Saturday
October 25, 2014

Posts by Reiny


Total # Posts: 27,555

Math Homework
1. keep in mind that both f(x) and g(x) would be undefined for x=0 so even though g/f = (1/x) / (1/x^2) = x the final function would still be undefined (actually it would be indeterminate) for x = 0 so the domain is : set of all real numbers, x ≠ 0
September 28, 2014

Pre-Calculus
How did you get -3 ? (f-g)(x) = 4 - (2x-1) = 4 - 2x + 1 = -2x + 5
September 28, 2014

Pre-Calculus
if f(x) = 2x-5 and g(x) = 4 then (f-g)(x) = 2x-5 - 4 = 2x - 9 Do #2 in the same way
September 28, 2014

geometry
Don't you just have a nice right-angled triangle? You should recognize 5-12-13 as one of the common ones with integer lengths, if not AC^2 = 5^2 + 12^2 = 169 AC = √169 = 13
September 28, 2014

Fractions
1. area of each piece = 8.5(11) = 93.5 inches^2 2. no definite answer since we don't know the dimensions of the larger piece. e.g. it could be 20 by 50, or 25 by 40 , or 16 by 62.5, or .....
September 28, 2014

math
Using the simple interest formula I = PRT 6 = 100(R)(2/52) R = 6(52)/200 = 1.56 or 156 % per year (in the Middle Ages, they would have been burned at the stake for usury)
September 28, 2014

math
let the side of the smaller square be x let the side of the larger square be y 4x/4y = 1/5 x/y = 1/5 y = 5x area of larger = 250 y^2 = 250 y = √250 = 5√10 then 5x = 5√10 x = √10 perimeter = 4x + 4y = 4√10 + 20√10 = 24√10 or appr 75.9 m
September 28, 2014

Geometry
This is a more difficult problem than it first appears. Here is a complete solution to your problem using a radius of 10 Change the appropriate numbers to suit your solution http://www.analyzemath.com/Geometry/circles_problems.html
September 28, 2014

Pre-Calc
f(x) = 3x^2 + 2x + 4 whatever replaces x, replace it in the algebraic expression f(♠) = 3♠^2 + 2♠ + 4 f(☂) = 3☂^2 + 2☂ + 4 f(2) = 3(2)^2 + 2(2) + 4 = 20 follow the same pattern: f(a+h) = 3(a+h)^2 + 2(a+h) + 4 = 3(a^2 + 2ah + h^2) + 2a + 2h...
September 27, 2014

quanta tive skills and reasoning
N(math) + N(psych) - N(math AND psych) = N(math OR psych) 140+85-65 = N(math OR psych) = 160 (the 250 did not enter the picture unless you want to note that 90 took neither math nor psych )
September 27, 2014

Math plz help.
1, correct 2. correct 3. F 4. B 5. A 6. C
September 27, 2014

Algebra
number of ounces of $1 stuff --- x 4(40) + 1(x) = 2.2(40+x) solve for x, you should get x = 60
September 27, 2014

Pre-Calc
Wow , that would be overkill, but anyway .... first of all , it is very difficult to write it in matrix form in this format, so you would have the matrix 3 2 2-4 multiplied by the column matrix x y = 14 4 I will assume you know how to find the inverse of a 2by2 matrix, and how...
September 27, 2014

Pre-Calc
I would double the first then add that to the 2nd to get 8x = 32 x =4 sub into the first: 12 + 2y = 14 2y = 2 y = 1 x=4, y =1 check by subbing those values into both equations, they should work
September 27, 2014

Calculus
the whole problem becomes trivial when you realize that (0,0) does not lie on y = lnx If you recall your properties and definition of logs, you know that we can only take logs of positive numbers, that is, ln (0) is undefined. Your method is correct until you come to the point...
September 27, 2014

Math. I have a question.
2l+2w=800 l+w=400 so he can build an infinite number of such rectangles as long as the length + width = 400 e.g. 1 by 399 2 by 398 3 by 397 ... .1 by 399.9 .01 by 399.99 etc if you allow sides with non-integer values.
September 27, 2014

algebra
shortest side --- x each of the other sides --- 3x x + 3x + 3x = 126 7x = 126 carry on ....
September 26, 2014

algebra
amount of $8 coffee --- x amount of $ 4 coffee -- 60-x 8x + 4(60-x) = 5.25(60) 8x + 240 - 4x = 315 4x = 75 x = 18.75 lbs
September 26, 2014

Trigonometry
8% = 8/100 = .08 so tanØ = .08 Ø = 4.57 = 4.6° to the nearest tenth
September 26, 2014

math
You don't define what your x is, so your equation makes no sense to me. The left side of your equation has units of distance, while your right side is speed, thus it is gibberish. If x is the time needed the distance covered by the slower car = 15 + 50x the distance ...
September 25, 2014

Math URGENT QUICK QUESTION
9-6x-3x^2 notice the common factor of -3 = -3(x^2 + 2x - 3) = -3(x + 3)(x - 1) x^2 - 8x + k If we have 1x^2 at the front, then the sum of the roots equal the coefficients of the middle term, and the product of the constants. so x^2 - 8x +7 ?? two numbers that have a sum of -8 ...
September 25, 2014

calculus 1
According to your answer of a positive dy/dt, the laddder would be sliding UP the wall. Since the ladder is sliding away from the wall along he ground, dx/dt should be +4 ft/sec which would make dy/dt = -3 ft/sec, showing that y is decreasing, thus sliding DOWN the wall as ...
September 25, 2014

algebra
let the distance be x nautical miles x/12 + x/10 = 8.8 times 60 5x + 6x = 528 x = 48 n miles. check: one way = 48/12 = 4 hrs other way = 48/10 = 4.8 , for a total of 8.8 hrs
September 25, 2014

Calculus I
A function is even if f(-a) = f(a) a function is odd if f(-a) = -f(a) f(a) = a^3(a^3) + a^3 = a^3(a^3 + 1) f(-a) = -(a^3)(a^3) - a^3 = - (a^3)(a^3 + 1) notice that abs(a^3) is always positive So what do you think? You might try it with numbers, e.g. f(2) = 8(8) + 8 = 72 f(-2...
September 23, 2014

Algebra
Let the amount of the 4.50 coffee be x lbs 7.5(20) + 4.5x = 5(20+x) solve for x
September 22, 2014

math
questions in 2nd test --- x so 48/x = (1/2)(24/25) 48/x = 24/50 24x = 2400 x = 100 There were 100 problems check: 1st test = 24/25 = 96% 2nd test = 48/100 = 48% , which is 1/2 of 96%
September 18, 2014

Algebra 2
use brackets please (x/4 - 4/x) / (1 - 4/x) = (x/4 - 4/x) / (1 - 4/x) * (4x)/(4x) , actually multiply by 1 =(x^2 - 16)/(4x-16) = (x+4)(x-4)/(4(x-4)) = (x+4)/4 , x ≠ 4
September 18, 2014

Algebra 2
(5√7)/(√6) = (5√7)/(√6) * √6/√6 = 5√42/6 A good idea is to check your answer with your calculator evaluate the original, then evaluate your simplified answer, you MUST get the same answer.
September 18, 2014

math
let the original fraction be a/b equation #1: (a - 3)/b = 1/2 b = 2a - 6 equation #2: (a+5)/(b+7) = 3/4 4a + 20 = 3b + 21 4a - 3b = 1 sub in #1 4a - 3(2a-6) = 1 4a-6a+18 = 1 -2a = -17 a = 17/2 b = 2(17/2)-6 = 11 our fraction is (17/2)/11 = 17/22 When we check with 17/22, we ...
September 18, 2014

science/math
your numeral answer is correct (actually -7/3) As I noted in an earlier post, since it asks for the skater's "acceleration" and he slows down to a stop , your answer should be expressed as a negative so a = -2.3
September 18, 2014

science/math
I get 2.571 , which would be 2.6 correct to one decimal place
September 18, 2014

science/math
correct, assuming the runner starts from rest your answer should be in m/s^2
September 18, 2014

science/math
your of acceleration should be 8 m/s^2 your answer is correct
September 18, 2014

Math
did you mean y = -.25x + 5 ? several ways to do this, here is a way that is simple to understand Let's take two points on the line x = 0, y = 5 ---> (0,5) x = 4, y = 4 ---> (4,4) when we reflect across the x-axis, the x values stays the same, but the way values ...
September 18, 2014

science/math
Here is my mathematical approach physics has nice formulas for this v = at + c when t = 0, v = 25 so 25 = 0+c c = 25 then v = at + 25 when t = 10 , v = 6 6 = 10a + 25 10a = -19 a = -1.9 Whenever you see the word deceleration (things slow down) you can expect a negative result...
September 18, 2014

Algebra1
divide by -3 |2x+6| = 4 so 2x+6 = 4 OR -2x -6 = 4 ---> 2x = -2 , x = -1 or ---> -2x = 10 , x = -5
September 17, 2014

math
speed of plane --- x speed of wind ---- y 3927/(x+y ) = 7 ---> 7x + 7y = 3927 3437/(x-y) = 7 ----> 7x - 7y = 3437 add them 14x = 7364 x = 526 then but subbing in x - 526 into either equation y = 34
September 17, 2014

Analytic Geometry
divide by 9 x^2/(1/9) + y^2 = 1 a^2 = 1/9, a = ±1/3 b = ±1 so we have an ellipse with the major axis as the y-axis vertices: on x-axis ( 1/3,0) , (-1/3 , 0) on y-axis (0,1) , (0,-1) foci: c^2 + (1/3)^2 = 1^1 c^2 = 1-1/9 = 8/9 c= ± (2√2)/3 this will ...
September 17, 2014

Linear Algebra
t1(1,1) + t2(1,-1) = (13,-12) (t1,t1) + (t2,-t2) = (13,-12) (t1+t2 , t1 -t2) = (12, -12) so t1+t2 = 13 t1-t2 = -12 add them 2t1 = 1 t1 = 1/2 subtract them 2t2 = 25 t2 = 25/2 b) using he results of above replace 13 with x1 and -12 with x2 and repeat my steps
September 17, 2014

Algebra 1
4x^2 - 1 It is essential that you recognize and memorize the difference of squares pattern for your factoring skills
September 17, 2014

math
let the shortest be x inches let the longest piece be x+39 let the other piece be (1/2)(x+39) x + x+39 + (1/2)(x+39) = 132 don't like fractions, so multiply everybody be 2 2x + 2x + 78 + x+39 = 264 5x = 147 x = 29.4 inches shortest is 29.4 inches longest is 68.4 inches ...
September 17, 2014

Pre-Calculus
3 strikes ... 1. slope AB = (2-0)/(-2-3) = -2/5 slope CD = (4+1)/(-1+3) = 5/2 So perpendicular 2. slope AB = (1+3)/(1-4) = -4/3 slope CD = (1+3)/(2-5) = -4/3 so parallel 3. slope EG = (2-0)/(-3-2) = -2/5 so slope of perpendicular is 5/2 Looks like somebody has some serious ...
September 14, 2014

ccs trigo
info missing
September 14, 2014

Math
looks like Damon lost about $10,000 interest should have been $9,998.80
September 13, 2014

maths
I disagree with your reasoning. I read it that she spent 2/5 of her pocket money on a necklace so she spent 6 on a necklace So far she has spent 5 + 6 or 11 leaving her with £ 4 or 1/3 + 2/5 = 11/15 leaving 4/15 (4/15)(15) = 4
September 13, 2014

Math
looks like y = x^3 for x < 0 , y = -x^3 for x ≥ 0 to me
September 12, 2014

Pre-Calculus
I agree with your choices
September 12, 2014

Algebra 3-4
time of burn of 2nd stage = x seconds time of burn of 1st stage = x+28 x + x+28=152 2x = 124 x = 62 2nd stage takes 62 seconds 1st stage is x+28 = 62+28 = 96 sec
September 12, 2014

Algebra
Sam, did you not see Steve's reply? why not try some values? e.g. let a = 4, b = 5 then 2ab= 2(4)(5) = 40 a^2 + b^2 = 16 + 25 = 41 so what do you think?
September 12, 2014

Algebra
let's assume that the silo will be totally filled including the hemisphere. radius of cylinder and hemisphere is 15 let the height up to the hemisphere be h ft πr^2 h + (1/2) (4/3)πr^3 = volume π(15)^2 h + (2/3)π (15)^3 = 10800 225πh + 2250π...
September 12, 2014

College Algebra
rate of current --- x mph let the distance each way by y miles so upstream distance: y = (24/60)(5-x) downstream distance y = (16/60)(5+x) but they are both equal to y, so 24(5-x)/60 = 16(5+x)/60 times 60 24(5-x) = 16(5+x) 120 - 24x = 80 + 16x -40x = -40 x = 1 So the current ...
September 12, 2014

Algebra 1
amount of 10% solution ---- x L amount of 60% solution ---- 200-x L .1x + .6(200-x) = .5(200) times 10 x + 6(200-x) = 5(200) x + 1200 - 6x = 1000 -5x = -200 x = 40 check: .1(40) + .6(160) = 4+96 = 100 which is 50% of 200L
September 12, 2014

math
2=1(1+.127/2)^2t , where t is half-years (2t is years) 2 = (1+.127/2)^2t log2=log (1+.127/2)^2t by the rules of logs ... log2=2t log(1+.127/2) 2t = log2/log(1.0635) 2t = 11.26 So it would take about 11 1/4 years or 11 years and 3 months
September 11, 2014

math
The amount of salt stays the same .20(110-x) = .12x times 100 20(110-x) = 12x 2200 - 20x = 12x 2200 = 32x x = 68.75
September 11, 2014

math
distance to island --- n miles x/11 + x/10 = 4.2 times 110 10x + 11x = 462 x = 22 nautical miles
September 11, 2014

math
I suspect a typo
September 11, 2014

math
done, look for your other post
September 11, 2014

math
done, look for you other post
September 11, 2014

Trig
Make your sketch, label the person nearest the obelisk as A and the person's position as B Top of obelisk as P and its bottom as Q. Look at triangle PAB angle B = 44 angle PAB = 180-65 = 115 then angle APB = 21 by the sine law: AP/sin44 = 25/sin21 AP = 25sin44/sin21 In the...
September 10, 2014

math
400 m in 1min, 32 sec = 92 seconds so 100 m in 92/4 or 23 seconds you did not specify what rate we are talking about m/s or s/m or ...
September 10, 2014

Math
Using trig: let the speed be x km/h after making your diagram, x^2 = 10^2+3^2 - 2(10)(3)cos 135° = 151.426... x = 12.3 km/h angle: using the sine law: sinØ/3 =sin135/12.3055 sinØ = .17238... Ø = 9.9266.. direction angle would be S (45-9.93)° E ...
September 10, 2014

Math Problem (please help)
rate = 8.12/115.99 = .070006035 but since the $8.12 was most likely rounded off to the nearest cent, I would say it was .07 or 7% so y = .07x so when x = 530.50 y = .07(530.50) = $37.14
September 10, 2014

Math!
mmmhhh, let's see if 2 hours make sense. to go another 2 hours at 55 mph, would take you another 110 miles, but you already went 275, so you went 110 + 275 or 385 miles. Looks like you stood up your friend. Why not just solve the simple equation given??? 55h + 275 = 440 ...
September 9, 2014

Math
2[4(9-7)+1]/3 = 2[4(2)+1]/3 = 2[8+1]/3 = 2[9]/3 = 18/3 = 6
September 9, 2014

Math Problem (please help)
I = kA when A = 4250, then I = 106.25 106.25 = k(4250) k = 106.25/4250 = .025 I = .025A
September 9, 2014

Math - Finding the Equation
(g∘f)(x) = g(f(x) ) = g(x+2) = -(x+2)^2 + 2(x+2) - 3 = -x^2 - 4x - 4 + 2x + 4 - 3 = -x^2 - 2x - 3 (g∘f)(-2) = -4 + 4 - 3 = -3 or f(x) = x+2 f(-2) = -2+2 = 0 then g(f(-2)) = g(0) = -0+0-3 = -3
September 9, 2014

7th grade math
let x be that fraction a/b so (5/6)/x = 1/4 then by cross-multiplying x = 4(5/6) = 20/6 = 10/3 so your fraction a/b = 10/3 check: (5/6) ÷ (10/3) = (5/6)(3/10) = 15/60 = 1/4 My answer is correct You should always check your answer in similar ways if possible
September 9, 2014

Math Problem (please help)
A fraction can only be zero if its numerator is zero so x^3 - 64 = 0 difference of cube factoring .... (x-4)(x^2 + 4x + 16) = 0 x = 4 or x = (-4 ± √(16- 64) )/2 x = 4 or x = -2 ± 4√3 i so the graph should cross the x-axis only once, at x = 4 ...
September 9, 2014

Math
1 p(1.045)^20 = 30000 p = 30000/1.045^20 = 12439.29 2. same method as #1 3. amount = 100(.5)^(15/25) = 65.98 g
September 9, 2014

math help
odd numbers differ be 2 let the first of the odd numbers be x then the next two odds are x+2, and x+4 x + x+2 + x+4 = 435 3x = 429 x = 143 so the largest is x+4 = 143+4 = 147
September 9, 2014

Math
so you want 40+39+38+...+1 or 1+2+3+...+39+40 a = 1, d = 1 for n=40 sum(40) = (40/2)(first + last) = 20(1+40) = 820
September 9, 2014

Math
total distance fallen = 16t^2 , where t is in seconds after 1 second --- 16(1)^2 = 16 after 2 seconds --- 16(2^2) = 48 after 3 seconds --- 16(3^2) = 144 Where did you get your data from, it certainly is not from this earth. But .... ignoring the silliness of your data, you ...
September 9, 2014

Algebra
In all 3 questions you are using the same formula term(n) = a + (n-1)d 1. term(101) = x-y + 100(2x+y-3) = x-y+200x + 100y - 300 = 201x + 100y - 300 2. a=2 , d=4 2 + (n-1)(4) = 106 4n-4 = 104 4n = 108 n = 27 It is the 27th term 3. give this one a try yourself
September 9, 2014

Math
x^3 , when x = -3 = (-3)^3 = -27 btw, you meant to say "How would I write this ? "
September 9, 2014

Math
Ms Sue answered this a while back http://www.jiskha.com/display.cgi?id=1409874255
September 9, 2014

algebra
.6L + .2(200-L) = .5(200) solve for L
September 9, 2014

math
width --- x length --- 4x - 4 2x + 2(4x-4) = 62 solve for x
September 9, 2014

MATH word prob!
let the amount to be added be x gal .7x + .23(30) = .6(30+x) times 100 70x + 23(30) = 60(30+x) 70x + 690 = 1800 + 60x 10x = 1110 x = 111 gallons
September 9, 2014

Math - Equation of the circle
the centre must be the midpoint of the diameter which would give you (1, -4) so the equation must be (x-1)^2 + (y+4)^2 = r^2 sub in one of the points on the circle , I will use (-3,6) (-4)^2 + (10)^2 = r^2 r^2 = 16+100= 116 so (x-1)^2 + (y+4)^2 = 116 check by subbing in the ...
September 9, 2014

Algebra
r = (1/27) ÷ (1/81) = 3 so the series diverges, that is, the terms are getting larger. Think about adding terms that keep getting larger. Clearly the sum will get larger and larger and eventually become infinitely large. That is why for the formula Sum (infinite number ...
September 9, 2014

Algebra
correct
September 9, 2014

Algebra
Just looked at the first of the "Related questions" below, which I had answered in June, and realized that your _____ , meant that -243 was actually the second term I am pretty sure you can make the suitable adjustments. (your first term will be -260)
September 9, 2014

Algebra
a = -243 d = -226 - (-243) = 17 term(67) = a + 66d = -243 + 66(17) = 879 sum(n) = (n/2)(2a + (n-1)d) sum (27) = (27/2)(-486 + 26(17)) = -594 Here is a nice new part to the question: For which terms does the sequence switch from negative to positive ?
September 9, 2014

Algebra
strange question. since she uses 8 cups of water for 15 plants, each plant will get 8/15 cups of water. Where does the $35 water bill enter the picture ???
September 9, 2014

Math
1. correct in interval notation in standard notation: -7 < x < 7 - when written in this notation, the word "and" is used 2. |x| ≥ 7 x ≥ 7 OR -x ≥ 7 x ≥ 7 or x ≤ -7 so yes, you are correct ( I don't like the way you showed your ...
September 9, 2014

math
amount of weaker solution --- x L amount of stronger solution -- (600-x) solve for x .025x + .1(600-x) = .05(600)
September 8, 2014

MATH HELP
ummhhh loads after day 1 = 46-8 = 38 loads after day 2 = 38-8 = 36 ....
September 8, 2014

math
Preliminary decision: In the first equation, both terms are positive, so to get zero as a sum , one must be + , the other - That rules out #1 and #2. Try subbing in the other pairs.
September 8, 2014

algerbra
done, look at your other post of this same problem
September 8, 2014

Calculus
You did not say where your difficuly lies. Can you find the integral or do you already have that ?
September 8, 2014

Calculus
so area = integral (x^2 - mx + 1) dx from 0 to 5 = x^3 /3 - (m/2)x^2 + x from 0 to 5 = (125/3 - 25m/2 + 5) - (0-0+0) but this equals 11.3024 times 6 250 - 75m + 30 = 67.8144 -75m = -212.1856 m = 2.8291
September 7, 2014

math
expand first 4(2g + 104) - 96 = 504 + 6(g - 14) 8g + 416 - 96 = 504 + 6g - 84 collect like terms and simplify 8g + 320 = 6g + 420 terms on one side, constants on the other side 8g - 6g = 420 -320 2g = 100 g = 50
September 7, 2014

math
Let each side of the base be x ft, and its height be h ft Volume = x^2 h 30/x^2 = h cost of base = 33x^2 cost of sides = 10(4)(xh) = 40x(30/x^2 = 1200/x cost of top = 24x^2 cost = 57x^2 + 1200/x
September 7, 2014

pre algebra
Can you find any numbers other than 1 and 97 itself which divide evenly into 97 ? If you cannot, then 97 is prime.
September 7, 2014

math
1 mechanic can do 4 machines in 6 hours - then 48 mechanic can do 192 machines in 6 hours - then 48 mechanic can do 192(160/6) or 5120 machines in 160 hours
September 7, 2014

geometry
= (1/8)(w)(u + v)
September 7, 2014

Math
5n + 10d + 25q = 12.85 d + q > 2d
September 7, 2014

Math - Urgent
I will rephrase the question: You owe your Mom 10 dollars. You borrow some more and you now owe her $17 How much more did you borrow ?
September 7, 2014

math
A number is divisble by 4 if its two right-most digits are divisible by 4 So our number can only end in 12 , 16, 24, 28, 32, 36, 40, 44, 48, 52, 56, .... , remember that each digit in the whole number is such that it is 1 less than the digit on its right only 56 fits that ...
September 7, 2014

math
m+t+w=39*3 = 117 , (how did you get 108 ?) w+th+f+s = 4*39.5 = 158 add them m+t+2w+th+f+s = 275 , but m+t+w+th+f+s = 9*40= 240 subtract them w = 35
September 7, 2014

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