhhh ? Did you try plugging in 8 for t in your given formula ? - remember you would have to square first
August 6, 2014

Math
1/4(8y+4)-18<-1/2(4y-6) times 4, ( so < sign stays the same ) 8y + 4 - 72 < -8y + 12 add 8y+68 to both sides, (no change in the < ) 16y < 80 divide by 16, (no change in < ) y < 5
August 6, 2014

Math- urgent
speed of hockey-puck ---- x (10/7)x = 170 10x = 1190 x = 119 mph
August 6, 2014

math test review
w=7r+6r+5r+4r+3r w = 25r the next multiple of 7r would be 28r for any positive integer of r so we need to add 3r
August 6, 2014

math corrections
that would make it 900/300 = 3 a gear with 3 teeth ????
August 6, 2014

math corrections
2. x = .75x + 6 .25x = 6 x = 24 4. outer radius = .75/2 = .375 inner radius = .625/2 = .3125 so thickness of wall = .375-.3125 = .0625 14. no diagram 24. Think of the teeth laid out linearly For the first gear in 1 minute would cover 30x30 or 900 teeth for the 2nd gear, let ...
August 6, 2014

Geometry
Yup, I was so totally distracted by the second part of his post, that I completely missed and ignored the actual question. Another senior moment!!! but... wasn't that a great explanation?? reminds me of my teaching years, when during an exam a student replied to a certain ...
August 6, 2014

Geometry
both are variations of the relation cos 2A = cos^2 A - sin^2 A or cos 2A = 2 cos^2 A - 1 or cos 2A = 1 - 2sin^2 A We use this to either find trig ratios of double an angle or 1/2 an angle e.g. if we know sin 50° , I could now find ratios for 25° or 100° e.g. you ...
August 6, 2014

math
x^2 + 12x + 4 = 0 does not factor, so I will complete the square, easiest way for this one. x^2 + 12x + 36 = -4+36 (x+6)^2 = 32 x+6 = ±√32 = ±4√2 x = -6 ± 4√2
August 6, 2014

math
Must be mathemagics
August 6, 2014

math
Your post makes no sense to me How is this related to the binomial theorem? 32 ÷ 7 = 4 with a remainder of 4
August 6, 2014

college algebra
number of gallons of the 30% stuff --- x .3x + .14(60) = .2(60+x) 30x + 14(60) = 20(60+x) 30x + 840 = 1200 +20x 10x = 360 x = 36
August 5, 2014

geometry
I interpreted " two of its interior angles are 127 degrees and 135 degrees, and the remaining interior angles are 173 degrees each. " the wrong then. so I should have had 130 + 130 + 130 + 127 + 135 + 173(n-5) = 180(n-2) which gives 652 + 173n - 865 = 180n - 360 n = ...
August 5, 2014

geometry
But Damon's answer contradicts the sum of the inside angles property if n = 21 the sum of the interior angles = 127+135 + 19(173) =3949 which must be a multiple of 180
August 5, 2014

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