Wednesday
September 17, 2014

Posts by Reiny


Total # Posts: 27,114

math
distance = √( (-3-8)^2 + (-10+10)^2) = √(121 +0) = √121 = 11 We can see this without any calculation. Since the x values are the same for both points, the line is a vertical one. So all we have to do is take the difference between -3 and 8 , which is 11
May 16, 2014

math
number of $5 tickets --- x number of $10 tickets --- y number of $15 tickets ---- 180-x-y x + (180-x-y) = 2y x + 180 - x - y = 2y 180=3y y = 60 income equation: 5x + 10y + 15(180-x-y) = 1900 5x + 600 + 15(120-x) = 1900 5x - 15x + 600 + 1800 = 1900 -10x = -500 x = 50 x=50 y=60 ...
May 16, 2014

math(compound interest )
What you wanted as an equation is ... [ x( 1 + .1/360)^20 - 600 ](1+.1/360)^108 = 8900 x(1+.1/360)^20(1+.1/360)^108 - 600(1+.1/360)^108 = 8900 x((1.00557024)((1.03045024) - 618.2701442 = 8900 x(1.036190095 = 9518.270144 x = 9185.83
May 16, 2014

math trigonometry
I don't understand your question. Are we looking at two different equations ? Are we solving 10 sec Ø + 13sinØ = 0 and 5tan Ø - 12 = 0 ???? or .... ? is (0,90°) the domain?
May 15, 2014

Algebra 1
first equation: -2x - 2y = 4 ----> x+y = -2 2nd equation: 2y = -2x - 4 2x + 2y = -4 x + y = -2 looks like they are the same line, so you have one line any ordered pair that works in one of them, will work in the other. There will be an infinite number of solutions.
May 15, 2014

Math-- Ms. Sue??
#1 , wrong. If you plot your points you will see that it is (8,5) notice that now two pairs of points have the same x , making the lines vertical, and 2 pairs of points have the same y, making the horizontal. #2, ok #3, ok #4, your answer: (5,-4) and (-2,1) -- slope = (1-(-4...
May 15, 2014

Math
prob(brown, then violet) = (8/16)(1/16) = 1/32
May 15, 2014

Math - Int Trig
y = √x shift up 4 units -----> y = √x + 4 reflect about the y-axis ---> y = √-x + 4 , for x ≤ 0 shift right 2 units -----> y = √(-(x-2)) + 4 , x≤2 again, Wolfram verifies this http://www.wolframalpha.com/input/?i=y+%3D+√%28-%...
May 15, 2014

Math - Int Trig
start: y = |x| shifted right : y = |x-3) stretched by factor of 3 : y = 3|x-3| vertically down 2: y = 3|x-3| - 2 reflected about x-axis y = -3|x-3| + 2 behold the wonders of Wolfram http://www.wolframalpha.com/input/?i=y+%3D+%7Cx%7C+%2C+y+%3D+%7Cx-3%7C+%2C+y+%3D+3%7Cx-3%7C+%2C...
May 15, 2014

math
multiply each of the prob. answers I just gave you by 100
May 15, 2014

math
Four possible outcomes: HH HT TH TT prob(HH) = 1/4 prob(TT) = 1/4 prob (TH or HT) = 2/4 = 1/2 notice the 3 answers add up to 1, since one of those possibilities must happen
May 15, 2014

Geometry
(-3,-1) ---- dilation factor of 2 ----> (-6, -2) show it by plotting the two points how does the distance to the origin change ?
May 15, 2014

Algebra 1
looks like f(3) = 2 then g( f(3) ) = g(2) = -3
May 15, 2014

Trig 3
sloppy way of writing the trig expressions ( when you write tan2, you are asking for the tan(2 radians. What you meant was something like tan^2 Ø It has to be the sine of something, the cosine of something, or the tangent of something. anyway ..... (1 - cos^2 Ø)/...
May 15, 2014

Geometry
Any regular n-gon can be changed to n isosceles congruent triangles by drawing all radii to the vertices of the polygon. the area of a triangle = (1/2)(base)(height) the area of one of these = (1/2)(side)(apothem) where the apothem is the distance from the centre of the ...
May 15, 2014

math(compund interest )
Major Hint: Did you notice that from 16 April to 16 Oct is 6 months? So your time can be very easily expressed in half-years, and quarter-years. From all the knowledge you have gained by having received many answers for similar questions to the above, you should now be able to...
May 15, 2014

mathematics for management
NO you used the concept of continuous compounding but it said it was compounded monthly Even with the above in consideration your expression of 8888(e^0.06(0.25)) makes absolutely no sense. i = .06/12 = .005 n = 3(12) = 36 months PV = 8888(1.005)^-36 = $7427.21 For a single ...
May 15, 2014

math
How do you expect us to know what table you are working from. With today's excellent scientific calculators, the use of "tables" that were found in the back of most textbooks in the past is no longer common practise. Your question is simply PV = 100000(1.05)^-50...
May 15, 2014

math
what is 20000(1.06)^15 ?
May 15, 2014

math(urgent)
Just use the formula. Amount = payment( (1+i)^n -1)/i Amount = 1000(1.08)^3 -1)/.08 = 3246.40
May 15, 2014

Trig
3x^2 + 4y^2 = 12 divide by 12 x^2/4 + y^2/3 = 1 we know sin^2 t + cos^2 t = 1 so sin^2 t = x^2/4 = (x/2)^2 ---> sin t x/s ----> x = 2sin t and cos^2 t = y^2/3 = (y/√3)^2 cos t = y/√3 ----> y = √3cos t x = 2sint y = √4cost confirmation: http://...
May 14, 2014

Calculus
dy/dx = 2tan (x^4) * sec^2 (x^4) * 4x^3
May 14, 2014

ALGEBRA
using the ratios, let the width be 8x and the length be 15x led d be the diagonal d^2 = (8x)^2 + (15x)^2 = 64x^2 + 225x^2 = 289x^2 d = 17x or x = d/17 width = 8x = 8d/17 length = 15x = 15d/17
May 14, 2014

geometry
volume of similar solids is proportional to the cube of their corresponding sides so ratio of volume = 3^3 :^3 = 27 : 125
May 14, 2014

Math
so you want 9(2)(t/9) = 1000000 2^(t/9) = 111,111.111.. t/9 log2 = log111111.11 t/9 = log111111.11../log 2 = 16.7616.. t = 150.8548 years so 1909 + 150.8548 yrs = appr 2060 just what Ms Sue got by continuing her chart.
May 14, 2014

math
1.75 years = 21 months monthly rate = .18/12 = .015 PV = 900(1.015)^-21 = $658.35
May 14, 2014

math
100% of something = the whole thing or 1 50% of something = .5 or 1/2 of the whole thing = .5 145% of something = 1.45 yes, C is the right choice.
May 14, 2014

math (urgent )
my answer confirmed by Wolfram http://www.wolframalpha.com/input/?i=13.875-0.1875%2856.375%29%2F8-2+%281%2F8%2B27.125%2F300.875%29+
May 14, 2014

math (urgent )
This is what you typed: 13.875-0.1875(56.375)/8-2 (1/8+27.125/300.875 I added a bracket at the end, or else they are mismatched. Followed the order of operation, and got 12.1234035... The way you wrote it, there is now way to get 1.1908 check how you placed your brackets.
May 14, 2014

Geometry Help & Proofs
based on : ratio of volumes is proportional to the cube of their corresponding sides. so ratio of volumes: A : B = 1 : 5 A : C = 1^3 : 2^3 = 1 : 8 B : D = 1^3 : 3^3 = 1 : 27 A/B = 1/5 B = 5A A/C = 1/8 C = 8A B/D = 1/27 D = 27B ratio of volume of C :D = 8A : 27B = (8/27)(A/B...
May 14, 2014

Math
9/9 = 1 = 12/12 2/3 = 8/12 5/6 = 10/12 4/12 = 4/12 0/2 = 0 , obviously the smallest now can you tell ?
May 12, 2014

Algebra
(x - y) (3x + xy - 4y) + xy^2 - x^2y = (x-y)(3x + xy - 4y) - xy(x - y) = (x-y)(3x + xy - 4y - xy) = (x-y)(3x - 4y)
May 12, 2014

Math
The total of the first 16 students' marks was 16x66 or 1056 the total of the new students' marks was 6x74 or 444 so the total of the 22 students was 1500 giving an average of 1500/22 or appr 68.2
May 12, 2014

finance
WoW! I recognize the formula Future Value = Present Value (1 + i/n)^(cn) where n is the frequency of compounding per year and c is the number of years from your (1.089/12)12*5 I gather that the interest rate was 8.9 % per annum compounded monthly , for a time of 5 years and ...
May 12, 2014

Algebra 1 Answer Evaluation
anything squared cannot be negative in the real number set, so your first one has no real number solution 2. correct
May 12, 2014

math
distance (d) ∝ time (t) d = kt case 1: when t = 2 , d = 90 90 = k(2) k = 45 so d = 45t , the constant of proportionality is 45 the unit rate is 45 mph check on the others t = 3 --> d = 45(3) = 135 ✔ t = 5 --> d = 45(5) = 225 ✔ t = 6 --> d = 45(6...
May 12, 2014

Algebra 1 (Reiny)
x^2 + 3x - 18 = 0 (x+6)(x-3) = 0 x = -6 or x = 3
May 12, 2014

MATH: TRIG
you should recognize the 3-4-5 right angled triangle. so if cosx = 3/5 then sinx = 4/5 sin 2x = 2sinxcosx = 2(4/5)(3/5) = 24/25 you can always check your result with a calculator.
May 12, 2014

Maths
use substitution x^2 + 3x - 5 = x-2 x^2 + 2x - 3 = 0 (x+3)(x-1) = 0 x = -3 or x = 1 check with Wolfram http://www.wolframalpha.com/input/?i=Y%3Dx-2+%2C+Y%3Dx%5E2%2B3x-5 if x = -3, y = -3-2 = -5 if x = 1 , y = 1-2 = -1 x=-3, y=-5 ---> point (-3,-5) x = 1 , y = -1 --->...
May 12, 2014

Algebra II
quick way: for any linear equation written in the form Ax + By + C = 0 the slope is -A/B so here, the slope is -6/5
May 12, 2014

math
Don't post the same question using different names please.
May 12, 2014

math
3+x/7+x= 3/7 + 3/7 I would multiply each term by 7 , the LCD 21 + x + 7x = 3+3 8x = -15 x = -18/8 I seriously suspect a typo
May 12, 2014

math
3(40+x) = (2+3)(3+4)(4+5) 120 + 3x = 5(7)(9) = 315 3x = 195 x = 65
May 12, 2014

geometry
He has not seen 5 of the comedies and 7 of the dramas Since you want the non-seens from one OR the other there are 12 movies he has not seen prob(nonseen) = 12/18 = 2/3
May 12, 2014

Algebra 1--Please, help me!
1. 4x^2 + 8x = 32 4x^2 + 8x - 32 = 0 x^2 + 2x - 8 = 0 let y = x^2 + 2x - 8 now graph this, and look at where it crosses the x-axis. From Wolfram's graph http://www.wolframalpha.com/input/?i=y+%3D+x%5E2+%2B+2x+-+8 we can see x = -4 or x = 2 2. x(x + 3) = 32 x^2 + 3x - 32 = ...
May 12, 2014

oops - MATH
just noticed an arithmetic error.. in my evaluation of y, should be 60 - 2x = 60-2(20) = 20 so ..... max profit is 30(20) + 50(20) or 1600 , when 20 of the first product and 20 of the second product are made
May 12, 2014

MATH
let the number of the first product be x let the number of the 2nd product by y So we need to look at the regions 2x+y ≤60 and x+y≤30 and x+3y≤80 The profit function is 30x+50y which has a slope of -3/5 move that profit line to the right, parallel to itself, ...
May 12, 2014

Math
I tried a slightly different approach I looked at the trapezoid, and drew two verticals upwards from the base, creating a rectangle of 25 by 50 cm and two right-angled triangles , each of height 50 and base 75/2 I drew a water line, of height h and width of r in each of the ...
May 12, 2014

Math
You don't have an equation, so "solving" is the wrong instruction. are you expanding 2a(a^2 + 4a) ? then... = 2a^3 + 8a^2
May 11, 2014

algebra
I don't know what h=−16t<E> 6<E>+s is supposed to say, but I know that h = -16t^2 is the relation between t seconds and the distance fallen in feet Since we just want to find the distance, let's use h = 16t^2 when t = 3 h = 16(9) = 144 feet If this is...
May 11, 2014

Math
slope for the first 2 points = (0-1)/(4-2) = -1/2 y = -1/2 x + b , but (2,1) lies on it 1 = -(1/2)(2) + b b = 2 y = -(1/2)x + 2 check if third point is on it LS = -1 RS = (-1/2)(6) + 2 = -1 yes, all is good y = (-1/2)x + 2
May 11, 2014

Math
nothing to "solve", you don't have an equation. did you mean: evaluate 5(3^n) for n = 1,2,3, ... then you would get 5(3) , 5(9), 5(27), 5(81) .. = 15, 45, 135, 405, looks like that is what you are doing, if so, you are correct.
May 11, 2014

Math
First of all you have not defined x and y Secondly, 2(x+y) does not look like an area, it looks like the perimeter of the original rectangle. I will attempt it anyway: I drew a rectangle of length x and width y I then drew two lines, one parallel to the length, the other ...
May 11, 2014

MATHHH
case1: no defence in 1st row - we can choose any 6 of the 8 players = C(8,6) = 28 case2: 1 defence - four ways to choose the defenseman, choose 5 from the remaining 8 = 4 x C( 8,5) = = 224 Case3 : 2 defense = C(4,2) x C(8,4) = 420 total = 28+224+420 = 672 for choosing the 6 ...
May 11, 2014

Math
first do this: 4√6/√30 = 4/√5 now multiply top and bottom by √5 4/√5 * √5/√5 = 4√5/5
May 11, 2014

alegbra
first of all your "equation" makes no sense. LS = 25 RS = 1/25 25 ≠ 1/25 secondly , equations tend you have a variable in there somewhere, else it simply becomes a mathematical statement which is either true or false e.g. 2+3 = 4 --- false 1+1 = 2 ---- true ...
May 11, 2014

alegbra
amount = initial (.5)^(t/5730) .75 = 1 (.5)^(t/5730) log .75 = (t/5730) log .5 t/5730 = log .75/log .5 = .415... t = 2378.16 age is about 2400 years to the nearest century
May 11, 2014

math
The way the question stands, the "bottom" of the kite could be any length along the missing part of the diagonal. The angle at the shorter diagonal's end wasn't a right-angle ?
May 11, 2014

math
I think we are missing information Was there an angle given?
May 11, 2014

ALGEBRA
13.29 = 14.7 e^(.21a) .90408.. = e^(.21a) by rules of logs .21a = ln .90408... .21a = -.0100835.. a = -.48016 miles or - 2535 ft below sealevel !!!!!!! Wow, since the lowest point in North America, Death Valley is only about 260 ft below sea level, you city is a mystery. ... ...
May 11, 2014

Math
The surface area is proportional to the square of their radii (1.5r)^2/r^2 = x/36π 2.25/1 = x/36π x = 2.2(36π) = 81π
May 11, 2014

Math
From 1 to 10, isn't 6 the only number divisible by both 3 and 2 ? so prob = 1/10
May 11, 2014

math 7Probability help
mmmmmhhhhh possible sums of 2 dice is 2 , 3, 4, .... 11, 12, there are 11 of those the evens are: 2 4 6 8 10 12 or 6 of them so prob(even sum) = 6/11
May 10, 2014

Finance
I will do the last one, you do the other two in the same way c) PV = 5000(1.09)^-4 = $3542.13
May 10, 2014

Math
suppose we just look at 1/3^x (1/3^x - 2) = 15 3^-x(3^-x - 2) = 15 let 3^-x = a for easier typing then we have a(a-2) = 15 a^2 - 2a - 15 = 0 (a-5)(a+3) = 0 a = 5 or a = -3 3^-x = 5 log 3^-x = log5 -x log3 = log5 -x = log5/log3 x = -log5/log3 the other part of 3^-x = -3 has no ...
May 10, 2014

MATHHH
success if you draw 2 granolas or 2 fruits or 2 cheese prob(success) = (12/30)(12/30) + (10/30)(10/30) + (8/30)(8/30 = 4/25 + 1/9 + 16/225 = 77/225
May 10, 2014

maths
I will use a for alpha and b for beta then from the properties of zeros of a quadratic a+b = -1 ab = 1 then 1/a + 1/b = (b+a)/(ab) = -1/1 = -1 a^2 + b^2 = (a+b)^2 - 2ab = (-1)^2 - 2(1) = 1 - 2 = -1
May 10, 2014

Math
You could do the tedious task of expanding and then collecting powers of y^3. I let Wolfram do this for me http://www.wolframalpha.com/input/?i=expand+%281%2By%2Bky%5E2%29%5E7 It might be easier to read the expansion in reverse order 1 + 7y + 21y^2 + ... Notice that y^3 ...
May 10, 2014

Calculus Please Help
What a mess! http://integrals.wolfram.com/index.jsp?expr=sqrt%28100x%5E2-400%29%2Fx&random=false add C to the result
May 9, 2014

Alegbra
I suspect that this is a log question and your IN is actually ln ( the natural logarithm) so let's try: t = -62.5 ln(1 - N/80) or is it t = -62.5 ln( (1-N)/80) look at the first of the Related Questions below. It is the same question and Steve had his doubts about the same...
May 9, 2014

Math
1^2-(2-x)^2=2^2-x^2 1 - (4 - 4x + x^2) = 4 - x^2 1 - 4 + 4x - x^2 = 4 - x^2 4x = 7 x = 7/4 I don't understand why a textbook would write a term as 1^2 and 2^2 in an equation. That is just silly.
May 9, 2014

Algebra (proportions)
let the number of bears be x 50/x = 2/100 2x = 5000 x = 2500
May 9, 2014

Calculus
y = u^3 + u^2 - 1 dy/du = 3u^2 + 2u u = 1/(1-x) = (1-x)^-1 du/dx = -1(1-x)^-2 (-1) = 1/(1-x)^2 when x = 2, u = 1/(1-2) = -1 du/dx = 1/(1-2)^2 = +1 dy/du = 3(-1)^2 + 2(-1) = 1 dy/dx = dy/du * du/dx = 1(1) = 1 check my arithmetic, I made several arithmetic errors tonight.
May 9, 2014

Math
It didn't, n = 0 became a solution. Are you not familiar that if you have a factored form = 0, such as (A)(B) = 0 , then A = 0 or B = 0 ???
May 9, 2014

Math
I took out a common factor of n expand n(1-2n) What do you get ?
May 9, 2014

Math
n(1 - 2n) = 0 n = 0 or 1 - 2n = 0 n = 0 or n = 1/2
May 9, 2014

Calculus
y= sqrt[(3x^2+2)^3] = (3x^2 + 2)^(3/2) dy/dx = (3/2)(3x^2 + 2)^(1/2) (6x) = 9x(3x^2+2)^(1/2) or = 9√(3x^2 + 2) , which is valid for all values of x since (3x^2 + 2) is always positive.
May 9, 2014

oops - Algebra
looks like I can't do a simple subtraction of course 50-32 = 18 as MathMate had
May 9, 2014

Algebra
let amount of stronger solution to be used be x L amount of weaker solution is 50-x L .8x + .3(50-x) = .62(50) .8x + 15 - .3x =31 .5x = 16 x = 16/.5 = 32 needs 32 L of the stronger and 36 of the weaker solution.
May 9, 2014

math
.48x = .35 x = .35/.48 = appr .73
May 9, 2014

Algebra
original width --- x original length --- y xy= 280 y = 280/x new width --- x+1 new length --- y-5 new area = (x+1)(y-5) = (x+1)(280/x - 5) = 280 - 5x + 280/x - 5 = 275 - 5x + 280/x = (275x - 5x^2 + 280)/x = -5( x^2 - 55x - 56)/x perfect squares in the neighbourhood of 280 are ...
May 9, 2014

Algebra
1/12 = 1/30 + 1/r The LCD is 60r , so multiply each term by 60 r 60r(1/12) = 60r(1/30) + 60r(1/r) 5r = 2r + 60 3r = 60 r = 20 or 1/12 - 1/30 = 1/r 5/60 - 2/60 = 1/r 3/60 = 1/r 1/20 = 1/r cross-multiply r = 20
May 9, 2014

Algebra
rate of passenger boat --- x mph rate of freighter --------- x-6 mph 2592/(x-6) - 2592/x = 72 , assuming they travel 24 hours per day multiply each term by x(x-6) 2592x - 2592(x-6) = 72x(x-6) 2592x - 2592x + 15552 = 72x^2 - 432x 72x^2 - 432x - 15552 = 0 9x^2 - 54x - 1944= 0 (x...
May 9, 2014

Calculus
#1 ??? #2. dy/dx = x cos x^2 y = (1/2) sin x^2 + C when x=0, y = -3 -3 = (1/2) sin 0 + c -3 = 0 + c c = -3 so y = (1/2)sin x^2 - 3 when x = π y = (1/2) sin (π^2) - 3 = -3.215... #3. let N = a e^(kt) when t = 2 ---> 100 = a e^(2k) when t = 4 ---> 300 = a e^(4k) ...
May 9, 2014

Algebra
From the choices of answers, I think you typed the equation incorrectly Looks like it should be y = 3√(6x+42) since we cannot take the square root of negatives, 6x + 42 ≥ 0 6x ≥ -42 x ≥ -7 , which is your last choice.
May 9, 2014

Calculus
at its vertex. the x of the vertex is -b/(2a) = -40/-10 = 4 it will change direction at t = 4 seconds
May 9, 2014

Math
There can't be a^2 in your answer just looking at the a's you had a^2/a^3 which is 1/a once more: 54 a^2 b^3 ___________ 81 a^3 b^2 = (3/2) (1/a) (b) = (3/2)b/a or 3b/(2a)
May 9, 2014

Math
You are right, I should have had (3/2)b/a or 3b/(2a)
May 9, 2014

Math
54 a^2 b^3 ___________ 81 a^3 b^2 = (54/81)(a^2/a^3)(b^3/b^2) = (2/3) b/a or 2b/(3a) I don't see that choice, but that is your answer.
May 9, 2014

calculus-answer check
1st two are corrrect #3. my derivative was f ' (x) = 15(x+1)(x-1)^9 (x+2)^4 = 0 for x = -1, 1, -2 verify at Wolfram http://www.wolframalpha.com/input/?i=plot+y+%3D+%28x-1%29%5E10%28x%2B2%29%5E5
May 9, 2014

Algebra
t=√(d/16) so you want √(d/16) > 1 square both sides d/16 > 1 d > 16
May 9, 2014

Mathematics
sketch triangles in quad 2 and quad 1 for the given info if sin a = 3/5 in II cos a = -4/5 if sin b = 5/13 in I cos b = 12/13 sin(a+b) = sina cosb + cosa sinb = (3/5)(12/13) + (-4/5)(5/13) = (36 - 20)/65 = 16/65
May 9, 2014

math
(3/5)(84+72+96)/3 + (2/5)x ≥ 80 times 5 84+72+96 + 2x ≥ 400 2x ≥ 148 x ≥ 74 check: average of first 3 tests = 84 going towards final mark = (3/5)(84) = 50.4 final mark = 74 (2/5) of that is 29.6 final mark = 50.4 + 29.6 = 80
May 9, 2014

MATH
two identities you should have in your bag of ID's is csc^2 Ø -1 = cot^2 Ø , and sec^2 Ø - 1 = tan^2 Ø LS = left side = csc^2 Ø - 1 + sec^2 Ø - 1 = csc^2Ø + sec^2 Ø - 2 = 1/sin^2 Ø + 1/cos^2 Ø - 2 = (cos...
May 9, 2014

Maths
For this one the 30-60-90° and the 45-45-90° right-angled triangles are your friend. from those you should know cos30°= √3/2 sin30° = 1/2 cos60° = 1/2 sin60° = √3/2 sin45° = √2/2 cos45°=√2/2 cos15 = cos(45-30)° = ...
May 9, 2014

Trig
One of the ID's you should know is cot^ Ø + 1= csc^ Ø then: csc^2x -(√3+1)cotx+(√3-1)=0 cot^2 x + 1 - (√3+1)cotx + (√3-1)=0 cot^2 x - (√3+1) cotx + √3 = 0 cot^2 x - cotx - √3cotx + √3=0 cotx(cotx - 1) - √3...
May 9, 2014

Math (Calculus)
y-intercept is 6 y = 6-3x 3x = -y + 6 x = -y/3 + 2 x^2= y^2/9 - 4y/3 + 4 vol = π[integral] y^2/9 - 4y/3 + 4 dy from 0 to 6 = π[ y^3/27 - 2y^2/3 + 4y] from 0 to 6 = π( 8 - 24 + 24 - (0) ) = 8π better check my arithmetic
May 8, 2014

math
costA= 3.00 + .5(x-1) costB = 2.00 + .7(x-1) 2 + .7(x-1) - 3 - .5(x-1) = 15 .7x - .5x - .7 + .5 -1 = 15 .2x = 16.2 x = 81 check: if x = 81 costA = 3+.5(80) = 43 costB = 2 + .7(80) = 58 , which is $15 more
May 8, 2014

Math
right side = (2x-6)/(x+6) + 1 = (2x-6)/(x+6) + (x+6)/(x+6) now we have a common denominator = (2x-6 + x+6)/(x-6 = 3x/(x+6) as you required.
May 8, 2014

trigonometry
sinØ = 28/32 = .875 Ø = appr 61°
May 8, 2014

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