Posts by Reiny
Total # Posts: 40,239

Math
ok, back to my first question , what about it? are we estimating? are we evaluating? are we rationalizing the denominator? are we painting it yellow? 
Math
What about it? furthermore, do you mean: 4m/?m  5 , the way you typed it, or 4m/(?m  5) , or 4m/?(m5) ??? 
Math help again!
I will assume there is a comma between them in this way: y>x+5 , y<3x4 First one: y > x + 5 make a sketch of y = x + 5 and shade in the region above but excluding the line We do that by drawing the line as a dotted line Second one: y < 3x  4 again sketch y = ... 
Math please help
Simply translate the English into Math, (Mathematics is a language) "Three times our number plus a third of our number plus a fourth of our number plus you and me is two hundred sixty." let "our number" be x 3x + (1/3)x + (1/4)x + 1 + 1 = 260 3x + (1/3)x... 
Algebra 2
You could sketch the curve and see or take a look at this video from Khan Academy, one of the best sites on line your can find. Sal explains the Fundamental Theorem of Algebra https://www.khanacademy.org/math/algebra2/polynomialfunctions/fundamentaltheoremofalgebra/v/... 
Algebra 2
only possible choices at the front (3x .....)(x ......) for each of those, choices at the back (..... +4)(.....1) (..... 4)(..... +1) (..... +2)(..... 2) (...... 2)(..... +2) try them You should really learn one or more of the standard ways to factor trinomials. Surely one... 
Math
.07x = 35 x = 35/.07 
Math
difference in heights = 12351020 = 215 m I will assume your angle is 16° , not 160° , the latter would make no sense so you are looking at a rightangled triangle with height of 215 and a base angle of 16° horizontal distance between them  x tan16° = 215/x... 
math's
Wouldn't you be just hiding 4 faces ? Visualize it, or sketch the 3 dice joined. 
Math
We don't give answers to tests, that would be cheating. 
algebra 1
let the unit digit be x and the tens digit be y so the number is 10y + x if we reverse the digits, the number is 10x + y 10x + y  (10y + x) = 36 9x  9y = 36 x  y = 4 but we also know that x + y = 10 add them 2x = 14 x = 7, then y = 3 the original number was 73 check: 7337... 
math
number of dimes  x number of nickels x+2 pennies  3x 10x + 5(x+2) + 1(3x) = 64 solve for x, then sub into my definitions. 
math
7+(x9/24)(40) = 480 40(x  9/24) = 473 40x  15 = 473 40x = 488 x = 61/5 or 12.2 check: LS = 7 + (61/5  9/24)(40) = 7 + (473/40)(40) = 7 + 473 = 480 = RS my answer is correct according to the way you typed the problem. 
math
44(7695/x)=25 4425 = 7695/x 19 = 7695/x 19x = 7695 x = .... 
math
let the first be x then the next is x+1 x + x+1 = n+1 2x = n x = n/2 the numbers are n/2 and n/2+1 or (n+2)/2 , where n is an even number. e.g. let n = 6 then x = 3, and (n+2)/2 = 4 their sum is 7 OR n+1 which is also 7 
calculus
number = 400(1.06)^n , n is the number of years 400(1.06)^n ? 800 1.06^n ? 2 take logs nlog1.06 ? log2 n ? log2/log1.06 ........ Interesting sideline: look up "rule of 72" and see how it applies to this question. 
Math
Enough of these. Please show some work and effort on your part. What difficulty are you having with these? Did you even look at all the other replies to your previous problems? 
Math
We can find the area area = (1/2)(8)(9) = 36 area using the other altitude = (1/2)(h)(12) = 6h but the area must stay the same: 6h = 36 h = 6 
Math
Perimeter of triangle ABC = 19 If you are following standard convention of listing the vertices of similar triangles, QR corresponds with BC and since QR = 4/6 or 2/3 of BC the perimeter must be (2/3)(19) or 38/3 cm 
Math
I will assume thtat ACE and BDF are straight lines, then Ac/AE = BD/BF Ac/35 = 12/28 AC = 35(12/28) = ..... 
Math: quadratic function and equation
suppose k = 1 then y = x^2  x  2 = (x2)(x+1) since the line y = x+1 is to intersect it ... (x2)(x+1) = x+1 (x2)(x+1)  (x+1) = 0 (x+1)(x3) = 0 x= 1 or x = 3 y = 0, or y = 4 they would intersect twice at (3,4) and (1,0) http://www.wolframalpha.com/input/?i=plot+y%3Dx%... 
math
@ vera .... Just blurting out an answer serves absolutely no purpose! 4a + 11s = 148 7a + 5s = 145 solve the 2 equations in 2 unknowns I suggest multiplying the first by 7 and the 2nd by 5 and then subtracting them 
Alegbra 2
This looks like an assignment. The usual procedure is that you do and show some of your work, then indicate where you are encountering difficulties. I will do the first one for you. X^3+2x9=0 let f(x) = X^3+2x9=0 since you rational factors only, consider only factors of 9 ... 
Math
I agree with your angle. the angle of 21.55° is expressed in the normal mathematical notation where E is 0° and we rotate counterclockwise, no North is 90° etc. So look at the NE quadrant, and place your 21.55° It could technically be noted as E 21.55° N, ... 
Maths
You are just using the standard definitions here: 14th term > a + 13d = 96 25th term > a + 24d = 173 subtract them: 11d = 77 d = 7 back in a + 13d = 96 a + 91 = 96 a = 5 Now you can find any term, e.g. 19th term = a + 18d = 5 + 18(7) = 131 once you have the terms ... 
Math
"I am horrible at trig" is a copout. All you have to remember in a rightangled triangle is 3 pairs of sides combinations for the primary trig functions. Memorize the following word: SOHCAHTOA SOH  SinØ = Opposite/Hypotenuse , not the S,O, and H CAH Cos... 
math
You will need over 8068 miles of ribbon. A semitruck will be over early next week to deliver that. 
calculus
amount of solution #1  x L amount of solution #2  1x L .25x+ .20(1x) = .22(1) solve for x btw, this would not be considered Calculus. 
physic
vector A = (23,0) vector C = (x,0) vector B = (8,0) v(A) + v(C) = v(B) (23,0) + (x,0) = (8,0) (x,0) = (31,0) resultant has magnitude 31 in the negative x direction. 
Math
The sum of three times a number and 2 less than 4 times that same number is 15 The sum of ... + three times a number .... 3x 2 less than 4 times that same number 4x  2 is  = 15 so 3x + 4x  2 = 15 none of your choices match that solving: 7x = 17 x = 17/7 check: 3 times... 
trig transformations
we are comparing f(x) = sinx and g(x) = sin(x/9)= sin( (1/9)x) period of f(x) is 2? period of g(x) = 2?/(1/9) = 18? = appr 56.5, so you are looking at a stretch by a factor of 9 as you stated look at their graphs: http://www.wolframalpha.com/input/?i=y+%3D+sinx,+y+%3D+sin(x%... 
Math
I will assume f(x) = x^10 also note that g(x) = ln(x^10) = 10lnx Not sure if you know Calculus, so I will take an intuitive approach Why not look at their graphs? http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E10,+y+%3D+10ln(x)+,+y+%3D+10x notice that h(x) is just a ... 
math
A hexagon inscribed in a circle results in 6 equilateral triangles, each with sides of 12 units (the given radius) Look at one of these. Isn't the apothem the height of one of those triangles ? See ... https://en.wikipedia.org/wiki/Apothem draw in the altitude, (apothem) ... 
Algebra II
1 + ?(3x+3) = ?(7x+2) square both sides 1 + 2?(3x+3) + 3x+3 = 7x+2 2?(3x+3) = 4x  2 ?(3x+3) = 2x1 square again: 3x+3 = 4x^2  4x + 1 4x^2  7x  2 = 0 (x  2)(4x + 1) = 0 x = 2 , or x = 1/4 since we squared an equation, all answers MUST be verified in the original equation... 
Algebra II
That would work, but have you noticed that the denominators are conjugates of each other? so let's do it by finding a common denominator which would be (4+?6)(4?6) = 16  6 = 10 so we have 2/(4+?6)  2/(4?6) = (2(4?6)  2(4 +?6) )/10 = (8  2?6  8  2?6)/10 = 4?6/10... 
Math
Since 19.75 is about $20 and 39.50 is about $40 your answer is 1/2 or 50% of the original. So it looks like a decimal error. 5% = .05 , not .5 like you did A quicker way would be to take 1.05(39.50) to get the actual answer, which I see in the list 
math
Not totally familiar with US mortgage laws, since they differ slightly from my Canadian laws, but I'll take a shot we need the monthly payment over a 20 year period: i = .0625/12 = .00520833... ( I store that to keep accuracy) n = 20(12) = 240 paym( 1  1.00520833..^240... 
Math
Your questions cannot be answered, since you did not state how these angles are related. 
Math
Is you tip before tax, as it should be ? amount = 45(1.0875) + 45(.2) = .... If you tip after tax ... amount = 45(1.0875)(1.2) = ..... 
math
mass = density x volume volume = ?r^2 h , of the flywheel diameter = 760 mm radius = 380 mm = .38 m height = 180 mm = .18 m volume = ?(.38^2)(.18)m^3 x 7800 kg/m^3 = appr 636.9 kg check my calculations, and check for any required significant digits. 
math
You are correct. The standard deviation measures the variation from the mean. So if you add values that are close to or equal to the mean, that would decrease that variation or deviation from the mean. Your example is a good one. 
Math
Unless you give the problem a different interpretation, Arora gave you a solution back here: /display.cgi?id=1516706057 Did you look at it? What don't you agree with? It said" a loose rope". By that I understood, as did Arora, that the rope ... 
maths
You need a better description and spelling. Are the semicircles located on the sides of a rectangle? If so, then you have a very easy problem. Make a sketch and you will see that you have area of rectangle + whole circle with diameter 42 + whole circle with diameter 30 
Math
I am sure you mean: 5/(x3) + 3/(2x) ? 1 5/(x3) + 3/(2x)  1 ? 0 (5(2x) + 3(x3)  (x3)(2x) ? 0 , skipping common denominator for easier typing 10  2x + 3x  9 + (x3)(x2) ? 0 1 + x + x^2  5x + 6 ? 0 (x^2 7x + 7)/((x3)(2x)) ? 0 , brought back the LCD The quadratic ... 
Math
At most 1 teacher > 1 teacher or no teacher so C(6,1)*C(15,2) + C(6,0)*C(15,3) = 6(105) + 1(455) = 1085 
PreCalc
RS = (1/2 cosx)(1 + 2cos^2 x 1) = cos^3 x = LS , if you meant cos^2 x 
sevier middle
Your School Subject is MATH pay = 82 + .1(80) = ...... 
go with Damon  algebra
I don't know where I got the 4 from. 
algebra
I will assume you meant ln4 + ln(3x) = 4 then ln(12x) = 4 12x = e^4 x = e^4/12 , you do the button pushing. 
Algebra
According to the order of operation, the exponent part has to be done first, so ... 5/8  (1/4) ^2 = 5/8  1/16 = 10/16  1/16 = 9/16 btw, this would not be called an equation, it is an expression. 
Math
Ms. Sue already answered this for you, and told you to check for a typo. If the angles are inside a triangle and two of them already add up to 185, then you don't have a triangle. The question the way it stands is bogus and cannot be answered. 
Math
brother's age  x my age  x3 sisters age  x5 mom's age  3x1 x + x3 + x5 + 3x1 = 87 6x = 96 x = 16 sub back into my defitions 
math
Mathematics is all about patterns. Consider the following 2^3 = 8 , no discussion there, right? 2^2 = 4 2^1 = 2 2^0 = ?? , to fit the pattern 2^0 = 1 2^1 = 1/2 etc I can set up the same pattern for any number. or (x^a)(x^0) = x^(a+0) = x^a if (x^a)(x^0) = x^a x^0 behaves just... 
MATH (PLZ HELP)
It said nothing about the length of JK, so ... "D is the midpoint of LM" is the only logical conclusion we have 
Alegebra
number in 3rd month  x number in first 2 months = 3x x + 3x = 2100 carry on 
Math
That is a problem. They clearly multiplied the left side by 1, so the right side should have been > 0 (x^2 + 2x + 14)/(x + 3) < 0 , those brackets are essential (x^2  2x  14)/(x+3) > 0 (x+2.873)(x4.873)/(x+3) > 0 the critical values are 3, which we can't ... 
math
I agree with Ms. Sue price after 25% discount = .75(349) after sales tax, price = 1.04(.75(349)) = $272.22 
Math trigonometry
your question has been answered. Why are you repeating it ?? /display.cgi?id=1516706057 
Maths
same type of question: /display.cgi?id=1516722947 
Math
so the inside measurements are: 2.5 by 1.5 by .5 m continue 
math
Make your sketch showing the man at some position. let the distance he is from the post be x, let the length of his shadow by y you have similar triangles, so we have: 6/(x+y) = 2/x 2x + 2y = 6x y = 2x dy/dt = 2dx/dt = 2(5) km/hr 
Math
How many seconds per minute ??? 
Algebra
I can't see any obvious pattern 
Algebra
It is $14 in Ontario, which is about $11.25 US 
math
no, how can the cross section be larger than the original rectangular base ? 
math
smaller  x larger  8x just translate: "Four less than five times the smaller is equal to the larger" > 5x  4 = 8x take over since their sum is only 8, it would have been quite easy to do this by simple trialanderror 
Math
3 months > 4500 6 months > x 3/6 = 4500/x crossmultiply: 3x = 27000 x = 9000 , or we could have just doubled the wages, since the time doubled 3 months  4500 5 months  y 3/5 = 4500/y 3y = 22500 y = 7500 3 months  4500 t months  19500 3/t = 4500/... 
math
so we had .3(600) boys or 180 boys let the number of boys that joined be x so .4(600+x) = 180+x solve for x 
Math Mysteries....
#1  good #2  (assuming you don't know algebra) make a list that match the description: 1/7 , 2/9, 3/11, 4/13, 5/15=1/3 , yeahhh #3  good #4  why not do what you did in #3, they are the same question. however , if you picked 20/30 , the HCF would be 10 not 5 so the ... 
Math
Please state a problem. 
Calculus!!!!
see the correction I added in: /display.cgi?id=1516660073 
Calculus
so f'(x) = 12x^2  sinx f(x) = 4x^3 + cosx + c f(0) = 2 2 = 0 + cos0 + c 2 = 1 + c c = 3 f(x) = 4x^3 + cosx  3 f(2?) = 32?^3 + 1  3 = 32?^3  2 
oops  Calculus
that should have been: s(t) = (1/4)t^4 + c ... s(t) = (1/4)t^4 + 3 s(2) = (1/4)(16) + 3 = 7 please ignore the gibberish I had above 
Calculus
v(t)=t^3 s(t) = (4/3)t^4 + c s(0) =3 3 = 0 + c s(t) = (4/3)t^3 + 3 s(2) = (4/3)(8)+3 = 41/3 
Algebra 1
your graph should look like this: http://www.wolframalpha.com/input/?i=plot+y+%3D+%E2%80%93x+%2B+2+,+y+%3D+3x+%E2%80%93+1 notice the scale is not 1 : 1 
algebra
y = 0.8(300  x) y = 240  .8x x = 0.7(300  y) x = 210  .7y sub y = 240  .8x into x = 210  .7y x = 210  .7(240  .8x) x = 210  168 + .56x .44x = 42 x = 42/.44 = 4200/44 = 1050/11 
Math
make a sketch, let the shed touch the wall at A and the ground at B Let the ladder touch the wall at P and the ground at Q Let R be the point where the ladder touches the shed let O be the bottom of the wall meeting the ground. I am also going to scale down the values given by... 
Math
I will assume that the "3 m from the edge of the table" is the horizontal distance, so 3 = .5t, where t is the time in seconds t = 6 seconds vertical distance = 4.9t^2 = 4.9(36) = 176.4 m not a very logical answer. So let's assume the 3 m is the direct line from ... 
Math Algebra 2
look below at Marie's question and my reply to that You should be able to answer the rest of these You also replied in that question, so it should be easy to find 
Math
time = distance / rate plug in your numbers 
math
number of students in Mr. Jones' class ? number of students in Mrs. Smith's class  ?  4 What did you not understand about this question?? 
Algebra 2 Sine Function
I will assume h = 82.5 sin (3 pi (t+0.5) )+97.5 , (you had no equation and no h) so when t = 6 h = 82.5 sin (3?(6.5)) + 97.5 = 82.5(1) + 97.5 = 15 check: period = 2?/(3?) = 2/3 minutes (that is a fast ride considering how huge it is) So 6 ÷(2/3) = 9 , at the 6 minute ... 
Math
amount of Kenyan coffee  x amount of Sumatran coffee  24x 11x + 15(24x) = 13(24) solve for x 
Math
number of A vials  x number of B vials  40x solve for x: 39.95x + 30.49(20x) = 1446.64 
math
One rotation is 2? radians so (3/5)(2?) = ...... 
Math
1 x (4)8 x 9/3 or 1*4  8*9/3 = 4  72/3 = 4  24 = 20 
PreCalculus
ok so far (cot^2)2x = 1/3 tan^2 (2x) = 3 tan (2x) = ±?3 I recall that tan 60° = ?3 so 2x = 60 2x = 120° in quad II 2x = 240° in quad III 2x = 300° in quad IV so x = 30°, 60°, 120°, or 150° for 0 ? x ? 360° in radians: x = ?/6, ?/3, 2... 
Math
If the assumption is that men are either tall or short, then prob(short) = 1  .15 = .85 
math
DrBob, on my Mac I press "option" V, on my PC , hold down the ALT key and press 251 on the numberpad, as Ms. Sue stated. You can also open Word or something like that. There should be a symbol table and I know Word has the ? in that list. The just copy and paste it. ... 
math
is 8?2 + 2?2 = 10?2 ? Yes, just like 8apples + 2apples = 10apples 8 boys +2 boys = 10 boys 8x + 2x = 10x 
Math
Make a sketch and draw in the altitude. See that rightangled triangle with hypotenuse 5 and height of 4 ? You should recognize the 345 rightangled triangle, if not, use Pythagoras to find the base. Area of triangle = (1/2)base x height = (1/2)(6)(4) = ..... 
geometry
figure A since you have a rhombus with perimeter of 20, each side must be 5 Make a sketch, drawing in the two diagonals. diagonals bisect each other, so you get 4 congruent rightangled triangles. Consider one of them, let the missing halfdiagonal be x so x^2 + 4^2 = 5^2 x = ... 
Math (please help asap)
4 times in 1 hour so 4(24) in 1 day = 96 , since there are 24 hrs in a day so 7(96) in a week = 672 , since there are 7 days in a week 
Math
"at least 5 tosses" to means: 5 tosses, or 6 tosses, or 7 tosses, etc so we don't want 2, 3, or 4 tosses. agree? btw, 5 tosses would be quite a few more than TTTHT. What about HHHHT, THHHT, TTTHT, etc 
Math
This is a bit more complicated than it first appears Let A be the event of ... HT case 1. it happens in 2 tosses HT** Prob(A on 2 tosses) = 1(1/4) case 2. (3 Tosses) THT, HHT, Prob(A on 3 tosses) = 2(1/8) = 1/4 case 3. (4 tosses) TTHT, THHT, HHHT prob(A on 4 tosses) = 3(1/16... 
Math
dy/dx=28(3x+4)^0.5 y = 2x + (16/9)(3x + 4)^(3/2) + c or y = 2x + (16/9)(1/?(3x+4)^(3/2) + c but (0, 4/3) lies on it , so 4/3 = 2(0) + (16/9)(1/4^(3/2) + c 4/3 = (16/9)(1/8) + c c = 6 y = 2x + (16/9)(3x + 4)^(3/2) + 6 check my algebra, should have written it out on paper ... 
math
(a,b) > reflected across the xaxis > (a, b) (a,6) > translated 5 units to the right > (a+5, b) 
math
There must be a 90° angle, that is, two of the lines must be perpendicular, or the slopes of two of the lines must be negative reciprocals of each other. So .... take the slope of the 3 lines and check for the above property. A longer method would be to find the lengths of... 
Lesson 2 Unit 2 Connexus SS
Just listened to Bob Marley's story about them, called Buffalo Soldier. 
math
prob(spots) = 12/180 = 1/15 so of the 1200 frogs, (1/15)(1200) should have spots, so .. how many should not have frogs ? or prob(not spots) = 14/15 number who don't have spots = (14/15)(1200) = ... You will of course get the same answer from either method, right ?