Monday
August 3, 2015

Posts by Reiny


Total # Posts: 30,531

@ Nick - calculus
Nick, with a little effort on your part to complete the solution I gave you and some small adjustment for this question, you could have saved the duplication of this solution by Damon.
July 19, 2015

math
We could extend the terminal arm to (12,5) without changing the angles. Ahhh, now you should recognize the 5-12-13 right-angled triangle values x=12 y=5 r=13 You just have to memorize the definition of the basic trig functions in terms of the x,y, and r values that is, sin&...
July 19, 2015

Math
Never heard of a term in math called bcm complementary angles add up to 90° , so ... let one of them be x then the other is 90-x 4x + 20 = 90-x 5x = 70 x = 14 State your conclusion
July 19, 2015

maths
Use standard keyboard keys to type your expresssion. Use ^ to indicate exponents, e.g. x^2 is "x squared"
July 19, 2015

Math
Steve explained to you yesterday, (before you posted the question above), what the meaning of '' and ' is in the US system of measurement. He also answered your question which is very similar to the above problem http://www.jiskha.com/display.cgi?id=1437257316
July 19, 2015

math
I will assume you mean that the whole property is 80 m by 60 m, and the swimming pool lies within. area of whole thing = 4800 m^2 area of pool = 120 m^2 area of lawn = 4800-120 = .... multiply that by Rs 30 to get the cost.
July 18, 2015

Algebra
3^m goes over 3 digits at 3^7 so m<7 let m = 6 to get 3^6 = 729 so that leaves 270 for 2^n I know 2^8 = 256 , using 2^9 would put me over. 3^6 + 2^8 = 729+256 = 985
July 18, 2015

Calculus
use implicit differentiation, .... 2y^3 + y^2 - y^5 = x^4 -2x^3 +x^2 6y^2 (dy/dx) + 2y (dy/dx) - 5y^4 (dy/dx) = 4x^3 - 6x^2 + 2x dy/dx = (4x^3 - 6x^2 + 2x)/(6y^2 + 2y - 5y^4) for a horizontal tangent, dy/dx = 0 ---> the numerator is zero 5x^3 - 6x^2 + 2x = 0 x(5x^2 - 6x + 2...
July 18, 2015

Mathematics
so the new equation must be y = (-1/52)x + b with (-4,0) lying on it 0 = (-1/52)(-4) + b b = -1/13 new line: y = (-1/52)x - 1/13
July 18, 2015

calculus
Good grief ! You changed one of your equations from y = 12x to y = .5x and you can't make the necessary changes in my solution ??
July 18, 2015

calculus
intersection of y = 6/x with y = 2x 2x = 6/x x^2 = 3 x = √3 intersection of y = 6/x with y = 12x 12x = 6/x x^2 = 1/2 x = √2/2 According to my sketch I would find the area of the triangle from x = 0 to √2/2 with a height of 12x - 2x or ∫10x dx from 0 to...
July 18, 2015

math
600*8 = 4800 , no 611*8 = 4888 , no 622*8 = 4976 , no 633*8 = 5064 , bingo!! A = 3, B = 6
July 18, 2015

locus
By definition, that would be a parabola. Using that definition, let any point on the locus be P(x,y) then √( (x-2)^2 + (y-4)^2 ) = √( (x-x)^2 + (y+4)^2) square both sides and expand x^2 - 4x + 4 + y^2 - 8y + 16 = y^2 + 8y + 16 x^2 - 4x + 4 = 16y looks like the ...
July 18, 2015

small correction - MATH
the interior angle of a heptagon = 900/7 and 360 ÷ (900/7) is not exact (Same conclusion, don't know what I was typing above ! )
July 18, 2015

MATH
Try this experiment: cut out about 5 or 6 of each of 1. identical equilateral triangles 2. identical squares 3. identical pentagons 4. identical hexagons 5. identical heptagons (7 sided polygons) ... Now for each set place them against each other, with sides matching up. You ...
July 18, 2015

maths
I have just answered 5 of your previous 6 questions. You have shown no sign of any effort on your part. Mmmhh, I wonder what makes me think that I am doing your assignment for you ? Until I see some effort shown on your part, or some indication where your difficulties lie...
July 18, 2015

maths
let the acceleration be a m/s^2 v = at + c s = (1/2)a t^2 + ct + k at the beginning of our observation: t = 0 , s = 0 , then k = 0 s = (a/2) t^2 + ct when t = 2 6 = (a/2)(4) + 2c 6 = 2a + 2c a+c = 3 when t = 4 16 = (a/2)(16) + 4c 16 = 8a + 4c 4 = 2a + c subtract those last two...
July 18, 2015

Trigonometry
make a sketch label the top of the taller building A and its bottom as B label the top of the residential building as C, and draw a horizontal line to hit AB at P So now you have two right-angled triangles notice that BP = 10 in the bottom triangle, tan 72 = 10/CP CP = 10/...
July 18, 2015

maths
let speed of boat in still water be x km/h let the speed of the current be y km/h time to go with the current is 2 hrs 40/(x+y) = 2 2x + 2y = 40 x + y = 20 time to go against the current is 4 hrs 40/(x-y) = 4 4x - 4y = 40 x - y = 10 add the two equations: 2x = 30 x = 15 sub ...
July 18, 2015

maths
let the distance b x km time taken at 4 km/h = x/4 time taken at 5 km/h = x/5 but the difference in those two times is 9 minutes or 9/60 hrs = 3/20 hrs x/4- x/5 = 3/20 times 20, the LCD 4x - 4x = 3 x = 3 She lives 3 km from school
July 18, 2015

maths
After 5 minutes the sailboat will be 3 + 1.5((5/60) km or 3.125 km from shore so the speed boat has to go 3.125 km in 5 minutes to catch it: speed = distance/time = 3.125/(5/60) = 37.5 km/h
July 18, 2015

maths
let him use x kg of product B , then 2.4(20) + 3.3x = 2.7(x+20) 48 + 3.3x = 2.7x + 54 .6x = 6 x = 10
July 18, 2015

Math
I am going out on a limb here and guess that for the first one you mean: (45y+20)/5 + (3/4)(12y+24) = 19 , ... the + and = are on the same key on a keyboard, thus typos can happen 9y + 4 + 9y + 18 = 19 18y = -3 y = -1/6 your 2nd last line would be mathematical jibberish.
July 17, 2015

correction - College
re-thinking part A there are 2 cases, 1. the number ends in a 0 then there are 5 ways to start the front, then 4 ways to have the middle digit number of ways = 5x4x1 = 20 2. then number ends in a 5 then there are 4 ways to start, no zero at the start but then again 4 ways to ...
July 17, 2015

College
consider this template for your 3 digit number __________ | ? | ? | ? | *********** A) the last digit can only be a 5 or 0, so two choices the front can only be the 1,3,7, or 8, or 4 choices (can't be zero) leaving 4 choices for the middle, now I could use the zero ...
July 17, 2015

Geometry
My powers of clairvoyance to see your diagram seem to be slightly lacking this afternoon.
July 17, 2015

math
Argghhh, just noticed that I answered this same question back in 2011 http://www.jiskha.com/display.cgi?id=1294093445
July 17, 2015

math
using two variables: original number of Simons stamps --- x original number of Jimmy's stamps --- y x+y = 167 or y = 167-x after giveaway: Simon had (3/7)x Jimmy had (y-37) --> it says, those two expressions are the same, so 3x/7 = y-37 times 7 3x = 7y - 259 3x - 7y = -...
July 17, 2015

math
It is your turn to apply the concepts that both Steve and I just gave you in two previous posts of the same style of question.
July 17, 2015

math
area of room = 288 ft^2 areas of similar figures area proportional to the square of their sides so the area of the model is (1/4)^2 or 1/16 of the original area = (1/16)(288) = 18 ft^2 or sides of the model: length = (1/4)(18) = 4.5 width = (1/4)(16) = 4 area of model = 4(4.5...
July 17, 2015

math
Where does point E come in ?
July 17, 2015

math
Hope you get an answer by the end of "today" .
July 17, 2015

Algebra
add the 2nd and 3rd: y + z = -1 ... #4 Twice the 3rd added to the first: 7y -5z = 29 .... #5 5 times #4 ---> 5y+5z = -5 #5 ---------> 7y - 5z = 29 add them: 12y = 24 y = 2 in #4 2 + z = -1 z = -3 in #1 2x - 2 - 3 = -7 x = -1 x=-1, y=2 , z=-3
July 16, 2015

Math
make a sketch to see that tan 19° = height/4.3 height = 4.3tan19° = ..
July 16, 2015

Sj
Sj is not a "school subject" , label it Math to have the corresponding tutors look at it So if this is a GS, then we are given: ar^3 = 24 and ar^6 = 192 ar^6 / ar^3 = 192/24 r^3 = 8 r = 2 back in ar^3 = 24 8a = 24 a = 3 now you have a and r, and the whole world of ...
July 16, 2015

Math
Please be more specific To find the "length" of a parabola you will need to know integral calculus. "turning point" formula of a parabola?? for any y = ax^2 + bx + c the x of the vertex is -b/(2a), once you have the x plug into the equation to get y
July 16, 2015

rearabilwe
I agree with Steve. I think your reply should become a standard "cut-and-paste" answer for these type of questions.
July 16, 2015

Intermediate algebra
quarters --- x dimes ----- 2x nickels --- 50 - 3x equation based on "value" of those coins: 25x + 10(2x) + 5(50-3x) = 550 25x + 20x + 250 - 15x = 550 30x = 300 x=10 there are 10 quarters, 20 dimes and 20 nickels
July 15, 2015

Math
average speed = total distance/total time we don't know how far it is to her place of work, let that distance be x time on first part = x/70 time for return trip = x/100 total time = x/70 + x/100 = 17x/700 avg speed = 2x/(17x/700) = 2x(700/17x) = 1400/17 km/h or appr 82.4 ...
July 15, 2015

Math
What is going to happen to the current "average" part-time associate ? Is he/she going to get fired? If he/she stays on, will he/she get the new rate ? Currently 30 hrs a week at $8.26 is $247.80, so that is where the $250 comes in ?? The additional help needs 30($9...
July 15, 2015

Math
number of pears --- x number of apples --- x+15 solve for x: x + x+15 = 35
July 15, 2015

Algebra
Assuming you meant it the way you typed it .... multiply each term by 21, the LCD 21x - 3 = 42x - 14x - 21 -7x = -18 x = 18/7 If you meant otherwise, put in the essential brackets e.g. (x-1)/7 = 2x - 2/(3x-1) is just one such case The solutions and answers would be totally ...
July 15, 2015

Math
paycheck --- x she saved (1/2)x + (1/4)x or (3/4)x leaving her with (1/4)x after spending $22.76 on t-shirt, leaves her with (1/4)x - 22.76 (1/4)x - 22.76 = 16.68 (1/4)x = 39.44 x = 157.76
July 14, 2015

calculus
Looks pretty straightforward, both equations say y = ... let's find their intersection: 3 + √x = 3 + (1/5)x √x = x/5 square both sides, x = x^2/25 25x - x^2 = 0 x(25-x) = 0 x = 0 or x = 25 if x = 0, y = 3 if x = 25, y = 8 effective height of regions = 3+√...
July 14, 2015

Math
I assume the exercise is based on the fact that you know what the graph of f(x) = lnx looks like sketch fx) = ln x , remember x > 0 the inverse of f(x) = lnx is h(x) = e^x We can sketch the inverse of a function by simply reflecting it in the line y = x suppose we have y = ...
July 14, 2015

collage math
amount invested at 7% --- x amount invested at 13% --- 13000-x .07x + .13(13000-x) = 1390 solve for x btw, it is college, not collage a collage is an arrangement of pictures
July 14, 2015

Geometry
Since perimeter is a linear measurement, the ratio of their perimeters is the same as the ratio of their sides. The sides are doubled, so their perimeter is doubled, namely 120 cm or so 12/24 = 60/x 12x = 1440 x = 1440/12 = 120
July 14, 2015

Maths
see your previous post
July 14, 2015

Math
This makes absolutely no sense to me.
July 14, 2015

Quantitative method probability
outcomes: the last letter is a winner, Prob of each is found: X = 1/4 = (1/4) XY = (3/4)(1/4) = (1/4)3/4) XYZ =(3/4)(3/4)(1/4) = (1/4)(3/4)^2 XYZX = (3/4)(3/4)(3/4)(1/4) = (1/4)(3/4)^3 XYZXY = ... XYZXYZ = .. XYZXYZX = (1/4)(3/4)^6 Prob that X wins = (1/4) + (1/4)(3/4)^3 + (1/...
July 14, 2015

Math
Cases: LL -- (2/5)(1/4) = 1/10 TT -- (3/5)(2/4) = 3/10 LT -- (2/5)(3/4) = 3/10 TL -- (3/5)(2/4) = 3/10 SUM = 1/10 + 3/10 + 3/10 + 3/10 = 10/10 = 1 in combination format choose 2 of the 5 coins = C(5,2) = 10 Two loonies = C(2,2) = 1 Two toonies = C(3,2) = 3 one of each = C(3,1)...
July 14, 2015

math
nickels --- x dimes ---- x+10 quarters --- 2(x+10) = 2x + 20 now for the value of your coints 5x + 10(x+10) + 25(2x + 20) = 925 solve for x , easy to solve
July 13, 2015

Algebra
You must be talking about C since we are using ≥ and ≤ , we can use equations. r = 16-t sub into the 2nd 5t + 4(16-t) = 80 5t + 64 - 4t = 80 t = 16 then r = 0 I will leave it up to you to decide if "combination" would include the case of only one type of ...
July 13, 2015

Algebra
You told me the following t + r ≥ 16 5t + 4r ≤ 80 take over
July 13, 2015

Math
109% ---> 3927.27 1% ----> 3927.27/109 9% = 9(3927.27/109) = ...
July 13, 2015

Math
let the side be 2x let the height , (your apothem) be h then x^2 + h^2 = (2x)^2 h^2 = 3x^2 h = √3 x ratio of side : apothem = 2x : √3 x = 2 : √3
July 13, 2015

math
recall that the inverse of a function results in a reflection in the line y = x Any even function has a reflection in a vertical line, usually the y-axis Thus its inverse would result in a reflection in a horizontal line. Thus a vertical line test, (a test if the relation is a...
July 13, 2015

maths
i) 210 is correct ii) So what we don't want is to have all-men committees number of all men committees = C(5,4) = 5 so the number with at least one woman = 210 - 5 = 205
July 13, 2015

LNU
Use Venn diagrams and this becomes quite easy. Start with the intersection of the three circles and place 3 in that regions. Now working from the inside out, enter the data Make sure you don't count items more than once. e.g. for the 10 taking Math and History, remember ...
July 13, 2015

algebra
if -2(x-3y)-3(x+5y)-(6x-8y) then = -2x + 6y - 3x - 15y - 6x + 8y = -11x - y if -2(x-3y)-(3x+5y)-(6x-8y) . then = -2x + 6y - 3x - 5y - 6x + 8y = -11x + 9y
July 13, 2015

algebra
I see mismatched brackets ... is it -2(x-3y)-3(x+5y)-(6x-8y) or -2(x-3y)-(3x+5y)-(6x-8y) or .... (the brackets going left must have the same count as the brackets to the right)
July 13, 2015

forgot some cases - prob&stat
ok jil, I forgot the case where only one of "swing players" is in the lineup 6. X plays guard, Y does not play GXFCF C(5,1) x 1 x C(4,2) x C(3,1) = 90 7. X plays forward, Y does not play GGXCF C(5,2) x 1 x C(4,1) x C(3,1) = 120 We have the same cases if Y plays, but ...
July 12, 2015

prob&stat
number of ways to choose any 5 of the 14 = C(14,5) = 2002 number of "legitimate" starting lineups Cases: GGFCF 1. X and Y excluded: C(5,2) x C(3,1) x C(4,2) = 180 GXFCF 2. X plays guard, Y included in the forwards C(5,1) x C(5,2) x C(3,1) = 150 GYFCF 3. Y plays guard...
July 12, 2015

math
Best done with a Venn diagram. For the intersection of all three circles which I called F, H, and B, label it x Then fill in the regions of the circle using the given data. e.g. I labeled the part which is only hockey and basketball as 50-x and the part which is only hockey as...
July 12, 2015

math
Looks like Steve answered the same question in the first of the "Related Questions" below http://www.jiskha.com/display.cgi?id=1410269873
July 11, 2015

Math
Not enough information. since volume of a rectangular prism, a plain ol' box, is (length)(width)(height) any 3 numbers that will multiply to give you 256 will work e.g. L = 16 W = 8 H = 2 or L = 32 W = 8 H = 1 or L = 10 W = 6.4 H = 4 etc
July 11, 2015

math probability
Actually looking back at my answer in the Related Question, I see that I made an error The logical connector was OR , so multiples of 3 : 3,6,9,12,15,18 or less than 7: 1,2,3,4,5,6 can't count the 3 and 6 twice, so there are 10 such numbers prob = 10/18 = 5/9
July 11, 2015

Algebra 2
I will assume An is supposed to mean term(n) ?? term(n) = a + (n-1)d 136 = a + 19(7) a = 3 so sum(n) or your Sn = (n/2)(2a + (n-1)d ) = (n/2)(6 + 7(n-1) ) = (n/2)( 7n -1 ) or = (7n^2 - n)/2 or some other variation of that
July 11, 2015

math
from the first: x = 12-3z plug that into the 2nd: -12+3z-2y+z = 10 4z - 2y = 22 2z - y = 11 , #4 plut x = 12-3z into the 3rd 36-9z +5y + 2z = -7 -7z + 5y = -43 , #5 #4 times 5 ---> 10z - 5y = 55 add this to #5 3z = 12 z = 4 in #4: 8-y = 11 y = -3 back in x = 12-3z x = 12-12...
July 10, 2015

changing
s(1) = t(1) = 2+5 = 7 s(2) = 2(2^2) + 5(2) = 18 s(3) = 2(9) + 5(3) = 33 s(4) = 2(16) + 5(4) = 52 .. t(2) = s(2) - s(1) = 18-7 = 11 t(3) = s(3) - s(2) = 33-18 = 15 t(4) = s(4) - s(3) = 52-33 = 19 so we have: 7,11,15,19,... looks like an AP with a = 7 , d = 4 term(n) = a + (n-1)...
July 10, 2015

math-percentage
If that answer is supposed to be correct, then males = 352 , females = 440 percentage of males = 352/792 = appr 44.4% percentage of females = 440/792 = appr 55.6% which is NOT 20% difference. So the choice are clearly all wrong. Since I showed that my answer is correct, what ...
July 10, 2015

math-percentage
let the number of males be x then the number of females = 792-x percentage of males = x/792 percentage of females = (792-x)/792 (792-x)/792 - x/792 = .20 times 792 792-x - x = 158.4 -2x = -663.6 x = 316.8 , can't have partial people So there are 317 males and 475 females ...
July 10, 2015

Math
the primes in that range are: 2,3,5, and 7 Assuming it is a true random generator, the prob would be 4/10 or 2/5
July 10, 2015

Algebra 2
When simplifying, each new line should have an equal sign at the front You are saying: "my next line is equal to the previous line" Don't just make piece-meal statements Here is what I would have expected from my students when I was still teaching: 6x^5/(2x^3...
July 9, 2015

math
geeehhh, math is getting harder all the time.
July 9, 2015

math
I assume your are looking for (√25)x = 12 5x = 12 x = 12/5 Repeat the above for each of the others
July 9, 2015

math
Steve, I was thinking along these lines, can you find a flaw in this? number of 3-person committees that can be formed from the 15 without any restrictions = C(15,3) = 455 number of 3-person committees WITH BOTH John and Mary = C(13,1) = 13 so the number without both John and ...
July 9, 2015

Algebra
I don't think Steve is on line right now, so I will try. Did you notice the the right side of both of Steve's equations are the opposite of yours? Steve's solution would result in s = 4 c = 2 Yours give inadmissible results of s = appr -14 and c = 16.7 Your ...
July 9, 2015

math (algebra)
The x^32 can only come from multiplying the first tems of all those binomials The -1 can only come from multiplying the constants notice that if we multiply the first terms , the x's, in the right side we get (x^16)(x^8)(x^4)(x^2)(x) = x^31 so the missing bracket must be (...
July 8, 2015

Evaluate the difference, and write the result in t
(6- 1/2 I)-(3+ 9/2 I) = 6- 1/2 I - 3- 9/2 I = 3 - 5 l don't know there the t is supposed to come from.
July 8, 2015

math (algebra)
oops, forgot the link to the graph http://www.wolframalpha.com/input/?i=%28x-2%29%5E2%28x-1%29%5E3%28x%2B1%29%5E4%28x%2B2%29%5E5+%3D+0
July 8, 2015

math (algebra)
each factor could be zero, thus x-2 = 0 ---> x = 2 x-1 = 0 ---> x = 1 x+1 = 0 ---> x = -1 x+2 = 0 ---> x = -2 Look how Wolfram graphed it. How many times and where does the graph intersect with the x-axis ?
July 8, 2015

Math
A: true B: true C: false e.g. 0.5 = .499999.... D: true
July 8, 2015

Math
so we are looking at area of base of cylinder + area of sleeve of cylinder + area of cone without its base = π(.29)^2 + 2π(.29)(5) + π(.29)(1) = .... you do the button pushing (surface area of cone = πr^2 + πrs, where s is the slant height of the cone...
July 8, 2015

Calculus
very detailed solution: let 2log4 9 = x log481 = x 4^x = 81 2^(2x) = 81 let log2 3 = y 2^y = 3 2^4y = 3^4 = 81 then 2^(2x) = 2^(4y) ---> 2x = 4y x = 2y So 2log4 9 - log2 3 = x - y = 2y-y = y = log2 3
July 8, 2015

Math
let present amount be x x(1.05)^5 = 50000 x = 50000/1.05^5 = 39176.31
July 8, 2015

Algebra (Normal Distribution)
Here is the perfect website for your problem http://davidmlane.com/hyperstat/z_table.html
July 8, 2015

maths
Did you mean: (√(196/x) )*(√(90/x) ) = 4 or (√196)/x * (√(90)/x = 4 It makes a big difference
July 8, 2015

mathematics
I don't understand your question. You said that the five numbers given were picked, so the probability that five numbers should be selected would be 1 Not sure what you are asking.
July 8, 2015

math
the other is (-28/81) ÷ (14/27) = (-28/81)(27/14) = -2/3
July 8, 2015

Math
"...either a multiple of 3 or a number less than 7" only 2 elements satisfy that condition, namely the 3 and 6 so prob(of your event) = 2/18 = 1/9
July 8, 2015

Maths
If you are studying this, you must know (1+x)^n = 1 + nx + n(n-1)(x^2)/2! + ... valid only for |x| < 1 now let's apply it to your problem of 31^(1/5) = (32 - 1)^(1/5) = 32^(1/5)(1 - 1/32)^(1/5) = 2 (1 - 1/32)^(1/5)) = 2( 1 + (1/5)(-1/32) + (1/5)(-4/5)/2 (-1/32)^2 + (1/5...
July 8, 2015

Algebra
amount of the 20% stuff --- x L amount of the 50% stuff --- 200-x L .2x + .5(200-x) = .3(200) times 10 2x + 5(200-x) = 3(200) 2x + 1000 - 5x = 600 -3x = -400 x = 400/3 The chemist needs 400/3 L of the 20% solution and 200/3 L of the 50% solution
July 7, 2015

Calculus
dy/dx = x(-sinx) + cosx = 0 for a max/min xsinx = cosx sinx/cosx = 1/x tanx = 1/x No direct algebraic method to solve this, so we have to resort to other means let's look at the graph by Wolfram A preliminary look at y = xcosx shows that there would be an infinite number ...
July 7, 2015

Calculus
since v'(t) = a(t), which is the acceleration a(t) = -32 since a(t) is a constant, we get the acceleration due to gravity at -32 ft/s^2 and v'(1) = a(1) = -32 ft/s^2
July 6, 2015

math
Can we expect a question? btw, use 1/2 and 1/8 to show your fractions
July 6, 2015

Algebra
a + s = 598 s = a - 52 sub s = a-52 into the first equation a + a-52 = 598 2a = 650 a = 325 s = 325-52 = 273
July 6, 2015

Math
Let one be x metres long then the other is 150 - x x+40 = 2(150-x) x+40 = 300 - 2x 3x = 260 x = 260/3 m one is 260/3 m, the other is 150-260/3 or 190/3 m or in decimals, appr 86.67 m and 63.33 m. check: one is 86.67 twice the other is 126.67 which is 40 m more
July 6, 2015

mathematics : intergration
S = 4t - (1/2)t^2 + c "given that S=S when t=0" ????? I will assume you meant: given that S=0 when t=0 0 = 0 - 0 + c ---> c = 0 S = 4t - (1/2)t^2
July 6, 2015

maths
original --- x after first increase --- x + 1200 now decrease of 11% -- 89% are left .89(x+1200) = x-32 .89x + 1068 = x - 32 1100 = .11x x = 10,000
July 6, 2015

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