Monday
August 3, 2015

Posts by Reiny


Total # Posts: 30,528

Second thoughts - Ndmc
Even though the above solution is mathematically correct, it makes no sense and the question is ridiculous. let's look at what time their speeds are the same 5t = 50 t = 10 after 10 seconds, the bus is going at 50 m/s and the car is going at a constant speed of 50m/s but ...
June 20, 2015

Ndmc
The question is poorly worded. It says, "At the same time" a car .... overtakes and passes the bus. So the time would be zero. I will assume that the car was a certain distance behind the bus bus: a = 5 v = 5t + c but when t=0, v=0 , so c=0 v = 5t s = distance = (5/2...
June 20, 2015

math
7 = 1x7 8 = 2x2x2 12 = 2x2x3 Everybody must be represented, so LCD = 1x2x2x2x3x7 = 168
June 20, 2015

geometry
d miles correspond with 9 inches on the map so 1 mile corresponds to 9/d inches d+1 miles corresponds to (9/d)(d+1) inches on the map doodle with (9/d)(d+1) any way you want.
June 19, 2015

Math
The period: 2π/k = 5 then k = 2π/5 the amplitude = 35/2 = 17.5 your ferris wheel behaves like h = 17.5sin(2π/5) but you said it is 50 m high and the max height of the function is 17.5 so we need h = 17.5sin(2π/5) + 32.5 looks like I am overthinking this ...
June 19, 2015

algebra
However, since both sides were squared, all answers must be checked in the original equation √(10-x) + x = 8 if x = 6 LS = √4 + 6 = 8 = RS if x = 9 LS = √1 + 9 = 10 ≠ RS so the only solution is x = 6
June 19, 2015

Math
how about this approach: Simone's money --- 2x Fiona's money --- 3x after mom's gift: 2x/(3x+5) = 4/7 14x = 12x + 20 2x = 20 x = 10 so Simone had 2x or $20 Fiona had 3x or $30
June 18, 2015

Math (Need help Urgent)
I am sure you meant: y ≤ -2(x - 2)^2 - 2 which would be everything below and including the parabola, which itself opens downwards and has a vertex of (2,-2) http://www.wolframalpha.com/input/?i=y+%E2%89%A4+-2%28x+-+2%29%5E2+-+2
June 18, 2015

algebra
amount invested at lower rate --- $x amount invested at higher rate ---$ 3x .02x + .03(3x) = 27.50 times 100 2x + 9y = 2750 11x = 2750 x = 250 so she invested $250 at 2%, and $750 at 3% check: .02(25) + .03(750) = 27.5
June 18, 2015

maths
let a man's rate be x fields/h let a boy's rate be y fields/h so 2/x + 6/y = 1/3 times 3xy 6y + 18x = xy 6y - xy = -18x y = -18x/(6-x) = 18x/(x-6) , x > 6 also given: x = (2/3)y then x = (2/3)(18x)/(x-6) x(x-6) = 12x x^2 - 18x = x(x-18) = 0 x = 18 (or x = 0, which ...
June 18, 2015

algebra
looks like an AS, with a = 20 , d = -1 , n = ? (n/2)(2a + (n-1)d ) = sum(n) (n/2)(40 + (n-1)(-1) ) = 200 n( 40 - n + 1) = 400 -n^2 + 41n - 400 = 0 n^2 - 41n + 400 = 0 n = (41 ± √81)/2 = 25 or 16 so term(25) = 20 + 24(-1) = -4 which makes no sense or term(16) = 20...
June 17, 2015

Maths trig
I am sure you meant f(x) = 3/(x+1) http://www.wolframalpha.com/input/?i=plot+y+%3D+3%2F%28x%2B1%29+%2C+y+%3D-2x-4 look at the 2nd graph, the vertical blue line is an anymptote
June 17, 2015

algebra
let the number be x 3x - 7 = x + 39 take over, the equation is easy to solve
June 16, 2015

maths
I have no clue what v =TT is supposed to say, but my formula for volume of a cylinder is V = πr^2 h so for your data, V = π(4^2)(12) = 192π so your can holds a volume of 192π cm^3 which is 192π ml or appr 603.2 ml
June 16, 2015

math
As Steve pointed out to you in your previous posting of the same question, x = 0 and x = 35 are the values which give you an area of zero, which is not what you want. A = (70-2x)(x) is represented by a parabola which opens downwards, so its vertex shows its maximum and at what...
June 16, 2015

Maths
using substitution, x^2 - 7x + 23 = 7x - 1 x^2 - 14x + 24 = 0 (x - 12)(x - 2) = 0 x = 12 or x = 2 if x=12, y = 7(12)-1 = 83 if x=2 , y = 7(2)-1 = 13 they intersect at (12,83) and (2,13) confirmation here: look at the first graph http://www.wolframalpha.com/input/?i=plot+Y%3Dx%...
June 15, 2015

calc
if a(t) = cos(t) − sin(t) v(t) = sin(t) + cos(t) + c given: v(0) = 0 3 = sin0 + cos0 + c 3 = 0 + 1 + c c = 2 v(t) = sin(t) + cos(t) + 2
June 14, 2015

Trigonometry
But I showed you that it is NOT true, so you can't prove it to be true.
June 14, 2015

Trigonometry
Hard to prove something which is not true LS= (.11697..)(.41317..)(.9698..) = appr .0469 ≠ 3/2 (I assumed your . meant multiplication, and you were in degrees. It is also false in radians)
June 14, 2015

Math (Finite)
So you want 2 R's and 1 D prob = C(5,2)xC(6,1)/C(11,3) = 10(6)/165 = 4/11
June 11, 2015

math
And why do you think it took 4 seconds? (wrong guess by the way)
June 11, 2015

Math Help
number of choices of any 2 of the 10 = C(10,2) = 45 number of choices of any 2 of the 4 engineers = C(4,2) = 6 Prob(of stated event) = 6/45 = 2/15 or, simply prob(of stated event) = (4/10)(3/9) = 2/15
June 11, 2015

Trig/ algebra 2
sin(π/2) - cos(π/4) = 1 - √2/2 = (2-√2)/2
June 10, 2015

Functions
for what function ?? if it is y = cosx then dy/dx = -sinx and -sin(π/4) = -1/√2 so you are correct if y =cosx
June 10, 2015

Probabilities
let g be good bulb let b be bad bulb so your events are: gbb ---> (4/7)(3/6)(2/5) = 4/35 bgb ---> (3/7)(4/6)(2/5) = 4/35 prob(as stated) = 4/35 + 4/35 = 8/35 or appr .229
June 10, 2015

MATH 117A
-9x^2 + 7x + 2 = 0 9x^2 - 7x - 2 = 0 x = (7 ± √121)/18 x = 1 or x = -2/9
June 10, 2015

Calculus 1
you are solving 4.9t^2 - 21.5t - 3 = 0 , after multiplying each term by -1 You must have learned the quadratic equation to be solving these type of questions, go ahead.
June 10, 2015

pre-calculus 11
is it y = 1/x - c , like you typed it, or y = 1/(x-c) comparing it to y = 1/x for the first interpretation the graph of y = 1/x would simply be translated vertically by c for the 2nd interpretation the graph of y = 1/x would be translated horizontally by -c , e.g if y = 1/(x+2...
June 10, 2015

pre-calculus 11
from the definition of absolute value, we know the right side must be ≥0 so x+1 ≥ 0 x ≥ -1 algebraically: (1/2)x + 1 = x+1 OR (-1/2)x - 1 = x+1 x + 2 = 2x + 2 OR -x - 2 = 2x + 2 x = 0 OR -3x = 4 x = 0 or x = -4/3 which is what you had remember at the top we ...
June 10, 2015

pre-calculus 11
let's look at the graph. http://www.wolframalpha.com/input/?i=plot+y%3D-%7Cx%5E2+-9%7C+%2C+x+from+-10+to+10 notice that the entire graph must lie below the x-axis, since we have y = -(some positive stuff) so for x<-3 OR x>+3, we have y = -x^2 + 9 for -3 ≤ x &#...
June 10, 2015

Precalc
we know sinØ = y/r and cosØ = x/r and tanØ = y/x then for the given: sinØ = x = y/r rx = y ---> r = y/x 3cosØ = y = 3x/r ry = 3x (y/x)y = 3x y^2 = 3x^2 y = ±√3 x
June 10, 2015

math help trigonometry
yup, that's what you typed the first time. And I pointed out to you that that is not an identity.
June 10, 2015

math help trigonometry
tan x cos x/sin x=1/sin x cos x or tan x cos x/sin x=1/(sin x cos x) ? For either case, LS = tanx(cosx/sinx) = tanx cotx = 1 For any given x, RS ≠ 1 Your equation is NOT an identity, so it cannot be proven to be true.
June 10, 2015

Algebra
2nd: 10x^2 + 70x + 100 = 10(x^2 + 7x + 10) = 10(x+5)(x+2) 3rd: 2x^2 + 9x + 4 = 0 (2x + 1)(x + 4) = 0 carry on 4th: real easy ... (x-5)^2 - 81 = 0 (x-5)^2 = 81 take √ of both sides x-5= ±9 x = 5 ± 9 = 14 or -4
June 10, 2015

Geometry
If I read this correctly, the radius of his model is 6 inches Volume of sphere = (4/3)π r^3 = (4/3)π(216) = 288π cubic inches or appr 904.8 cubic inches SA = 4πr^2 = 4π(36) = 144π inches^2 or appr 452.4 inches^2 to double the radius results in ...
June 9, 2015

Geometry
As the question suggests, the line joining your two points is a diameter. So the centre is the midpoint, which is ((-5+11)/2 , (-11+19)/2 ) = (3, 4) radius = √(3+5)^2 + (4+11)^2 = √(64+225) = √289 = 17 equation of circle: (x-3)^2 + (y-4)^2 = 289 if x = 24 21^...
June 9, 2015

Geometry
Where is E ? Where is P ? Are your given points A,B,and C on the circle?
June 9, 2015

Geometry
Have you learned about b^2 - 4ac, called the discriminant, of the quadratic equation? If the discriminant is zero, there is only one solution, so evaluate b^2 - 4ac. If the discriminant is positive, there are 2 real and different solutions, If the discriminant is negative, ...
June 8, 2015

Math
5/36 is correct
June 8, 2015

Geometry
from the linear equation: x = 7y - 75 intersect the two relations, x^2 + y^2 = 225 (7y-75)^2 + y^2 - 225 = 0 49y^2 - 1050y + 5625 + y^2 - 225 = 0 50y^2 - 1050y + 5400 = 0 divide by 50 y^2 - 21y + 108 = 0 (y - 12)(y - 9) = 0 y = 12 or y = 9 if y = 12, x = 9 if y = 9 , x = -12 ...
June 8, 2015

calculus1
Did you make a sketch? Here is Wolfram's take on the situation. http://www.wolframalpha.com/input/?i=plot+y%3D3x%2Cy%3Dx%2Cy%3D4-x You need the intersection of the lines I assume you want the area of the enclosed region. the intersection points are (0,0), (1,3), and (2,2) ...
June 8, 2015

math
perimeter = 1 length + 2 width + (1/2)circumference of circle = 16 + 2(7) + (1/2)(2π)(8) = 30 + 8π = appr 55.13 using a better value than 3.14
June 8, 2015

Algebra
Joanie's equation is (x+16)(x-2) = 0 x^2 + 14x - 32 = 0 , in hers the -32 is wrong, the 14x is correct Kelvin's equation is (x+36)(x-2) = 0 x^2 + 34x - 64 = 0 for his, the 34x is wrong , but the -64 is right the teacher's equation is x^2 + 14x - 64 = 0
June 3, 2015

math
take two identical rulers and lay them across each other at 30° to get a mental image of the problem. Is the overlapping area not a rhombus with acute angles of 30° and obtuse angles of 150° ? So make that sketch, all 4 sides are equal, label them x draw a vertical...
June 3, 2015

math
I don't know what your diagram looks like, but try this I will assume that this is a question dealing with vectors. let O be the centre of you NS, EW grid draw a line OB with a heading of N65°W , and mark it x km/h this will be your resultant vector draw in your wind ...
June 3, 2015

Math
arggh, go with Damon on the first question, I read it as 1/3 of the time, not 1/3 hour less
June 3, 2015

Math
rate at first part --- x mph rate for return --- x + 5 mph time on first part = 120/x time on 2nd part = 120/(x+5) (these should be entries in your chart) now it says: time on return = (1/3) time of first part 120/(x+5) = (1/3)(120/x) divide by 120 1/(x+5) = 1/(3x) 3x = x+5 2x...
June 3, 2015

Algebra
One 12 oz can = 12(29.6) ml or 426.4 ml so a six pack = 6(426.4) ml or 5116.8 ml cost of 2 L bottle = $2.19/2000 ml = .001095 $/ml cost of six pack = 2.99/5116.8 = .00058 $/ml draw your conclusion
June 3, 2015

Algebra
1 litre costs 1.31 1 gallon = 3.7854 L 12 gallons = 12(3.7854) L 12 gallons cost CND $1.31(12)(3.7854) = CN $59.51 1 CND = US 1.02 C 59.51= US (1.02)(59.51) = $60.70 cost per gallon in US$ = 60.70/12 = $5.06 actual cost TODAY: 12 gallons cost 12(3.7854)(1.06) = $48.15 CND $1...
June 3, 2015

algebra
I bet you meant: x^2/(x+4) ÷ ( (x-2)/(x^2+x-12) ) = x^2/(x+4) * (x+4)(x-3)/(x-2) = x^2(x-3)/(x-2) , x ≠ -4,2
June 3, 2015

Geometry.
Steve is right, pardon the senior moment, and my diagram even has D corresponding with A
June 3, 2015

Geometry.
angle A = 180-121-35 = 24° since angle FDE corresponds with angle CAB angle D = 35°
June 3, 2015

Calculus
At a stop, the velocity is zero, so t^3 - 3t^2 + 3t = 0 t(t^2 - 3t + 3 ) =0 t = 0 or t^2 -3t + 3 = 0 t^2 - 3t + 3 = 0 has no real solution to slow down a(t) would have to be negative a(t) = 3t^2 - 6t + 3 let's see where it is zero t^2 - 2t + 1 = 0 , after dividing both ...
June 3, 2015

probability
9 cars, 3 of which are red so prob(red,red) = (3/9)(2/8) = 1/12 you do the decimal stuff
June 2, 2015

Math
cos^4 Ø - sin^4 Ø + sin^2 Ø = (cos^2 Ø + sin^2 Ø)(cos^2 Ø - sin^2 Ø) + sin^2 Ø = (1)(cos^2 Ø - sin^2 Ø) + sin^2 Ø = cos^2 Ø
June 2, 2015

Math
Took me a while, but I was sure that Steve had answered this for you http://www.jiskha.com/display.cgi?id=1432887186 and again here http://www.jiskha.com/display.cgi?id=1432801604
June 2, 2015

Algebra
I have a feeling you meant: (x+2)/8 + 1 = 4x/2 multiply each term by 8 x+2 + 8 = 16x 10 = 15x x = 10/15 = 2/3
June 2, 2015

Math
the first chair can be filled in 8 ways, for each of those the 2nd chair can be filled in 7 ways, (one is seated) and for each of those, the 3rd chair can be filled in 6 ways, so number of ways = 8*7*6 = 336 ways
June 2, 2015

Algebra
9y/7 = 12y - 24 times 7 9y = 108y - 168 99y = 168 y = 168/99 y = 56/33
June 2, 2015

Math
nope, what you wrote is the opposite of what you had That is like saying can 5 be written as -5 ?
June 2, 2015

Math
one problem, you should have brackets around n-1 so a(n) = 5(-2)^(n-1) otherwise, good job
June 2, 2015

Algebra
divide both sides by -9 (4-k)/12 = -(k+1)/8 cross-multiply 8(4-k) = -12(k+1) 32 - 8k = -12k - 12 4k = -44 k = -11
June 2, 2015

Alegebra
multiply each side by 12 7(w+2) = 4(w-7) 7w + 14 = 4w - 28 3w = -42 w =-14
June 2, 2015

Algebra 1
You first started asking this question under the name of Gabs, now you are Amy The above question is clearly based on some previous problem which we cannot see. e.g. how can we possible know how many men and how many women are in the cast?
June 2, 2015

math
I agree
June 2, 2015

Math
let's start with dimes ---- x then quarters ---- x+8 nickels ------- 5(x+8) now to the VALUE of these 10x + 25(x+8) + 5(5)(x+8) = 700 10x + 25x + 200 + 25x + 200 = 700 60x = 300 x = 5 so 5 dimes 13 quarters 65 nickels check: 5(10) + 13(25) + 65(5) = 700 my answer is correct
June 2, 2015

math
You started off ok, but then your logic exploded. You only have to consider the unit digit listing only the unit digit: 2^1 -- 2 2^2 -- 4 2^3 -- 8 2^4 -- 6 2^5 -- 2 2^6 -- 4 2^7 -- 8 2^8 -- 6 .... notice they cycle 2,4,8,6 If the exponent is evenly divisible by 4, the last ...
June 2, 2015

mathh
number of 5's --- x number of 7's ---- y 5x + 7y = 130 5x = 130-7y x = (130-7y)/5 x must be a whole number, so 130-7y must be divisible by 5, only if 7y is a multiple of 5 to get the least number of stamps we should use as many of the 7's (the y) as we can if y = ...
June 2, 2015

Math
in effect, each day the turtle gains 2 ft after 1st day/night -- 9 after 2nd day/night -- 7 after 3rd day/night ---5 after 4th day ---- since he crawls 5 ft during the day, he is at the top at the end of the 4th day.
June 2, 2015

Algebra 1
ok, I misread your question total number of castings = 35 number of casting with the one brother and sister = 1 number of castings with the one brother and two sisters = 1 x 2 = 2 prob (bother and sister in casting) = 3/35
June 2, 2015

Algebra 1
missing information. In what way are the sibling choices affecting the casting? e.g. can the 2 siblings not be cast together?
June 2, 2015

Algebra 1
no, any of the 7 men could have the leading role, for each of those, there would be 5 choices for the female role, so number of ways = 7x5 = 35
June 2, 2015

Algebra 2
Nothing wrong in your steps, except at the end when you have x = 3 or x = -2, we can't allow x = 3, since we then would have divided the original by zero, which we can't do so the only answer is x = -2 Had you factored like in the previous .... (x+5)(x-3)/(x-3) = 3 x+5...
June 2, 2015

Algebra 2
(x^2+bx-18)/(-2x+4) = 4 = 4/1 same as before, cross-multiply x^2 + bx - 18 = -8x + 16 now let's sub in the x = -17 (-17)^2 - 17b - 18 = 136 + 16 -17b = 152 + 18 - 289 -17b = -119 b = 7
June 2, 2015

Algebra 2
So I read that as: (x^2-7x+12)/(x^2+x-12) = 3 (x-3)(x-4)/((x+4)(x-3)) = 3 (x-4)/(x+4) = 3/1 cross-multiply 3x+12 = x-4 2x = -16 x = -8
June 2, 2015

Algebra
give it a try, this one is really easy
June 1, 2015

alegbra2
50 = 40(1.08)^n 50/40 = 1.08^n n log 1.08 = log(5/4) n = log(5/4) / log 1.08 = 2.899 or appr 2.9 years check: 40(1.08)^2.9 = 50.002 Your expression is incorrect
June 1, 2015

Algebra
times 6 -66(5-b) = 3b -330 + 66b = 3b 63b = 330 b = 330/63 = 110/21
June 1, 2015

Math
The LCM of 7,11, and 30 = 7*11*30 = 2310 So 2311 would not divide by any of those, in each case there would be a remainder of 1
June 1, 2015

Math
multiply each term by 11 10v + 110 = 88(v-7) 10v + 110 = 88v - 616 -78v = -726 v= 121/13
June 1, 2015

Maths
I assume you want to find the surface area a) two circle + a rectangle = 2π(5^2) + 2π(5)(13) = 50π + 130π = 180π = appr 565.49 cm^2 (Nobody would use π as 3.1 in 2015) b) if it is open at one end, the use only one circle and repeat my steps
June 1, 2015

math
amount of 45% stuff --- x ml amount of 15% stuff ---- 780-x mls .45x + .15(780-x) = .35(780) times 100 to get rid of decimals 45x + 15(780-x) = 35(780) take over from here
June 1, 2015

Math
your first response tells me you are having difficulties evaluating a function for a given x x = -1 , y = 3(-1)^2 - 5(-1) - 5 = 3+5-5 = 3 so the point is (-1,3) x = 0 , y = -5 , so the point is (0,-5) x = 1 , y = 3(1)^2 -5(1) - 5 = -7 so the point is (1,-7) x = 2 , y = -3 , ...
June 1, 2015

Math
make a sketch of the graph using x = -1,0,1,2,3
June 1, 2015

Math (check answers)
correct , see http://www.wolframalpha.com/input/?i=plot+y+%3D+16x+%2B+150%2C+y+%3D+-x%5E2+%2B60x+-+10
June 1, 2015

math
trust yourself!
June 1, 2015

Linear quadratics and inequalities
I meant to say: ".. they intersect at a negative x and a value of x which would result in a negative height."
June 1, 2015

Linear quadratics and inequalities
I graphed your functions using Wolfram and they don't intersect at a negative x and a value of showing which would show a negative height. check your equations, or else the question is bogus http://www.wolframalpha.com/input/?i=plot+y%3D-0.1x%5E2+%2B2.9x%2C+y+%3D+-x%2B10
June 1, 2015

math
816 is correct, but I am interested to know why you decided on A.
June 1, 2015

math
amount of dextr... ----- x amount of water ------ 980-x .55x + 0(980-x) = .275(980) .55x = 269.5 x = 490 mls so you need 490 mls of the dextrose and 490 mls of water (notice that 27.5% = (1/2) of 55% )
June 1, 2015

maths
cos^2 30° cos^2 45° + 4sec^2 60° + (1/2)cos^2 90° - 2tan^2 60° these are all special angles and you should memorize the trig ratios of the 30-60-90 and the 45-45-90 triangles = (√3/2)^2 (1/√2)^2 + 4(2)^2 + (1/2)(0) - 2(√3)^2 = (3/4)(1/2...
June 1, 2015

mathematics
What's the question? How many kids are in the pool? What is the water temperature? ??
June 1, 2015

Trigonometry
Did you make your sketch?? If so, then you will see that tan41° = 50/d d = 50/tan41 = ....
June 1, 2015

Math Algebra 1111
Whatever the domains of F(x) and G(x) are they would be the same for (F+G)(x) but for (F/G)(x) you would have to restrict any values for which G(x) = 0 In effect you stated that with an example
June 1, 2015

Math
mine: 3x^2 - 15x + 6 = 0 x^2 - 5x + .... = -2 + ..... x^2 - 5x + 25/4 = -2 + 25/4 (x-5/2)^2 = 17/4 (x - 5/2)^2 - 17/4 = 0 suppose I multiply by 3 3(x-5/2)^2 - 51/4 = 0 looks like they were both correct
June 1, 2015

math
let the original number be 10a + b where a is the tens digit and b is the units digit. New number: 10(a+4) + b-4, where 4 < b < 9 10(a+4) + b-4 = 2(10a + b) 10a + 40 +b-4 = 20a + 2b 10a + b = 36 a = (36-b)/10 the only value of b which would make 36-b a multiple of 10 is ...
June 1, 2015

Math
sin^-1 x is the angle Ø so that sinØ = x or x/1 so you have a right-angled triangle with opposite side x and hypotenuse 1 then y^2 + x^2 = 1 y = √(1 - x^2) and cos(sin^-1 x) = cosØ = √(1 - x^2) test for some value of x let's say x = .1234 ...
June 1, 2015

Math
wecome, please stick to one name, switching names makes it hard to go back in replies
June 1, 2015

Math
RS = 1 + sin^2 x/cos^2 x = (cos^2 x + sin^2 x)/cos^2 x , using common denominator = 1/cos^2 x = sec^2 x = LS
June 1, 2015

Math
As you can see from Steve's graph, your "critical" values are x = -1,2,3 so you have the following line segments 1. for x ≤ -1 : let x = -2, y = 10 let x = -1 , y = 7 , slope = -3 y-7 = -3(x+1) -----> y = -3x + 4 2. for -1 ≤ x ≤ 2 let x = -1...
June 1, 2015

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