Saturday

August 1, 2015

August 1, 2015

Total # Posts: 30,513

**Math**

The slopes of perpendicular lines must be negative reciprocals of each other, so... what do you think ?
*May 30, 2015*

**Math**

No idea what you mean by "x's cannot repeat" The definition of a function is found in every textbook that deals with that topic
*May 30, 2015*

**Hanahan**

I would subtract them to get 10y = 80 y = 8 back into the second: 4x + 24 = -40 4x = -64 x = -16
*May 30, 2015*

**linear systems**

To have an infinite number of solutions, both equations are really the same equation if we multiply the first by 3, 2x + 3y = 48 comparing with the 2nd: kx + 3y = 48 there would be an infinite number of solutions if k = 2 One solution, k ≠ 2 to have no solution, the two ...
*May 30, 2015*

**Math**

I assume you mean $10.22 So the rate is 10.22/145.99 = .07 or 7% y = .07x
*May 30, 2015*

**Math word problem**

number of $1 coins --- x number of quarters ---- y x + y = 21 100x + 25y = 1275 --> 4x + y = 51 subtract them: 3x = 30 x = 10 then y = 11 He has 10 dollar coins and 11 quarters check value: 100(10) + 25(11) = 1275 cents = $12.75
*May 30, 2015*

**maths**

I don't understand your notation
*May 30, 2015*

**Math please help!!**

did you make a sketch? let the shorter diagonal be x by the cosine law: x^2 = 78^2 + 90^2 - 2(78)(90)cos35° ... x = 51.8 to the nearest tenth let the longer diagonal by y y^2 = 78^2 + 60^2 - 2(78)(90)cos145° etc
*May 30, 2015*

**maths**

tan70 = tan(90-20) = cot 20 but cot 20° = y then 1 + tan^2 70 = 1 + cot^2 20° = 1 + y^2
*May 30, 2015*

**math**

so he has 63/7000 m^3 and 1 m^3 is 100^3 cm^3 so he has 63/7000 * 1000000 cm^3 or 9000 cm^3 available let the length be h area of cross-section = 12(15) - (10)(12) = 60 cm^2 60h = 9000 h = 150 cm long or 1.5 m
*May 30, 2015*

**math**

first of all: (x - 1/x)^3 = x^3 - 3x + 3/x - 1/x^3 so we will need x^3 if x = 1 - √2, then x^3 = (1-√2)^3 = 7-5√2 , I will leave it up to you to expand it So we have : (7 - 5√2) - 3(1 - √2) + 3/(1 - √2) - 1/(7 - 5√2) rationalize the ...
*May 30, 2015*

**math**

1/(1+√2) + 1/(√2 + √3) + 1/(√3 + √4) rationalize each term: 1/(1+√2) = 1/(1+√2) * (1-√2)/(1-√2) = (1-√2)/-1 = √2 - 1 1/(√2 + √3) = 1/(√2 + √3) *(√2 - √3)/(√2 - √3...
*May 30, 2015*

**math**

x = 1 - √2 , then x^2 = 1 - 2√2 + 2 = 3 - 2√2 then (x - 1/x)^2 = x^2 - 2 + 1/x^2 = 3-2√2 - 2 + 1/(3-2√2) = .... rationalizing 1/(3-2√2) 1/(3-2√2) =1/(3-2√2 * (3+2√2)/(3+2√2) = (3+2√2)/1 so back in ... = 3 - 2&#...
*May 30, 2015*

**Algebra/Math**

"above" ---> greater than temp > -15
*May 29, 2015*

**math**

shorter piece --- x longer piece ---- 3x-2 solve for x: x + 3x-2 = 10 take it from here
*May 29, 2015*

**Maths**

Clearly Steve answered this for you in great detail here http://www.jiskha.com/display.cgi?id=1432801604
*May 29, 2015*

**math**

the centre must be the midpoint of A and B and that midpoint is (1/2 , 5) so the equation must be: (x - 1/2)^2 + (y - 5)^2 = r^2 but (5,7) lies on it, so (5-1/2)^2 + (7-5)^2 = r^2 81/4 + 4 = r^2 r^2 = 97/4 (x - 1/2)^2 + (y - 5)^2 = 97/4 btw, the fact that a diameter subtends a...
*May 29, 2015*

**Mathematics**

time = distance/rate blue car's time = 150/25 = 6 hrs red car's time = 150/60 = 2.5 hrs so, since the blue car left at 9:30 am, it will arrive 6 hours later , at 3:30 pm the red car left at noon, so will arrive 2.5 hours later, at 2:30 pm Why would you need to ...
*May 29, 2015*

**college geometry**

"college" geometry? Why not just plot the 3 given points and then count to find what the 4th point has to be?
*May 29, 2015*

**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*