Tuesday

September 16, 2014

September 16, 2014

Total # Posts: 27,117

**Math**

2H + 1F = 8 ===> F = 8-2H 6H + 6F = 30 or H+F=5 using substitution: H + F = 5 H + 8-2H = 5 -H = -3 H = 3 then F = 8-6 = 2 each hamburger costs $3.00 and each fries costs $2.00
*April 29, 2014*

**Math**

width --- x lengyth -- x+11 x(x+11) = 2040 x^2 + 11x - 2040 = 0 (x-4)(x+51) = 0 x = 40 or x = - 51 , negative width makes no sense, so x = 40 the rectangle is 40 cm by 51 cm
*April 29, 2014*

**math**

I have a feeling you have typos here. Is that supposed to be 24x^2 at the top and 32x^2 ... at the bottom ?
*April 29, 2014*

**calculus**

(9x^3+5x-8) ÷ (3x-2) I assume you are studying long algebraic division, I got 3x^2 + 2x + 3 - 2/(3x-2)
*April 29, 2014*

**math**

number of tickets bought ---- x 2x ≤ 30
*April 29, 2014*

**Algebra**

(89+88+78+95+92+x)/6 = 90 solve for x
*April 29, 2014*

**grade 3 math**

There is no such rectangle. I can make the length some ridiculous length and the width very very small. e.g. length = 5000 width = 39/5000= .0078 check: the area is 5000(.0078) = 39 Perimiter is 2(.0078) + 2(5000) = 1000.0156 ft length = 20,000 width = 39/20000 = .00195 ...
*April 29, 2014*

**Trig**

This is exactly the same type of question as your previous one. Just follow my steps using these numbers.
*April 29, 2014*

**Trig**

if t1 = 7 and t2 = 205 then d = 205-7 = 198 sum(100) = (100/2)(2(7) + 99(198)) = 50(19616) = 980800
*April 29, 2014*

**Trig**

Just use your definition of term(2) and plug in the values.
*April 29, 2014*

**Trig**

a9 = 120 ----> a + 8d = 120 a14 = 195 ---> a + 13d = 195 subtract them 5d = 75 d = 15 then a+8(15) = 120 a = 0 so term(6) = a+5d = 0 + 5(15) = 75
*April 29, 2014*

**maths**

5cosx + 3 = 0 cosx = -3/5, and 180° < x < 306° so that x is in quadrant III did you notice the 3-4-5 right-angled triangle ratios? so sinx = -4/5 tanx = 4/3 3tanx + 25sin^2 x = 3(4/3) + 25(16/25) = 20 ( you can use your calculator to check this result Ø = ...
*April 29, 2014*

**math**

let the distance be d miles for Hannah: let her speed be x mph d = 6.5x for Dylan: let his speed be x+30 mph d = 2.6(x+3) 6.5x = 2.6(x+30) 6.5x = 2.6x + 78 3.9x = 78 x = 20 then d = 6.5(2) or 130 miles (I would have that "caps lock" malfunction looked after on your ...
*April 29, 2014*

**math:mensuration plane shapes**

If radius of cone is 4 cm, and its height is 3 cm, then the "slant" length of the cone is 5 cm (3^2 + 4^2 = 5^2) If cut open , this translates into a "pac-man" game looking sector with arc length equal to the circumference of the base of the cone and its ...
*April 29, 2014*

**math**

2^ = .125 2^x = 1/8 2^x = 1/2^3 = 2^-3 then x = -3
*April 29, 2014*

**Calculus**

go with Steve's I forgot to multiply the .02 by the 3 in front
*April 28, 2014*

**Calculus**

write it as P(t) = 20 (1 + 3e^(-.02t)^-1 P ' (t) = -20(1+3e^-.02t)^-2 (-.02 e^(-.02t) ) now use the product rule to get the 2nd derivatives I suggest cleaning up the first deriv. a bit
*April 28, 2014*

**Math**

I just can't see a pattern even Wolfram, which surprised me with a "pattern" function, could not see anything (I tested to see if Wolfram was able to pick up a pattern. I used n + 2^n to get the terms 3,6,11,20,37 and entered pattern { 3,6,11,20,37} look what it ...
*April 28, 2014*

**Math**

from the 1st ---- y = 8-2x so 8 - 2x = -3(x-3) 8-2x = -3x + 9 x = 1 in y = 8-2x, y = 8-2 = 6 looks like D
*April 28, 2014*

**math (1)**

Just drop in the values and stir. e.g. c) x = 2, y=1 h(2,1) = (4+8)/(2-1) = 12 That's all there is to it.
*April 28, 2014*

**Math**

(3√8 + 4√9)^2 = (3√8 + 12)^2 = 72 + 72√8 + 144 = 216 + 72(2√2) = 216 + 144√2 or appr 419.65
*April 28, 2014*

**math**

2x+8=3x+2 2x - 3x = 2 - 8 -x = -6 x = 6
*April 28, 2014*

**math**

5x-2(x+4)=3(2x+1) 5x - 2x - 8 = 6x + 3 5x - 2x - 6x = 3 + 8 -3x = 12 x = -4
*April 28, 2014*

**Physics waves- check answers please**

agree with all of them
*April 28, 2014*

**Integrated Trig**

if compounded annually 1.03^t = 2 t ln1.03 = ln2 t = ln2/ln1.03 = appr 23.45 years
*April 28, 2014*

**Integrated Trig**

5000 e^(.03t) = 10000 e^(.03t) = 2 take ln of both sides , and use rules of logs .03t = ln 2 t = ln 2/.03 = appr 23.1 years
*April 28, 2014*

**math**

solve for x 2x + 2(3x) = 64
*April 28, 2014*

**Math 1314**

width of pond --- x length of pond --- 3x width of whole thing = x+6 , (3 feet on each end) length = 3x + 6 2(x+6) + 2(3x+6) = 100 2x + 12 + 6x + 12 = 100 8x = 76 x = 9.5 ft the pond is 9.5 ft wide and 28.5 ft long
*April 28, 2014*

**Math 120**

d = -16t^2 , if we have to consider direction or d = 16t^2 if all we care about is distance when t = 17 d = 16(17)^2 = 4624 ft some deep well !!
*April 27, 2014*

**Math HELP HELP**

use Venn diagrams, fill in your data starting with the intersection of all three, then the intersection of two at a time, etc.
*April 27, 2014*

**Maths**

check your previous post for this
*April 27, 2014*

**math/ratio**

let the number of apples, oranges, and pears be 3x, 5x, and x respectively. 5x+x - 3x = 12 3x = 12 x = 4 so 12 apples, 20 oranges and 4 pears check: oranges + pears = 24 apples = 12 is 24 more than 12 by 12 ?? YES
*April 27, 2014*

**Calculus**

area = integral ( e^-x) from 0 to infinitiy = [ - e^-x] from 0 to infinity = [-1/e^x] from 0 to infinity now clearly as x ---> ∞ , 1/e^x --> 0 so we have ( 0 - (-1/1) = 1
*April 27, 2014*

**Math**

Do you want the probability of drawing 2 green balls? = (3/5)(2/4) = 3/10
*April 27, 2014*

**Maths**

the 17 would cancel, leaving you with 93/97
*April 27, 2014*

**Math**

The way you typed it: 5x/6 = 15 5x = 90 x = 18
*April 27, 2014*

**Precalculus**

A = {2,3,5,7,11,13} B = {1,2,3,4,6,9,12} c= {4,8,12,16} Just noticed that in your listing of C you don't have the 16 Does that result in your difficulties? A intersect B = {2,3) (A intersect B)' = {1,4,5,6,7,8,9,10,11,12,13,14,15,16} which in "union" with C...
*April 27, 2014*

**Math**

18 ft / 2 seconds = 9 ft/sec = (9/5280) miles / (1/3600) hours = (9/5280)(3600/1) m/h = (135/22) mph = appr 6.1 mph or 18 ft in 2 seconds = 9 ft in 1 second = 540 ft in 1 minute = 32400 ft in 1 hour = 6.1 mph
*April 27, 2014*

**algebra**

tried: ±1 , ±2 and found x = 2 to be a triple root. successive synthetic divisions shows x^5−8x^4+28x^3−56x^2+64x−32=0 (notice how we show exponents) x=2 to be triple root so x^5−8x^4+28x^3−56x^2+64x−32=0 (x-2)^3 (x^2 - 2x + 4...
*April 27, 2014*

**Math - Trigonomety**

What a silly and unrealistic problem, anyway .... I made a sketch the main working triangle has the height of the tree, its opposite angle as 10°, and the other angles as 105° and 65° The side opposite the 105° is also the hypotenuse of a right-angled triangle ...
*April 27, 2014*

**Geometry**

Ms Sue solved the "same" question. Just change the numbers http://www.jiskha.com/display.cgi?id=1398287442
*April 27, 2014*

**MATHS**

x/2 + 2y/3 = -1 ---> 3x + 4y = -6 x - y/3= 3 --------> 3x - y = 9 elimination: subtract them: 5y = -15 y = -3 sub into the 2nd 3x - (-3) = 9 3x = 6 x = 2 x = 2, y = -3 by substitution: from the 2nd: y = 3x-9 into the 1st: 3x + 4(3x-9) = -6 3x + 12x - 36=-6 15x = 30 x = 2...
*April 27, 2014*

**math**

to me this says: x = 4sin^3 t y = 7cos^3 t dx/dt= 12(sin^2 t)(cost) = 12cost(sint)^2 dy/dt= 21(cos^2 t)(-sint) or -21sint(cost)^2 both dx/dt and dy/dt must be zero for dx/dt =0 , dy/dt=0 12cost(sint)^2 = 0 , -21sint(cost)^2 = 0 in other words, wherever the sine or cosines are ...
*April 27, 2014*

**Pre algebra**

1 km/h = (1/60) km/minute (how many minutes are there in 1 hour? ) You don't post an actual speed (typo?). so suppose you have 80 km/h = (80/60) km/min = (4/3) km/min replace my speed with whatever speed you have, then simplify ??/60 to lowest term fractions.
*April 26, 2014*

**Jim and Mia : - Math (6)**

Jim, they do intersect at one point only, thus creating an open region on the left. By squaring you are introducing a part of the graph which was originally undefined. y = √x is defined only for x ≥ 0 Mia: Both Steve and I gave answers to this earlier http://www....
*April 26, 2014*

**math (4)**

graph of your function http://www.wolframalpha.com/input/?i=y%3D++-xe%5E%28-x%5E2%29++from+0+to+1 notice the region will be below the x-axis, so height = 0 - (-xe^(-x^2)) = xe^(-x^2) area = integral (xe^(-x^2)) dx from 0 to 1 = (-1/2) e^(-x^2) from 0 to 1 = (-1/2) e^-1 - (-1/2...
*April 26, 2014*

**math (2)**

Here is what your curve looks like from x = -1 to +1 http://www.wolframalpha.com/input/?i=y%3D+2x%2F%28x%5E2%2B4%29+from+-1+to+1 So where is the shaded region? Are you finding the area between the curve and the x-axis? (That is the usual case for this question, but let me know...
*April 26, 2014*

**Trig**

Or use the old sum of roots and product of roots property sum of roots = 5+i√2 + 5-i√2 = 10 product of roots = (5+i√2)(5-i√2) =25-2i^2 = 25+2 = 27 x^2 - (sum)x + product = 0 x^2 - 10x + 27 = 0
*April 26, 2014*

**Calculus**

draw a sketch of the situation, at a time of t hours after 9:00 am let A1 be the position of Aida let I1 be the position of Ian Join A1 and I1, to get a right-angled triangle let D be the distance between them D^2 = (6t)^2 + (20-8t)^2 = 36t^2 + 400 - 320t + 64t^2 = 100t^2 - ...
*April 26, 2014*

**Deepa**

let the number of 50 cents increases be n NOW: number of riders = 10000 cost per ride = 20 after increase number of riders = 10000- 200n cost per ride = 20+ .5n Revenue = (10000-200)(20 + .5n) expand this and you will have a quadratic representing a parabola that opens ...
*April 26, 2014*

**For fizz - math**

I answered this for you already http://www.jiskha.com/display.cgi?id=1398482333 I counted about 8 problems dealing with series of discounts, plus numerous questions that have been answered dealing with compound interest. I don't see a single reply by you or even a response...
*April 26, 2014*

**math (trade and cash discount)**

let the list price be x .85(.92)x = 239.29 x = 239.29/(.85(.95)) = ....
*April 26, 2014*

**math**

One step calculation price = 1780(.7)(.9)(.95) = 1065.33 Discount = 1780-1065.33 = $714.67 or first discount = .3(1780) = 534 leaving 1246 2nd discount = .1(1246) = 124.60 leaving 1121.4 3rd discount = .05(1121.4 = 56.07 leaving 1065.33 Discount = 1780 - 1065.33 = 714.67 as ...
*April 26, 2014*

**MATH**

tried: ±1, ±2, ±3 success at x = -3 by synthetic division 21x^3+67x^2-36=(x+3)(21x^2+ 4x - 12) = (x+3)(3x-2)(7x+6) so what do you think?
*April 26, 2014*

**good catch- maths**

Good catch Steve, the smallest 3-digit number divisible by 7 is 105 So count one more, 128 of them
*April 26, 2014*

**maths**

smallest 3 digit number divisible by 7 is 112 largest 3 digit number divisible by 7 is 994 look at the arithmetic sequence 112, 119, .... 987 , 994 how many terms are there? a=112, d = 7 term(n ) = a+(n-1)d 994= 112 + (n-1)(7) 882 = 7n - 7 889 = 7n n = 127 2. really!? (I will ...
*April 26, 2014*

**maths**

I will assume you meant, "How many red marbles should be added" let the reds to be added be x so we have 10+x reds total = 40+x (10+x)/(40+x) = (3/5) 50 + 5x = 120 +3x 2x = 70 x = 35 #5 reds should be added check: reds = 45 total = 75 percentage of reds = 45/75 = .6 ...
*April 26, 2014*

**Maths**

a) flipping 2 counters, Cam's outcomes: 11 , 12 , 21, and 22 , two ways to get a 3 ---> prob(3) = 2/4 = 1/2 flipping a die, outcomes 1,2,3,4,5,6 , one way to get a 3 --> prob(3) = 1/6 prob(both get a 3) = (1/2)(1/6) = 1/12 CA DE ---- Cam's loss ---> Dean's...
*April 26, 2014*

**math**

amount left of 1 unit after the series of 3 discounts = (.8)(.9)(.96) = .6912 amount left of 1 after a single discount of 32% = .68 which is the better discount?
*April 25, 2014*

**Math**

Just like 3(2x+5) = 6x + 15 just like 3(7+2) = 21 + 6 so is √5(2+√5) = 2√5 + √25 = 2√5 + 5 you could also check by evaluating it with your calculator.
*April 25, 2014*

**Math**

√5/(2-√5) ?? what about it? If you are rationalizing it, then = √5/(2-√5) * (2+√5)/(2+√5) = (2√5 + 5)/(4-5) = -2√5 - 5
*April 25, 2014*

**Calculus**

" 50 m away from you" -measured along the string, or measured along the ground? There is not enough information , there are 3 rates involved, but you only give one. Are we ignoring the fact that the string cannot form a straight line ? Is the kite always 40 m high?
*April 25, 2014*

**Algebra 1**

sure, if it exists For a "vertical " parabola there will always be a y-intercept For a sideways parabola, there may not be one.
*April 25, 2014*

**math (9)**

picture: http://www.wolframalpha.com/input/?i=plot+y%3D+-x%5E2%2B2x%2B4+%2C+y+%3D-x%2B4 looks like they intersect at (0,4) and((3,1) (the points satisfy both equations) area = ∫( -x^2 + 2x + 4 - (-x+4)) dx from 0 to 3 = ∫( -x^2 + 3x ) dx from 0 to 3 = [ -x^3/3 + 3x...
*April 25, 2014*

**math (2)**

we see no shaded region.
*April 25, 2014*

**Math (6)**

Since x ≥ 0 for y = √x the graph shows that we cannot have a closed region. see ... http://www.wolframalpha.com/input/?i=plot+y%3D+√%28x%29+%2C+y%3D+x-2
*April 25, 2014*

**math**

must exclude no heads and 1 head prob(no heads) = (1/2)^6 = 1/64 prob(1 head) = C(6,1) (1/2)^1 (1/2)^5 = 6/64 prob (more than 1 head) = 1 - 1/64 - 6/64 = 57/64
*April 25, 2014*

**Calculus Please Help4**

You appear to have found their intersection correct as (3,3) and (19,-5) USING VERTICAL SLICES: y^2 = x+6 so y = ± √(x+6) = ± (x+6)^(1/2) so for the part from -6 to 3 height = (x+6)^ - ( -(x+6)^(1/2) = 2(x+6)^(1/2) integral of that is (4/3)(x+6)^(3/2) area ...
*April 25, 2014*

**Calculus Please Help3**

intersection points: y = 5 with 2y = 3√x ---> (100/9 , 5) y = 5 with 2x+2y = 5 ---> (-2.5, 5) 2y = 3√x with 2x + 2y = 5 ---> 1 , 3/2) So I see it as area = ∫(5 - (5-2x)/2) dx from -2.5 to 1 + ∫((5-(3/2)(x^.5) )dx from 1 to 100/9 = 6.125 + 14....
*April 25, 2014*

**Algebra**

Suppose the question had said: when a number is divided by 4 the quotient is 6 with a remainder of 1 we would write: number = 6(4) + 1 = 25 so f(x) = (x^3 + x^2 - 4)(x+3) + 8 = x^4 + 3x^3 + x^3 + 3x^2 - 4x - 12 + 8 = x^4 + 4x^3 + 3x^2 - 4x - 4
*April 24, 2014*

**Calculus Help Please Urgent!!!**

height = -1.6t^2 + 32t + 3 b) need the vertex of that parabola t of vertex = -b/(2a) = -32/-32 = 1 second height = -16(1) + 32(1) + 3 = 19 m c) hits the moon ground when h = 0 -16t^2 + 32t + 3 = 0 t = (-32 ± √1216)/-32 = -.089 or 2.09 seconds so , "in the air...
*April 24, 2014*

**Math**

prob(H win) = 1/3 , prob(A win) = 2/3 prob(H loss) = 2/3 , prob(A loss) = 1/3 a) not good on trees in this forum, hard to show b) Prob (HH) = (1/3)(1/3) = 1/9 Prob(AA) = (2/3)(2/3) = 4/9 c) to go 3 games, could be AHA or HAH prob of that = (2/3)(1/3)(2/3) + (1/3)(2/3)(1/3) = 4...
*April 24, 2014*

**mathematics**

1. What is 1 - 1/13 ? 2. ....... 3. to get a 2 ---> 11 to get a 5 ---> 14, 41, 23, 32 or 4 ways so to get a 2 or 5 ----> 5 possible outcomes prob(2 or 5) = 5/36 so in 1000 tosses we expect (5/36)(1000) or appr 139 times
*April 24, 2014*

**typo correction -Math**

my first equation should have been cosØ = 49/50 = .98
*April 24, 2014*

**Math**

Make a situation diagram where you have a triangle with the vertical angle as Ø, the hypotenuse 50 cm (the pendulum) and a vertical leg of 49 cm so we would get cosØ - 49/50 = .98 then Ø = .20033.. (I stored that in my calculator to keep accuracy) so we ...
*April 24, 2014*

**finances**

P(1.04^35 - 1)/.04 = 1000000 P = $ 13,577.32
*April 24, 2014*

**Algebra**

I did a synthetic division (or you can do a long algebraic division) to get a remainder of (c+1188) So for the division to be exact, x+1188 = 0 c = - 1188 http://www.wolframalpha.com/input/?i=%28x%5E4+-+3x%5E2+-1188%29%2F%28+x%2B6%29 look at "quotient and remainder" ...
*April 24, 2014*

**Math**

a) the only even prime is the number 2 so prob = 1/6 b) primes less than 5 are : 2 and 3 so prob = 2/6 = 1/3 c) if not a 6, then it must be: 1, 2, 3, 4, or 5 how many of those are prime? d) which of 1 or 2 is prime ? e) how many even's < 4 are prime? etc.
*April 24, 2014*

**Algebra**

(√5a^-2)/(√10a^-1) = (√5 a)/(√10 a^2) = 1/(√2 a)
*April 24, 2014*

**Math**

volume of whole apple = (4/3)π(6^3) = 288π cm^3 volume of inner part of apple with radius 5 cm = (4/3)π(5^3) = 500π/3 cm^3 part of apple within 1 cm of outside = 288π - 500π/3 = 364π/3 prob(being in outer part of apple) = (364π/3) / (288...
*April 24, 2014*

**Math**

expected income = .2(0) + .3(-1000) .25(-10000) + .25(20000) = 2200
*April 24, 2014*

**Math**

Let the line joining (1,-4) and (6,-4) be the base of your triangle. This is a horizontal line, and it should be easy to see that its length is 5 let the height be h (1/2)(5)h = 20 5h = 40 h = 4 so any point on the x-axis (or 4 units above your base) would be such a third ...
*April 24, 2014*

**math**

So they must enter in the order G B B B G number of ways = 2 * 3*2*1 * 1 = 12
*April 24, 2014*

**Math**

could be 1. YY --->(5/29)(4/28) = 20/812 2. GG ---> (7/29)(6/28) = 42/812 ... 5. BB ---> 4/29)(3/28) = 12/812) Add them up (20 + 42 + .. + 12)812 = ....
*April 24, 2014*

**Math**

so prob that 5 of the 10 smoke = C(10,5)(.4^5)(.6^5) = appr .2 40% of college students smoke ??? Are those stats from the 50's ?
*April 24, 2014*

**Math**

number of slices per pizza = 360/40 =9 so for 2 pizzas we have 18 pieces and at 1 slice per person, we would have 18 people. (cutting a pizza into 9 pieces ??? Good luck Are you going to lay a protractor on the pizza and measure 40° ?)
*April 24, 2014*

**Math - Answer Check**

What is (2/3) of (2 1/10) ? = (2/3)(21/10) = 7/5 units of distance or 1.4 units or 1 2/5 units
*April 24, 2014*

**Math**

First one is easy. The cow can cover 3/4 of a circle with radius 40 (the missing quarter is the barn) area = (3/4)(π(40^2) = 1200π yds^2 2nd one: let's tie the cow up at the top left corner. with a rope of 75 yds, the cow can cover (3/4)(π(75^2) or 4218.75&#...
*April 24, 2014*

**math**

Since cost usually varies with the area and the area is proportional to the square of the corresponding sides, the area would be 4 times as large, thus the cost would be 4($1.5) or $6.00 ( ratio of sides = 2:1 so ratio of areas = 2^2 : 1^2 = 4 : 1 ratio of costs = 4 : 1 )
*April 24, 2014*

**Math**

√(3f^3) = √3 * √(f^2) * √f = √3*f*√f = f√3√f = f√(3f)
*April 24, 2014*

**Math**

Taking it just the way you typed it ... = √3/( (√f)^-3) = √( 3/f^-3) = √(3f^3) = f√(3f)
*April 24, 2014*

**math**

? ? ? What does that mean?
*April 24, 2014*

**math**

I would make time (t) my horizontal axis marking it up to 5 hours. Make your vertical axis the calorie axis , marking it as 100 , 200, ... up to 1000 calories. plot the ordered pairs (1,300) , (2, 600) , (3, 900) and (4,1200) you should get a straight line Notice (0,0) should ...
*April 24, 2014*

**Calculus**

mmmhh v = ∫(5t/4)(t^2 + 1)^2 dt = (5t/4)(((1/3)(1/(2t)) (t^2 + 1)^3 + c = (5/24)(t^2 + 1)^3 + c differentiate to get ((5/4)(t)(t^2 + 1)^2
*April 24, 2014*

**Calculus**

right now: price of rent = 900 number of units rented = 50 Let the number of $25 increases be n (e.g. If n= 2 , new rent is 900+2(25) = 950 if n = 5 , the new rent 900 + 5(25) = 1025 so the new rent = 900 + 25n number rented = 50-n maintenance cost = 75(50-n) Profit = P = (900...
*April 24, 2014*

**Calculus**

Make a sketch ... Place the first vehicle A at the origin P, showing the position of the first vehicle draw a short line east of P and label it A2 Place the second vehicle B at a distance of 5 above P showing the initial position of the second vehicle draw line downwards from ...
*April 24, 2014*

**math**

Steve did this for you http://www.jiskha.com/display.cgi?id=1398006054 All that was required of you want a bit of "counting" .
*April 24, 2014*

**Math Help**

You have been helped repeatedly by several tutors for these same type of questions. I think it is time that you try them yourself and show where your difficulties lie with these. e.g In every one, wasn't the first step to find the LCD ? We then multiplied each term by that...
*April 24, 2014*

**trig**

16cos(x)-3sec(x)=0 16cos(x) = 3sec(x) 16cosx = 3/cosx cos^2 x = 3/16 cosx = ± √3/4 x = 1.123 or x = π - 1.123 = 2.0186 or x = P + 1.123 = 4.266 or x = 2π - 1.123 = 5.160
*April 23, 2014*

**algebra**

you LCD is 12 so .... 6x/12 + 4y/12 - 3z/12 = (6x + 4y - 3z)/12
*April 23, 2014*

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