Wednesday
September 2, 2015

Posts by Reiny


Total # Posts: 30,694

college geometry
let B be (x,y) then (x+1.7)/2 = 2.1 x+1.7 = 4.2 x = 2.5 find y in the same way, and you have B
May 29, 2015

Math
prob = (2/12)(1/11) = 1/66
May 28, 2015

math
I will interpret "There is an east wind blowing at 60 mph" as the wind is blowing from the east. anyway, ... we just have a right-angled triangle so that x^2 = 480^ + 60^2 solve for x
May 28, 2015

college geometry
for any point (a,b) , the image of (a,b) with symmetry with respect to the origin would yield the point (-a,-b) so for (3,4) ----> (-3,-4) I will let you do the others.
May 28, 2015

Math
complete the square .... y = 3(x^2 - 6x ....) + 4 = 3(x^2 - 6x + 9 - 9) + 4 = 3( (x-3)^2 - 9) + 4 = 3(x-3)^2 - 27 + 4 = 3(x-3)^2 - 23 I trust you can take it from here.
May 28, 2015

Math
I am an avid camper and have never seen a sleeping bag like that, ..... I will give you an example of the given shape of the sleeping big with points on the x-y plane let AB, with points A(0,12) and B(0,-12) be the zipper side let CD with C(6,-8) and D(6,8) be the side ...
May 28, 2015

@ Person helping
Unless you know what you are doing, it doesn't help to answer questions for other students incorrectly. your line of : 3.14*1.4*2*9=79.128 2*3.14*1.4*1.4=3.5168 79.128+3.5168=82.6448 is total mathematical gibberish.
May 28, 2015

math
Volume = π r^2 h = π(1.4)^2 (9) = appr 55.418 m^3 = appr 554000 L, rounded to the nearest thousand litres.
May 28, 2015

Math
Just "translate" 5/6 as many vans as trucks vans = (5/6)trucks or 6vans = 5trucks Suppose there are 18 trucks, then the number of vans = (5/6)(18) = 15 what is 15/18 ?
May 28, 2015

trig
As Steve pointed out, you answer makes no sense, nor can I understand what your calculations are supposed to represent. It almost looks like you are assuming there is a right-angled triangle. There isn't one. If you make a sketch for the problem you would see that this is ...
May 28, 2015

college geometry
or, you can notice that they lie on the same horizontal line, so (b,3) is either 3.5 units to the right or to the left of (7,3) so b = 7 ± 3.5 which is what Steve shows in his last line as well.
May 27, 2015

math
Dan ---- x Sarah ---(2/5)x Chris --- (6/5)x x + 2x/5 + 6x/5 = 6 times 5 5x + 2x + 6x = 30 13x = 30 x = 30/13 ft Sarah --- (2/5)(30/13) = 12/13 (chris has (6/5)(30/13)= 36/13 check: 30/13 +12/13 + 36/13 = 78/13 = 6 my answer is correct
May 27, 2015

Math
LS = (sin^2 Ø/(sin^2 Ø cos^2 Ø) - 1 = (sin^2 Ø/(sin^2 Ø cos^2 Ø - (sin^2 Ø cos^2 Ø)/(sin^2 Ø cos^2 Ø) = (sin^2 Ø - sin^2 Ø cos^2 Ø)/(sin^2 Ø cos^2 Ø) = sin^2 Ø (1 - ...
May 27, 2015

Algebra 2
The question makes no sense. There are an infinite number of points which are not part of the solution. Here is what the graph looks like http://www.wolframalpha.com/input/?i=plot+y+%3C+%E2%80%93%7Cx+%E2%80%93+4%7C
May 27, 2015

Calculus
f(x)=(1-x)/(1+x) and g(x)=x/(1-x) f(g(x)) = f(x/(1-x) ) = [ 1 - x/(1-x)] / [1 + x/(1-x)] multiply top and bottom by 1-x = (1-x - x) / (1 - x + x) = (1 - 2x)/1 = 1 - 2x check: pick an unlikely x value and using my calculator g(2.35) = -1.7407... f(-1.7407) = -3.699999 or -3.7 ...
May 27, 2015

Math
My equation was : x^2 = 2y + 1 (Yours in not even an equation.) manipulating this: y = (1/2)(x^2) - 1/2 from this I can read that the vertex is (0,-1/2) which is true according to the focus - directrix property in that the vertex is midway between the focus and the directrix. ...
May 27, 2015

math
sketch the sector to the right of the vertical. Label the centre as C, the end of the swing as A and the point on the horizontal hitting the pendulum B So AB = 15 cm we can find OA tan 35° = 15/OA OA = 15/tan35 = 21.422... so the length of the pendulum is 21.422 + 5.3 = 26...
May 27, 2015

Math
made a Venn diagram, labeled the intersection of the soccer circle and the tennis circle as x then ... 13-x + x - 8-x + 2 = 20 -x = -3 x = 3 All can now be seen from the Venn diagram soccer of tennis --- 18 both soccer and tennis -- 3 only soccer --- 10
May 27, 2015

Geometry - help please
Can't see the diagram, but this looks like a very common question I have seen many times, so OB^2 + 6^2 = 11.7^2 OB^2 = 100.89 OB = appr 10.0
May 27, 2015

pre-algebra NEED HELP!
#1, 4,5 are correct #3 SA of a sphere = 4π r^2 so if r = 4 SA = 4π(16) = appr 201 #2, can't see the diagram, will assume r = 8, height = 12 , cover the top but not the bottom SA = πr^2 + 2πrh = π(64) + 2π(8)(12) = appr 804
May 27, 2015

Geomery
correct (what is that jibberish at the end of your first post ? )
May 27, 2015

Math
well, 5 x 20 = 100 and 100 x 18 = 1800
May 27, 2015

precal
x = 3 + 6cost 6cost = x-3 cost = (x-3)/6 similarly , from the 2nd equation sint = (y-6)/6 but we know, sin^2 t + cos^2 t = 1 ( (y-6)/6)^2 + ( (x-3)/6)^2 = 1 (x-3)^2 /36 + (y-6)^2/36 = 1 (x-3)^2 + (y-6)^2 = 36 you should recognize that as a circle with radius of 6 and centre (3,6)
May 27, 2015

Math
Here is how I would have expected my students to show the steps: subtract the first equation from the second : 7x-3y=43 5x - 3y = 35 2x = 8 x = 4 sub that back into 5x-3y=35 20-3y=35 -3y = 15 y = -5 So the first two lines intersect at (4,-5) But the third line of 4x-ay=61 also...
May 27, 2015

Math
let the time taken by Jesse be x hrs then the time taken by Leah is 2x hrs then Jesse's rate is 1/x jobs/hr and Leah's rate is 1/2x jobs/hr combined rate = 1/x + 1/2x = (3/(2x)) but 1/(3/2x) = 4 1 = 4(3/2x) 2x = 12 x = 6 It would take Jesse 6 hrs to do the job alone, ...
May 26, 2015

Math
amount invested at 6% --- x amount invested at 4.5% --- 1200-x .045(1200-x) - .06x = 12 54 - .045x - .06x = 12 -.105x = -42 x = 400 so $400 at 6% and $800 at 4.5%
May 26, 2015

Math help
done,
May 26, 2015

Math
The sides for the 30-60-90° triangle could be 1, √3, and 2 so the perimeter = 1 + √3 + 2 = 3 + √3 so get the hypotenuse from 2 to 9 implies each side was multiplied by 4.5 so the perimeter of your triangle = 4.5(3 + √3) = 13.5 + 4.5√3 or appr ...
May 26, 2015

Math
translate the English into Math... "The sixth term of an A.P. is 5 times the first term" ---> a+ 5d = 5a or 5d = 4a a = 5d/4 "eleventh term exceeds twice the fifth term by 3" term(11) -2 term(5) = 3 a + 10d - 2(a + 4d) = 3 -a + 2d = 3 -5d/4 + 2d = 3 ...
May 26, 2015

math
draw a Venn diagram, fill in the given data and all mysteries will become clear to you
May 26, 2015

Precalculus
Surely, you meant: "...in a circle of radius 10 feet... " arc = rØ, where Ø is in radians so convert 35° to radians and plug in or , use a ratio 35°/360° = arc/circumference etc
May 26, 2015

Precalculus
Tell me where you are running into problems with this basic trig problem. To be successful in studying this topic your MUST be able to do this question.
May 26, 2015

Precalculus
Did you make your sketch? I will assume you want the height of the streetlamp? then tan30° = height/25 continue ....
May 26, 2015

Trigonometry
Your x-coordinate of the given point contains a non-readable character, is it (√12,5) ? If so, then tanØ = 5/√12 If it is something else, then tanØ is simply y/x
May 26, 2015

Calculus
umhh, We don't 'calculate' 5*(t-10)(t-20)=5500 we "solve" 5*(t-10)(t-20)=5500 and I believe I just did that for you.
May 26, 2015

Calculus
set 5(t-10)(t-20)+4500 = 10000 5(t-10)(t-20) = 5500 (t-10)(t-20) = 1100 t^2 - 30t + 200 = 1100 t^2 - 30 t = 900 I will complete the square.. t^2 - 30t + 225 = 1125 (t-15)^2 = 1125 t - 15 = ±√1125 = ±15√5 t = 15 ± 15√5 , but more than ...
May 26, 2015

math
mystery math!
May 26, 2015

algebra
Huh? You said g(x) = 5 which has no variables, and is always equal to 5 so g(-4) = 5 and g(-345) = 5, g(3.432) = 5 g(√89) = 5 , etc g by itself is meaningless, you cannot treat it as a variable and solve for it like you did, it is part of the notation g(...) and means: ...
May 26, 2015

Trigonometry
for any complex number a + bi the modulus is |√(a^2 + b^2) | and the argument is the angle Ø such that tanØ = b/a I will do the 2nd, you do the rest √3 + i or √3 + 1i or (√3,1) in the Argand plane the modulus is √(3+1) = 2 tanØ...
May 26, 2015

Math
Yes
May 25, 2015

Algebra
You don't have to use your real name, but stick to whatever name you pick
May 25, 2015

Algebra
Why are you switching names ? let sales be x .03x = 180 divide both sides by .03 x = 180/.03 = 6000
May 25, 2015

algebra
what percent of 8x is 5x? ---> 5x/(8x) * 100% , the x's cancel = (5/8)(100)% = 62.5% 65% of 80x = .65(80)x = 52x Don't make things more difficult than they are
May 25, 2015

Trigonometry
(cos(2pi)/7)+ i sin((2pi)/7))^5 = 1^5(cos (10π/7) + i sin(10π/7) = (cos (-4π/7) + i sin(-4π/7) , after subtracting 2π from the angle = (cos (4π/7) - i sin(4π/7) )
May 25, 2015

algbra 1
s + g = 58 4s + 2g = 150 or 2s + g = 75 subtract them: s = 17 then g = 41 there are 17 sheep and 41 geese
May 25, 2015

math
i = .012/4 , (compounded quarterly) = .003 n = 4 amount = 4000(1.003)^4 = 4048.22 interest earned = $48.22
May 25, 2015

Algebra
(12y/13)(11/24) = 11y/26
May 25, 2015

math
amount = 19400(1.12)^12 = ....
May 25, 2015

math
check the previous post
May 25, 2015

math
P(1.005)^3 = 4000 P = 4000/(1.005)^3 = 3940.60
May 25, 2015

Algebra
LCD is 7m , so 3/7 - 4/m = (3m - 28)/(7m)
May 25, 2015

Math
Here is a little trick that works with 9 and 3 add up the digits of your number. If that sum is divisible by 9, then so is the original number. The same rule applies to 3 e.g. is 12546 divisible by 3 ? add them up to get 18 since 18 divides evenly by 3, so does 12546 notice ...
May 25, 2015

maths
recall: cos(A-B) = cosAcosB + sinAsinB so .... 2cos(x-30) = 1 2(cosxcos30 + sinxsin30) = 1 cosx(√3/2) + sinx (1/2) = 1/2 times 3 √3cosx + sinx = 1 √3cosx = 1 - sinx square both sides 3cos^2 x = 1 - 2sinx + sin^2 x 3(1 - sin^2 x) = 1 - 2sinx + sin^2 x ... 4sin...
May 25, 2015

math
To get a sum of 5, we could have had 1 4 2 3 3 2 4 1 , or 4 cases prob(sum of 5 ) = 4/36 = 1/9
May 25, 2015

Algebra 1
I will assume your second equation is y = 2x + 1 sub that into the first: 2x + 1 = x^2 + 5x - 9 x^2 + 3x - 10 = 0 (x+5)(x-2) = 0 x = -5 or x = 2 if x = -5, y = 2(-5) + 1 = -9 if x = 2 , y = 5 so they intersect at (-5,-9) and (2,5)
May 25, 2015

Algebra
In typing exponents, we use the ^ to show exponentiation e.g. 2^3 = 2 cubed number = 30(2)^(t/3) where t is the number of hours number = 30(2)^3) = 30(8) = 240 Or Just do it using basic concepts, like you did in your second solution: now --- 30 after 3 hours --- 60 after 6 ...
May 25, 2015

Math
Since you want the distance horizontally from the starting point, you want y to be 4.3m which is the initial height, thus 0 = -.04x^2 + 8.3x x(.04x - 8.3) = 0 x = 0 , which would be our starting point and x = 8.3/.04 or 207.5 m your answer would be the distance from a height ...
May 25, 2015

Math
the t of the vertex is -b/(2a) = -92/-10 = 9.2 you had that sub in t = 9/2, h = 439.2 you were right, good job
May 25, 2015

Math
we know r^2 = x^2 + y^2 and sinØ = y/r so we have x^2 + y^2 = 1 + y/r x^2 + y^2 = 1 + y/√(x^2+y^2) I don't know to what level you want to simplify this, I will leave it up to you
May 25, 2015

trigonometry
cosØ = 9/10 Ø = appr 25.8°
May 24, 2015

math
I disagree with marks answer The crust can be chosen in C(3,1) ways or 3 ways the cheese can be chosen in C(3,1) or 3 ways if you want only one cheese But the 3 toppings can be chosen in C(7,3) or 35 ways So the number of possible pizzas with 3 toppings and 1 cheese with 3 ...
May 24, 2015

Calculus
let the base be x by x ft and the height be h ft Volume = x^2h 32 = x^2 h h = 32/x^2 SA = x^2 + 4xh = x^2 + 4x(32/x^2) = x^2 + 128/x d(SA)/dx = 2x - 128/x^2 = 0 for a max/min of SA 2x = 128/x^2 2x^3= 128 x^3 = 64 x = 4 then h = 32/16 = 2 so the box should have a base of 4ft by...
May 24, 2015

Math
correct
May 24, 2015

Combinatorics
The lowest sum will be 19 , (all 1's) the largest sum will be 114 (all 6's) each number between them will be possible, so the total number of sums = 114-19 + 1 = 96
May 24, 2015

Math
So let's cut out an x by x square from each corner. so the base we would be left with would be an (20-2x) by (20-2x) cm but 20-2x > 0 -2x > -20 x < 10, since you want x to be a natural number, that would be a 9 by 9 cm square
May 24, 2015

maths
btw, this is true not just for the median AM In fact, the same steps can be used to prove it true if M is any point on BC.
May 23, 2015

maths
In any triangle, the sum of any two sides > the third side so in triangle ABM: AB + BM > AM in triangle ACM AC + MC > AM adding: AB + AC + BM+MC > 2AM AB + AC + BC >2AM
May 23, 2015

correction - Algebra
Anon has it wrong 9^12 ÷9^3 = 9^9 , which is rather large To divide powers with the same base, keep the base and subtract the exponents.
May 22, 2015

math
amount = 1040(1.12)^6 = 2052.78 interest on the initial principal = 2052.78 - 1040 = 1012.78
May 22, 2015

geomotry
If angle C had been 60°, then we would have an equilateral triangle and all sides would have been equal. But, since angle C > 62, the side opposite C must be the greatest. (the largest side is opposite the largest angle)
May 22, 2015

maths
Please use proper English in your posts. This is an arrangement, so number = 15x14x13 = 2730
May 22, 2015

math
It specified "completing the square", so v(x) = 25x^2 - 750x + 10000 , you had v(t) but no t showed up in your function. = 25(x^2 - 30x) + 10000 = 25(x^2 - 30x + 225 - 225) + 10000 = 25( (x-15)^2 - 225) + 10000 = 25(x-15)^2 - 5625+10000 = 25(x-15)^2 + 4375 lowest ...
May 22, 2015

algebra
I believe the physics formula for comparisons of sound intensity in decibels is 10^(112/10) / 10^(118/10) = 10^11.2 / 10^11.8 = 10^-.6 = .2511... or appr 1/4 of the intensity
May 22, 2015

Calculus math
btw, these were not quadratics I find it strange that a person taking Calculus would not know how to solve two linear equations with two unknowns.
May 21, 2015

Calculus math
Step #1 is to replace c with 10000 in both equations to get 9a + 3b = -2025 ---> 3a + b = -675 36a + 6b = -3600 --> 6a + b = -600 subtract the two equations: 3a = 75 a = 25 plug that into 3a + b = -675 75 + b = -675 b = -750 check: 9(25) + 3(-750) + 10000 = 7975 check! ...
May 21, 2015

Algebra
since (2,1) lies on it 2A + B = 7 or B = 7 - 2a slope of 2x-7=3 is 2/7 slope of Ax + By = 7 is -A/B so -A/B = 2/7 2B = -7A 2(7-2A) = -7A 14 - 4A = -7A 3A = -14 A = -14/3 B = 7-2(-14/3) = 49/3 B - A = 49/3 - (-14/3) = 21
May 21, 2015

Calculus
a) is the correct choice
May 21, 2015

trigonometry
I have a triangle with sides 1000 and 1200 with an angle of 130° between them. Clearly a cosine law problem d^2 = 1000^2 + 1200^2 - 2(1000)(1200) cos 130° = ... d = √... = let me know what you get.
May 21, 2015

math
Did you mean the effective annual interest rate ? if so, then (1+i) = (1.02)^4 1+i = 1.0824.. i = .0824 or appr 8.24% per annum
May 21, 2015

Math
A quick sketch shows that your base is 25 units and the height is 7 units area = (1/2)(25)(7) = 87.5 units^2 or 87.5 m^2
May 21, 2015

Math
Damon did this yesterday in the first of the "Related Questions" below.
May 21, 2015

Maths
let's define everything in terms of the number of 10 cent coins, and then just translate the English into Math. let the number of 10 cent coins be x "The number of 20-cent pieces is twice the number of 10-cent pieces" --> number of 20 cent pieces = 2x "...
May 21, 2015

school
time to fill with smaller pipe --- x minutes rate of smaller pipe = 1/x units/min time to fill with larger pipe --- x-10 minutes rate of larger pipe = 1/(x-10) units/min combined rate = 1/x + 1/(x-10) = (x-10 + x)/(x(x-10)) = (2x-10)/(x^2 - 10x) 1/[ (2x-10)/(x^2 - 10x)] = 12 (...
May 21, 2015

Maths
I was only on my second cup of coffee when I did this .... equation should have been x/4 + (25-x)/12 = 3.75 multiply by 12 3x + (25-x) = 45 3x + 25 - x = 45 2x = 20 x = 10 So she walked 10 km by linear equations: let the distance walked be x let the distance biked by y x + y...
May 21, 2015

Maths
distance walked --- x km distance biked ----- 25-x km 4x + 12(25-x) = 3.75 solve for x
May 21, 2015

Math Please Help
Recall that cosØ = x/r but we are given that x = cosØ then y = cos^2 Ø + 8cosØ y = x^2 + 8x
May 20, 2015

Math
Right now, rise/run = 9/156 so tanØ = 9/156 Ø = 3.302° So she wants the angle to be 6.604° Then, assuming the rise will remain the same, tan 6.604° = 9/length length = 9/tan6.604 = 77.7 inches or 78 inches
May 20, 2015

Trig
So we know Ø is in quad III , where both sine and cosine are negative given : cosØ = -12/13 and recognizing the 5,12,13 right-angled triangle we know that sinØ = -5/13 sin 2Ø = 2sinØcosØ = 2(-5/13)(-12/13) = 120/169 cos 2Ø = cos...
May 20, 2015

math
what is (17/4)^3 ??
May 20, 2015

Trig
sinØ = √(1 - (-5/13)^2) = .923 which is none of the choices or sketch a triangle in the 2nd quad, x = -5 r = 13 x^2 + y^2 = r^2 25 + y^2 = 169 y^2 = 144 y = ± 12, but in quad II , y +12 so sinØ = 12/13 or appr .923 (same as above) your choices: 1 and...
May 20, 2015

Algebra 2
looks like each side is 4/5 of its previous , so 20(4/5)^n = 8 (.8)^(n-1) = .4 using logs (n-1) log .8 = log .4 n - 1 = 4.1 n = 5.1 so the 5th would be less than 8 and the 6th would be greater than 8 e.g. 1st --- 20 2nd -- 16 3rd -- 12.8 4th -- 10.24 5th -- 8.192 6th -- 6.5536...
May 20, 2015

ALG 2
you are looking at a hyperbola with its major axis on the x-axis. a^2 = 16 , a = ± 4 b^2 = 25 , b = ± 5 so the vertices are (4,0) and (-4,0) foci: c^2 = 16+25 = 41 c = ± √41 so foci are (√41,0) and (-√41, 0) The asymptotes are y = (5/4)x ...
May 20, 2015

Math
1. clearly A , since 4^8 < 4^12 2. clearly C, since 3^6 > 3^5
May 20, 2015

math
kids tickets ---- x adult tix's ----- 2x solve for x: 20x + 35(2x) = 1890
May 20, 2015

algebra
for #2, Steve meant to say: (x-6)(x+3)/(x+3) = x-6 , x ≠ -3
May 20, 2015

Algebra 2
ok, that makes it easy √2/2 + √2 = √2( 1/2 + 1) = √2(3/2) = 3√2/2
May 20, 2015

Algebra 2
Don't know what you want done with "solve" We solve equations, but you don't have one. Did you mean "evaluate" ? Also , did you mean it the way you typed it, or did you mean √2/(2+√2) ? Back before we had calculators, it was often useful...
May 20, 2015

College Algebra
mmmhhh, didn't you post this same question this morning. I told you what the problem was, and you did nothing about it http://www.jiskha.com/display.cgi?id=1432046868
May 19, 2015

algebra
or slope = (y-4)/5 = 5 (y-4)/5 = 5 y-4 = 25 y = 29
May 19, 2015

Algebra
1. no, I see a constant 2. yes, which you had but your "reasoning" statement makes no sense did you mean to say, "because (0,0) satisfies the equation?
May 19, 2015

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