Monday

January 26, 2015

January 26, 2015

Total # Posts: 28,739

**math algebra**

Let the length along the front be x let the width be y let the height be z x^2+ z^2 = 25^2 = 625 , #1 y^2 + z^2 = 20^2 = 400 , #2 subtract them x^2 - y^2 = 225 , #3 also x^2 + y^2 + z^2 = 28^2 = 784 , #4 add it to #3 2x^2 + z^2 = 1009, but x^2 + z^2 = 625 from #1 so 2x^2 + z^2...
*December 18, 2014*

**math algebra**

recall that if the line is written in the form y = mx + b, then m is the slope so ... 8y = -16 or, how about 8y = 0x - 16 y = (0/8)x - 2 y = 0x - 2 so the slope must be 0 in general if the linear equation can be written in the form y = k, where k is just a constant, you have a...
*December 18, 2014*

**Math**

Zyere is not correct 72/60 = x/40 60x = 40(72) 60x = 2880 x = 48 The ratio of height : shadow must be the same note: 72 : 60 = 6 : 5 , and 48 : 40 = 6 : 5
*December 18, 2014*

**Math**

use a simple ratio and solve for x 72/60 = x/40
*December 18, 2014*

**math algebra**

Use the last two points to find the equation slope = (697-522)/(100-75) = 175/25 = 7 so we have y = 7x + b sub in (75,522) 522 = 7(75) + b b = -3 so we have y = 7x - 3 From your knowledge of y = mx + b, what do you think?
*December 18, 2014*

**math**

Let the capacity of the tank be x L (1/4)x + 90 = (3/4)x times 4 x + 360 = 3x 2x = 360 x = 180
*December 18, 2014*

***repost* - Grade 11 math**

sketch a right-angled triangle. On the horizontal base mark W for Wes. let the fireworks be at P and let Q be the point below P, so that angle Q = 90° let the angle at W be 28° let A for Abby be a point between W and Q so that angle PAQ = 40° , and AW = 20 Look at ...
*December 17, 2014*

**Algebra 1**

http://www.wolframalpha.com/input/?i=plot+y+%3D+%7Cx%7C+%2C+y+%3D+%7Cx+%2B2%7C
*December 17, 2014*

**math**

ar^2 = 25 ar^7 = 25/32 divide the 2nd by the 1st: r^5 = 25/32 ÷ 25 = 25/800 = 1/32 r = 1/2 in ar^2 = 25 (1/4)a = 25 a = 100 where does t come into the picture ?
*December 17, 2014*

**Math (Repost)**

1. u^-3 = 1/125 1/u^3 = 1/125 u^3 = 125 u = 5 2. y-1 = 4y - 2/3 each term times 3 3y - 3 = 12y - 2 -9y = 1 y = -1/9 3. your are right 4. number of miles last week --- x x+40 = 4x + 10 -3x = -30 x = 10 She ran 10 miles last week 5. change it into the form y = mx + b (takes 2 ...
*December 17, 2014*

**Algebra 2**

= 200(1 + .08/12)^12 = 200(1 + .0066666..)^12 = 200(1.006666...)^12 = appr 216.60
*December 17, 2014*

**Algebra 1**

slope of given line = 8/3 so slope of your new line = -3/8 through (-2,3) y = 3 = (-3/8)(x+2) since the original was written in that form, I assume the new one is to be in that same format.
*December 17, 2014*

**Math**

(m + s)/2 = 74 m+s = 148 (m + e )/2 = 83 m+ e = 166 subtract them: e - s = 18
*December 17, 2014*

**Math**

Did you notice that if you multiply the 2nd equation by 4, you get the second? So , you basically only have one equation, thus an infinite number of solutions.
*December 17, 2014*

**Algebra 2**

you know that it must be (x+y)^9 to get a ?x^7y^2 so the term is C(9,7) x^7 y^2 = 36x^7y^2 Observe that the 10th row of Pascal's triangle is 1 9 36 84 126 126 84 36 9 1
*December 17, 2014*

**Algebra**

subtract your equations: 1 Sandwich = 4.75 in the 1st: 4.75 + Salad = 8.7 salad = 3.95
*December 17, 2014*

**MATH PLEASE HELP**

1 e^.012t = 2 take ln of both sides ln e^.01t = ln2 .012t ln e = ln 2 , but ln e = 1 .12t = ln 2 t = ln2/.012 = 57.76 years or 58 years to the nearest year.
*December 17, 2014*

**Math Help**

5^x =125 <----> log5 125 = x I had my students memorize this pattern, 2^3 = 8 <---> log28 = 3
*December 17, 2014*

**Algebra**

total area = 12000 ft^2 still to be mowed = (1/2)(12000) = 8000 ft^2 let the width mowed by Lisa be x ft wide area still to be done = (100-2x)(120-2x) = 12000-200x - 240x + 4x^2 4x^2 - 440x + 12000 = 8000 x^2 - 110x + 1000 = 0 (x-100)(x -10) = 0 x = 100 or x = 10 , but clearly...
*December 17, 2014*

**Calculus**

Steve , you are right, I read the question rather superficially. (notice it was my last post last night, must have been a bit tired)
*December 16, 2014*

**Calculus**

f(x) = e^(4x^2) f(-1/4) = e^(1/4) f(1/4) = e^(1/4) avg value = (e^(1/4) - e^(1/4) )/(1/2) = 0
*December 16, 2014*

**math help!!**

This one is easier than the previous question you posted about GS's Give this one a try, you can do it.
*December 16, 2014*

**math please hellp**

Done, look back
*December 16, 2014*

**algebra 1**

when it hits the water, h = 0 0 = -16t^2 + 20t + 24 4t^2 - 5t - 6 = 0 (t-2)(4t + 3) = 0 t = 2 or t = -3/4, the last answer is inadmissible It will take 2 seconds I have no idea what the last part of your post is. Is that supposed to be a solution ? If so, it makes no sense at ...
*December 16, 2014*

**math help**

a + ar = 12 a(1+r) = 12 , #1 a + ar + ar^2 = 62 a(1 + r + r^2) = 62 , #2 divide #2 by #1 (1+r+ r^2)/(1+r) = 62/12 = 31/6 6r^2 + 6r + 6 = 31 + 31r 6r^2 - 25r - 25 = 0 (r-5)(6r + 5) = 0 r = 5 or r = -5/6 if r = 5 , in #1 6a = 12 a = 2 the first 4 terms are 2 , 10, 50, 250 if r...
*December 16, 2014*

**math**

Draw a right-angled triangle DAC, AC as a base line Let CD be the height of the building. Let B be a point between A and C, so that AB = 230 angle A = 28° angle DBC = 43° Look at triangle ABD, you know angle A = 28, angle ABD = 180-43 = 137 angle ADB = 15° you can ...
*December 16, 2014*

**Math**

Just did this when you posted it as "John"
*December 16, 2014*

**calculus**

Just like taking slope C(101) = 101^2 - 10000 = 201 C(100) = 100^2 - 10000 = 0 average rate of change = (201-0)/(101-100) = 201 instantaneous rate of change = 2x at x = 100 rate = 200
*December 16, 2014*

**Algebra 1**

y+7 = -.54(x-4)
*December 16, 2014*

**math**

double the first: 2x + 4y = 16 subtract from the 2nd x = 4 back into the 1st: 4 + 2y = 8 2y = 4 y = 2 x = 4, y = 2
*December 16, 2014*

**algebra**

prob = (10/24(10/24) = 25/144
*December 16, 2014*

**Math**

1st + last = 100 2nd + 2nd last = 100 ... ... looks like I can form 50 such pairs sum = 50(100) = 5000 use the same concept for the second question.
*December 16, 2014*

**Literature - the Watch**

I am sure that you were not assigned this yesterday. In my days we used to call this "planning ahead". Giving you a summary would be contributing to plagiarism . Here is a page that lets you read the short story on line: http://www.readbookonline.net/readOnLine/22270/
*December 16, 2014*

**MATH**

When I divide 56 by 3 , I get 18 packages with 2 brownies left over. So none of your choices fit.
*December 16, 2014*

**math**

assuming a and b are constants, we have (1/a^n) x^n + (1/b^n) y^n = 2 (n/a^n) x^(n-1) + (n/b^n) y^(n-1) dy/dx = 0 so for (a,b) (n/a^n)(a^(n-1) + (n/b^n)(b^(n-1) dy/dx = 0 (n/a) + (n/b) dy/dx = 0 dy/dx = -(n/a) (b/n) = -b/a equation of tangent at (a,b) y - b = (-b/a)(x-a) toy ...
*December 16, 2014*

**one math question.**

yes
*December 16, 2014*

**contains typo - ^Maths^**

You have a typo. the right side of your equation should say 72^y log3(x-7) = 2y --> 3^(2y) = x-7 log2(x-6) = 3y --> 2^(3y) = x-6 then LS = x^2 - 13x + 42 = (x-6)(x-7) = ( 2^(3y) ) ( 3^(2y) ) = (8^y)(9^y) = 72^y = RS
*December 16, 2014*

**math algebra**

Obviously the diagonal of 10 must be greater than either the length, width or height, so the height cannot be greater than 10 and you are incorrect Look at the diagonal of the base, call it d d^2 = 8^2 + 2^2 = 68 d = √68 now the diagonal we want is the hypotenuse of the ...
*December 15, 2014*

**algebra**

so his effective speed downriver is 4+3 or 7 mph and he goes for 5 hrs distance = rate x time = ....
*December 15, 2014*

**Math**

A GS, with a = -4 r = -1/4 sum(∞) = a/(1-r) = -4/(1 -(-1/4) ) = -4/(5/4) = -16/5 or -3.2
*December 15, 2014*

**MATH**

= .5^0 + .5^1 + .5^2 + .5^3 + .5^4 = 1 + .5 + .5^2 + .5^3 + .5^4 or = 1 + 1/2 + (1/2)^2 + (1/2)^3 + (1/2)^4 we could just add them up, but I guess this question deals with the sum of a GS a = 1 r = .5 n = 5 sum(5) = 1(.5^5 - 1)/(.5 - 1) = (.03125 - 1)/(-.5) = 1.9375 or 31/16
*December 15, 2014*

**Math**

= 2/2 + 3/2 + 4/2 + ... 8/2 = ∑ (1+n)/2 for n = 1 to 7 This answer is not unique, there are many ways to express it
*December 15, 2014*

**Math**

a+(a+1)+(a+2)+.....+(a+n-1) looks like an arithmetic series with first term a common difference = a+1 - a = 1 for n terms so sum = (n/2) (2a + (n-1)(1)) = (n/2)(2a + n-1) so (n/2)(2a + n - 1) = 100 2an + n^2 - n = 200 2an = 200 - n^2 + n a = (200 - n^2 + n)/(2n) n .. a 2 - 49....
*December 15, 2014*

**Algebra**

Tell me what your answer is and I will critique it.
*December 15, 2014*

**Algebra**

The first element of the vertex in this case would be the time it took to reach the highest point, and the 2nd number would be that maximum height.
*December 15, 2014*

**Algebra**

the x-intercept would be the time taken to hit the ground
*December 15, 2014*

**Math**

Memorize the relationship: π radians = 180° from that you can solve for each unit : 1 radian = (180/π) ° <-------> 1 ° = (π/80) radians so which ever is given, proceed from there (13π/12) rad = (180/π)(13π/12) ° = 195° (...
*December 15, 2014*

**math**

one hectare is 10,000 m^2 , (100 m by 100m) so half of that is 5,000 m^2 so let each side be x then x^2 = 5000 for the diagonal d, d^2 = x^2 + x^2 = 2x^2 = 10000 d = 100 m
*December 15, 2014*

**7th grade math**

#1, at 10^2 - 1 = 100-1 = 99 #14, leave your answer as an inequality, since that is what you started with, thus c < -12.8 the rest are correct
*December 15, 2014*

**Calculus (math)**

if v(t) = t^3 - 5t^2 s(t) = (1/4)t^4 - (5/3)t^3 + c s(6) = (1/4)6^4 - (5/3)6^3 = -36 + c s(-1) = (1/4)(-1)^4 - (5/3)(-1)^3 = 23/12 + c distance traveled = 23/12+c - (-36+c) = 4550/12
*December 14, 2014*

**Steve saw the light - easy geometry**

The fact that the sides were not listed sequentially made me interpret the question in an entirely different way, so go with Steve' solution. Anyway, my interpretation led to a nice problem, lol
*December 14, 2014*

**For #1 easy geometry**

From my previous reply to this problem http://www.jiskha.com/display.cgi?id=1418471605 (it was called #3 ) I had given you "I drew a figure ABCD , with AD || BC AD = 10 AB = 20 BC = 30, and CD = 10 From A draw a line AP, so that AP is || to DC and P is on BC So AP=10 and ...
*December 14, 2014*

**easy geometry**

I'll take care of #2 first. the common formula is A = P(1 + r)^n , where r is the rate per interest period expressed as a decimal (e.g. 3% --> .03 ) and n is the number of interest periods I don't know where your a comes from. so 1690 = 1000(1 + r)^2 (1+r)^2 = 1.69 ...
*December 14, 2014*

**math**

i = .09/4 = .0225 n = 4(8) = 32 payment = P P( 1.0225^32 - 1)/.0225 = 8000 solve for P
*December 14, 2014*

**precalculus**

for domain, all you have to worry about is the denominator and make it does not become zero. x^2 + x + 9 = 0 has no real solution, (the b^2-4ac is negative) so the domain is the set of all real numbers for x b) Thus, since there are no breaks in the function, it is continuous ...
*December 14, 2014*

**Calculus 1**

I drew a circle and placed the woman at point A. She wants to go to point B, clearly where AB is a diameter. Label the centre as O. Pick a point P on the circle so that she will row from A to P, and then walk along the circumference from P to B I labeled AP = x and arc PB as a...
*December 13, 2014*

**Algebra**

from the 2nd: 4x = 20 - 3y x = 5 - (3/4)y plug into the 1st: 5x - 7y = -18 5(5 - (3/4)y) - 7y = -18 25 - 15y/4 - 7y = -18 -43y/4 = -43 y = -43(-4/43) = 4 x = 5 - (3/4)4 = 2 (substitution would have been my last choice in the methods to solve this, I would have used elimination)
*December 13, 2014*

**AP CaLC. AB**

Here is a solution to your problem, with sides 6 and 12 I suggest you print out the solution and change the constants to yours. I suggest you are careful that your base of x, and height of y are consistent with the x and y in the solution https://www.math.ucdavis.edu/~kouba/...
*December 13, 2014*

**AP CaLC. AB**

Where do x and y enter the picture ??
*December 13, 2014*

**Algebra**

strange question, clearly 9x^2 - 12x + 4 = 49 (3x - 2)^2 = 49 3x - 2 = ± 7 3x = 2 ± 7 3x = 9 or 3x = -5 x = 3 or x = -5/3 so I guess they just wanted the 2nd line .
*December 13, 2014*

**math**

This implies that either 4, 5 or all 6 will pass prob = C(6,4) (.6)^4 (.4)^2 + C(6,5) (.6)^5 (.4) + C(6,6) .6^6 I get .54432
*December 13, 2014*

**math**

arggh, go with Damon's factoring of the last part Whatever made me think that 2x5 = 16 ?????? It's clearly 2 x 8
*December 13, 2014*

**math**

your expression definitely needs brackets to make sense (n^2-4)/(n^2-2n) * n/(n^2+10n+16) = (n+2)(n-2)/(n(n-2) ) * n( (n+2)(n+5) = 1/(n+5) , n ≠ -2 , 0, 2 , -5
*December 13, 2014*

**math**

another way: find the intersection line of the two planes add the two equations, 4x -3y = 10 y = (4x-10)/3 pick any "nice" value of x let x = 1, y = -2 in the 2nd equation: 3 + 2 + z = 4 , z = --1 --> point (1,-2,-1) let x = 10, y = 10, in the 2nd 30 - 10 + z = 4...
*December 13, 2014*

**math**

year 1 = 19000 year 2 = 19000(1.04) year 3 = 19000(1.04)^2 .. year 10 = 19000(1.04)^9 I somehow expect that "they" want you to add them up. It would be a GS, with a = 19000, r = 1.04 , n = 10 BUT, from an actuarial point of few monies cannot just be added up unless ...
*December 13, 2014*

**Algebra 1**

y = |x-2| why not just take some simple values of x and see what points you get, then plot them 0,2 1,1 2,0 3,1 4,2 ... -1,3 -2,4 -3,5 .. can you see the pattern ?
*December 13, 2014*

**Algebra**

t2 = a + d = 2 t9 = a + 8d = 30 subtract them 7x = 28 d = 4 in a+d=2 a + 4 = 2 a = -2 t15 = a + 14d = -2 + 14(4) = 54
*December 13, 2014*

**#4 easy geometry**

x-17 + 24-x + 3x-40 + x+1 = 42 4x = 74 x = 18.5 , so the sides are 1.5 , 5.5, 15.5 , and 19.5 how about doubling each side, creating a "similar" quadrilateral, (angles won't change) 3 , 11 , 31 , and 39 , mmmh, what do you know about sides of a parallelogram ? #5...
*December 13, 2014*

**easy geometry**

1. In a rhombus, the diagonals bisect each other at right angles. So you have 4 congruent right-angled triangles with sides 5 and 12, and the hypotenuse is the side of the rhombus. s^2 = 5^2 + 12^2 (You should recognize that Pythagorean triple, if not, remember it) Find the ...
*December 13, 2014*

**Probability**

To get a plain cookie: we could have (1,P) or (2,P) prob (1, P)= (1/2)((30/40) = 3/8 prob (2,P) = (1/2)(20/40) = 1/4 prob(plain cookie) = 3/8 + 1/4 = 5/8 (checking: prob(1,C) = (1/2)(10/40) = 1/8 prob(2,C) = (1/2)(20/40) = 1/4 note 3/8+1/4+1/8+1/= 1 , check! ) could have ...
*December 12, 2014*

**Math**

PV = 5 e^-.03 + 5 e^-.06 + ... + 5 e^-(10(.03)) I see a GS with a = 5 e^-.03 r = e^-.03 n = 10 PV = a(r^n - 1)/(r-1) 5 e^-.03( e^-.3 - 1)/(e^-.03 - 1) = appr 43.85 million dollars
*December 12, 2014*

**College math 100**

white ribbons --- x blues ---------- x-2 reds ----------- x+3 form the equation and continue
*December 12, 2014*

**Math**

5 Σ 4(3/4)^k k=0 = 4(3/4)^0 + 4(3/4)^1 + 4(3/4)^2 + 4(3/4)^3 + 4(3/4)^4 + 4(3/4)^5 = 4[ 1 + (3/4) + (3/4)^2 + (3/4)^3 + (3/4)^4 + (3/4)^5 ] The part in the brackets is a GS with a = 1 , r = 3/4 and n = 6 = 4 ( 1( (3/4)^6 - 1)/(3/4 - 1) =4 (729/4096 - 1)/(-1/4) = -16(-3367...
*December 12, 2014*

**Math**

no 1/2 * 6 + 9^2 - (18/6) = 3 + 81 - 3 = 81
*December 11, 2014*

**math**

In a true scale , the units of the terms are the same, and thus the units would cancel 8 cm : 1000 m = 8 cm : 100000 cm = 1 : 12500 behold the beauty and simplicity of the metric system Had this been 1000 yards and 8 inches, it would be a lot messier.
*December 11, 2014*

**algebra**

Where did you get a kitten to weigh 1.5 kg ?? 4x+4x= 10 8x=10 x = 1.25 kg so each kitten weighs 1.25 kg and the cat weighs 4x or 4(1.25) = 5 kg check: does the cat weigh 4 times as much as a kitten what is 4(1.25) ? = 5, check! what is the total weight of the 4 kitten and the ...
*December 11, 2014*

**algebra**

kitten --- x kg cat ------4x kg 4(x) + 4x = 10 take over
*December 11, 2014*

**math**

It asked for the ratio which cannot just be one number. Ratios express the relationship between 2 or more items so 180:20 = 9 : 1
*December 11, 2014*

**math**

3000 ??? Are you just guessing wildly ??? what is 180 : 20 ?
*December 11, 2014*

**Geometry**

make a sketch. You will be able to construct similar triangles. Remember that for two similar triangles, corresponding sides are in the same ratio
*December 11, 2014*

**Math**

see http://www.jiskha.com/display.cgi?id=1418350095
*December 11, 2014*

**Calculus**

take the derivative using the product rule f ' (x) = x(3)(1-2x)^2 (-2) + (1-2x)^3 sub in the x of the point(1,-1) f ' (1) = 1(3)(1)(-2) + (-1) = -7 which will be the slope of your tangent Now you have the slope of -7 and a point (1,-1) Use your favourite method of ...
*December 11, 2014*

**Math**

(-3) - (-8) = -3+8 = +5 to add to negatives will always yield a negative. could you have two debts, add them up and suddenly have a profit ???
*December 11, 2014*

**Math**

Let two of the sides be x ft each let the other two sides by y ft each xy = 310 y = 310/x cost = 3(2x) + 3y + 14y = 6x + 17y = 6x + 17(310/x) = 6x + 5270/x d(cost)/dx = 6 - 5270/x^2 =0 for a min of cost 6 = 5270/x^2 6x^2 = 5270 x^2 = 878.333.. x = √878.333 = appr 29.64 ...
*December 11, 2014*

**Math**

No, you cannot just add two sums of money if they are not in the same time slot, unless you totally ignore the compound interest. amount = 1000( 1.07^10 - 1)/.07 * (1.05)^8 + 1000( 1.05^8 - 1)/.05 = $29,962.30 You must be able to analyse my equation and it should make sense to...
*December 11, 2014*

**4th**

could be 1,8 2,7 3,6 4,5 5,4 6,3 7,2 8,1 prob(1,8) = (1/10)(1/10) = 1/100 each of the remaining cases has the same prob so prob = 8(1/100) = 8/100 = 2/25
*December 11, 2014*

**Math-Calculus**

For hours ??? Slope of the given line is 1/2 so the slope of the line through (-2,1) and perpendicular to it must be -2 equation of that perp. y = -2x + b, with (-2,1) lying on it, thus ... 1 = -2(-2) + b -3 = b y = -2x - 3 solve the two equations to get the required point -2x...
*December 11, 2014*

**Precalculus**

Profit = Revenue - Cost subtract the two functions and simplify you will have a quadratic with a negative x^2 term, so it opens down, thus there will be a max find the vertex of that parabola
*December 11, 2014*

**Maths**

tan18° = 55/x take over
*December 11, 2014*

**Precalculus**

the y-intercept is 4, so the height is 4 the x-intercept is 4/3, so the base is 4/3 area = (1/2)base x height = (1/2)(4)(4/3) = 8/3 square units
*December 11, 2014*

**Precalculus**

let side parallel to river be y let the other two sides be x each 2x + y = 1000 , ----> y = 1000-2x area = xy = x(1000-2x) = 1000x - 2x^2 if you know Calculus..... d(area)/dx = 1000 - 4x = 0 for a max of area 4x =1000 x = 250 y = 1000-2(250) = 500 so max area = xy = 250(500...
*December 11, 2014*

**Algebra !**

a + (b/100)a = 12 a( 1 + b/100) = 12 a - (b/100)a = 8 a( 1 - b/100) = 8 divide the top equation by the last one (1+b/100)/( 1 - b/100) = 12/8 = 3/2 2 + 2b/100 = 3 - 3b/100 times 100 200 + 2b = 300 - 3b 5b = 100 b = 20 back in a(1-b/100) = 8 a(1 - 20/100) = 8 a(1 - 1/5) = 8 a(4...
*December 11, 2014*

**Math**

If I were you , I would go with Ms Sue's answer of 5/16 since often lawyers don't tell the truth. btw, Ms Sue's last line is 16/16 - 11/16 = 5/16
*December 11, 2014*

**algebra**

short side ---- x each of other sides (must be isosceles) ---- 3x x + 3x + 3x = 112 I will let you finish it
*December 11, 2014*

**algebra**

v = -6000t + 70000
*December 11, 2014*

**Algebra 1 Ohio 8th grade standards**

since in the form y = mx + b, the slope of the line is m so for your line y = (1/2)x + 1, the slope is 1/2 But for perpendicuar lines, their slopes are opposite reciprocals of each other, so the slope of your new line must be -2/1 or -2 and the new equation must be y = -2x + b...
*December 11, 2014*

**Math**

"How much must they deposit NOW" isn't that present ? PV = 5500( 1 - 1.02^-20)/.02 = $89932.88
*December 11, 2014*

**math**

let the number of boys be 7x and the number of girls be 4x 7x - 4x = 21 3x = 21 x = 7 so there are 49 boys and 28 girls for a total of 77
*December 11, 2014*

**algebra**

so you have 2 ordered pairs of the type (brownies, cost) , (2000,1500) , (4000, 2000) slope = (2000-1500)/(4000-2000) = 500/2000 = 1/4 using the 2nd point, ... cost - 2000 = (1/4)(brownies - 4000) 4 C - 8000 = B - 4000 B - 4C = -4000 (checking if 1st point satisfies ... LS = ...
*December 11, 2014*

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