Tuesday
May 31, 2016

Posts by Reiny

Total # Posts: 34,845

prealgebra or algebra1
Easiest way: since the lines are parallel, they would differ only in the constant so the equation is 4x + y = c plug in the given point to find c and you are done
March 24, 2016

Trigonometry
b) correct, the period would be 2π/60π = 1/30 c) when t = 3 d = (1/12)sin (180π) = 0 d) sin(60πt) = 0 when t = 0 , 1/30, 1/15 ... so the first positive value is 1/30
March 24, 2016

math
really ?
March 24, 2016

Geometry
The wording of this question is not clear It does not say if the sides of 15 and 18 are the parallel sides, or if they are adjacent sides. I must conclude that they are adjacent sides or else the height between them would be constant area of ||gram is base x height so 15(9) = ...
March 24, 2016

Check Mathh Answers!!
I agree with all you answers except #4 #4 , the outlier is 1.5
March 24, 2016

Math
I agree with what you have so far, other than skipping the integral sign and the dx from the last term. You seem to have the concept however. ∫e^(3x) sin(2x) dx = (-1/2)e^(3x)cos(2x) - ∫(-1/2)(3e^(3x))(cos(2x) dx = (-1/2)e^(3x)cos(2x) + (3/2)∫ e^(3x) cos(2x) ...
March 24, 2016

trigonometry
2sin^2 A + 5cosA = 4 2(1 - cos^2 A) + 5cosA - 4 = 0 2cos^2 A - 5cosA + 2 = 0 (2cosA -1)(cosA - 2) = 0 cosA = 1/2 or cosA = -2, the latter is not possible, so cosA = 1/2
March 23, 2016

Algebra, functions
to have one root, (actually two equal roots) b^2 - 4ac = 0 k^2 - 4(1)(5) = 0 k^2 = 20 k = ± √20 = ± 2√5 check: x^2 + 2√5x + 5 = (x + √5)^2 x^2 - 2√5x + 5) = (x - √5)^2
March 23, 2016

math
change in volume = 15x20x3 cm^2 which must have been caused by the volume of the rock.
March 23, 2016

algebra
your notation clearly did not show up as you intended. I will guess you meant: (b+7)/(b+4) = c/9 c = 9(b+7)/(b+4) I have this very old fashioned computer language called BASIC. I ran a stupid little program for b = -5000 to b = 5000 and it found the following pairs (b,c) >...
March 23, 2016

Geometry
Make a side-view of the pyramid, and drop a perpendicular. let the side of the base be 2x, (that way I don't have fractions in my variable) in the right-angled triangle tan 52° = 147/x x = 147/tan52 = ... then base side = 2x = ....
March 23, 2016

Calculus
You don't describe the diagram, but I am familiar with this type of question. Assuming there is a common width between the two fields let the width be x ft let the length of the combined field be y so 3x + 2y = 1200 y = 600 - (3/2)x area = xy = x(600 - (3/2)x) = 600x - (3/...
March 23, 2016

Math
Ruth's speed --- x km/h Tom's speed --- x+10 km/h in two hour: Ruth went 2x km Tom went 2(x+10) km solve for x 2x + 2(x+10) = 308
March 23, 2016

trig
No, it isn't the simplification of the expression is -1/sinx, as you can see from my steps however, if -1/f(x) = -1/sinx then f(x) = sinx
March 23, 2016

trig
I will "simplify and write the trigonometric expression in terms of sine and cosine" the part "=-1/f(x)=f(x)=____________ " makes little sense to me cot(-x)cos(-x)+sin(-x) = (cos(-x))/sin(-x))(cos(-x) + sin(-x) = (cosx/-sinx)(cosx) - sinx = - cos^2 x/sinx...
March 23, 2016

math
I certainly would not want to support laziness, so I will not answer you question. Why would you possible need papers to find 5/6 times 12 I did that in my head in about 3 seconds
March 23, 2016

Bus. Math
What is a rate of 9-15/18? Did you mean consecutive discounts of 9%, 15%, and 18% ? if so final percentage = .91(.85)(.82) = .63427 or 63.427% of the original price looks like b) is correct and you are right.
March 23, 2016

Math
A meaningless question. The value of c can be any real number to have a quadratic expression. "TheKnowItAll" found the value of c so that the expression becomes a perfect square, but that was not the question.
March 23, 2016

math !
surface area = 2lw + 2lh + 2wh = NOT 1134.375 , I get 731.5
March 23, 2016

mathematics-slope of tangent
differentiate implicitly, x^2 + xy + y^2 = 4 2x + x y' + y + 2y y' = 0 y' (x + 2y) = -2x - y y' = (-2x-y)/(x+2y) for (2,-2) y' = (-4 + 2)/(2 -4) = -2/-2 = 1
March 23, 2016

Algebra II
q = k(1/m^2)(rx) plug in the given values 2.5 = k(1/16)(8) solve for k
March 23, 2016

Algebra II
Did you find the equation for the flight path of the plane ? Did you find the equation of the parabola? Did you solve the two equations and got a real answer? If you have a solution, the the plane intersects the closed airspace. If you have no solution ...... etc
March 23, 2016

MATH
different shapes: 1 1 12 1 2 6 1 3 4 2 2 3 number of different bases for each one: 1 1 12 --->1 1 12, 1 12, 1 ----- 2 of them 1 2 6 ---> 1 2 6, 1 6, 2, 2 6 1 --- 3 of them 1 3 4 ---> 1 3 4, 1 4 3, 3 4 1 --- 3 of them 2 2 3 ---> 2 2 3, 2 3 2 ----- 2 of them 10 ...
March 23, 2016

Math
good job, they were all correct
March 23, 2016

division and remainder...error ws from my teacher not me
Sum(1) = 1 = 1mod5 sum(2) = 1 + 2^2 = 5 = 0 mod5 sum(3) = 5 + 3^3 = 32 = 2 mod5 sum(4) = 32 + 4^4 = 288 = 3 mod5 To divide by 5 all we need to do is look at the last digit. If the digit is form 0 to 4, then that digit is the remainder when dividing by 5 If the digit is from 5 ...
March 23, 2016

maths
for the additions, the common denominator is 60 grind out the sum of the inner bracket then multiply that by 5/8, simplify if needed finally multiply that by 8 let me know what you got, so I can check it for you btw, are you sure that -4/5 is not supposed to be +4/5 ?? It ...
March 23, 2016

geometry
None of the answers given are correct by the cosine law: f^2 = 8^2 + 13^2 - 2(8)(13)cos72° = 168.724... f = 12.989398... by sine law: sinG/8 = sin72/12.989... sinG = .58574... G = 35.86° correct to 2 decimals With modern calculators, there is no reason to round off ...
March 23, 2016

@ Steve - trigonometry
Steve, I worked on this for a while this morning, and I got that far as well. I also noticed that sinA = .618033989.. which is the decimal part of the golden ratio (1+√5)/2, ... interesting from xsinA= ycosA I had y/x = sinA/cosA = tanA from xsin^3A=y I had y/x = sin^3 A...
March 23, 2016

trigonometry
Did you mean: (tanA - sinA)/tan^2 A = tanA/(1+cosA) the way you typed it, it is not true LS = (tanA-sinA)/sin^2 A = (sinA/cosA - sinA)/sin^2 A = ( (sinA - sinAcosA)/cosA) /sin^2 A = (sinA(1 - cosA)/cosA)/sin^2 A = (1 - cosA)/(sinAcosA) RS = (sinA/cosA) / (1 + cosA) = (sinA/...
March 22, 2016

Arithmetic progression
S(n) = (n/2)(2a + (n-1)d) = 2n divide by n and double 2a + (n-1)d = 4 S(2n) = (2n/2)(2a + (2n-1)d) = n divide by n 2a + (2n-1)d = 1 subtract these two equations, (n-1)d - (2n-1)d = 3 nd - d - 2nd + d = 3 -nd = 3 nd = -3 S(4n) = (4n/2)(2a + (4n-1)d) = 2n(2a + 4nd - d) = 2n(2a -...
March 22, 2016

math
1st: Where did you get the denominator of 40 from, isn't it 9/20 ?? 2nd: correct 3rd: prob(odd and less than five) = 2/6 = 1/3 so out of 12 tries, (1/3)12 = 4 correct
March 22, 2016

Math
amount = 2000(1 + .05/4)^20 = ...
March 22, 2016

Math Probability
done, check further up in the listing for your later post
March 22, 2016

Algebra
amount invested in the 2% account --- x amount invested in the 4% account = 1500-x solve for x .02x + .04(1500-x) = 44
March 22, 2016

probobility
a) no condition: 7x7x7x7 = 7^4 = 2401 b) no repeats: 7x6x5x4 = 840 c) begin with A, can I repeat the others ? I will assume I can: 1x7x7x7 = 343 d) same as c) 7x7x7x1 = 343 e) 2nd letter is a vowel 7x2x7x7 = 686 In c), d) and e) I assumed that letters can be repeated, you did ...
March 22, 2016

Math
Your equation makes no sense to me at all An equation only is useful and meaningful if the variable has been defined. Let the number of nickels be x then the number of dimes is 21-x Now for the value of those coins: 5x + 10(21-x) = 165 5x + 210 - 10x = 165 -5x = -45 x = 9 then...
March 22, 2016

math
Number of possible pairs chosen = C(21,2) = 210 number of ways to choose 2 of the 3 friends = C(3,2) = 3 prob(of stated event) = 3/210 = 1/70
March 22, 2016

math
notice that 10 is added to a term to obtain the next one, so -1, 9, 19, 29, 39, 49, 59, ... none of the given choices is correct C has 69 instead of 59 at the end, unless you have a typo
March 22, 2016

Algebra
let the smaller be x then the larger is x+2 3(x+2) + (1/2)x = 34 3x + 6 + (1/2)x = 34 multiply each term by 2 6x + 12 + x = 68 7x = 56 x = 8 state your conclusion
March 22, 2016

matth....
√4 = 2 , so it is rational The other three are irrational
March 22, 2016

math
width ---- x length ----3x-4 perimeter = 2widths + 2 lengths 56 = 2x + 2(3x-4) carry on
March 22, 2016

remainder help!@steve and damon
Do you have a typo? your first 3 terms have exponents of 2, but the last term is 10^10. I will assume it is to be 10^2 sum of all squares up to n terms = n(n+1)(2n+1)/6 so if n = 10, sum = 10(11)(21)/6 = 385 which when divided by 5 leaves a remainder of zero
March 22, 2016

Algebra 2
Make sure you include brackets in your solution, at first look your equation made little sense. 4^(2b-3) = 8^(1-b) (2^2)^(2b-3) = (2^3)^(1-b) = 2^(4b-6) = 2^(3-3b) thus 4b-6 = 3-3b 7b = 9 b = 9/7 how did you get -9/7 ??
March 22, 2016

Math please help
Since she has 100 stamps in total, the number of stamps for each country matches the percentage for that country e.g. she has 24 French stamps and 29 Norwegian stamps Can you now answer the question?
March 22, 2016

Math
Let the total be x children = (2/5)x women = (5/8)(3/5)x = (3/8)x children + women + men = total (2/5)x + (3/8)x + 90 = x multiply each term by 40 16x + 15x + 3600 = 40x continue ....
March 22, 2016

maths
I constructed my trap ABCD, so that AB=5, BC=4, CD=8, and DA=6 with BC and AD both having a negative slope, (leaning to the left) I dropped perpendiculars from B and from A to meet CD at M and N respecively. (M is on the extension of DC) I let MC = x, then ND = 3+x Notice that...
March 22, 2016

maths
ax2+bx+c=0 ax^2 + bx = -c <--- subtracted c from both sides x^2 + (b/a)x = -c/a <--- divide everybody by a x^2 + (b/a)x + b^2/(4a^2) = -c/a + b^2/(4a^2) <--- "completed the square" (x + b/(2a) )^2 = (b^2 - 4ac)/(4a^2) <---simplified x + b/(2a) = ±...
March 22, 2016

math help pls pls pls
I see an x^5 in A and in C
March 21, 2016

math help pls pls pls
show powers like this: x^4 now in which expression do you see x^5 as the highest term ??
March 21, 2016

math help pls pls pls
Would it not be much easier to type : 15x^2 y^6 + 50x^4 y^3 - 20x^2 y ? You appear to have forgotten the divisor
March 21, 2016

Algebra 2
You need brackets to establish the correct order of operation (x^2-9)/(x^2-5x) (5x-x^2)/(x^2-x-12)(x^2-8x+16)/(x-4) = (x+3)(x-3)/(x(x-5)) (x)(5 - x)/((x-4)(x+3)) (x-4)(x-4)/(x-4) = -(x-3) , x ≠ 0, ±3, 4, 5 or = 3-x , x ≠ 0, ±3, 4, 5 Don't use the ...
March 21, 2016

Algebra
the -7 + i has a conjugate partner of -7 - i so (-7+i)(-7-i) = 49 - i^2 = 50 -7+i + (-7-i) = -14 so we can form the quadratic as x^2 + 14x + 50 as one of the factors. the other is (x+9) so the polynomial could be f(x) = (x+9)(x^2 + 14x + 50)
March 21, 2016

Algebra
what about it ? It is in point-slope form. Are you bothered by the decimals and/or the fraction ?
March 21, 2016

Math
Jerry has been doing these push-ups for quite some time, as you can see in the Related Questions below. Only the numbers keep changing. Change the solution here to fit your problem http://www.jiskha.com/display.cgi?id=1452469132
March 21, 2016

Math
at least 2 reds ---> 2 reds, or 3 reds, or 4 reds, or 5 reds or exclude 0 red and 1 red There are 20 cards of which 10 are red prob(red) = 10/20 = 1/2 number(no red) = C(10,0) C(10,5) = 252 number (1 red) = C(10,1) C(10,4) = 2100 number of 5-card hands without restriction...
March 21, 2016

Math
A - correct B - I assume we can now use the 1 ?2?4? , so we can use only 7 other digits number of ways = 7x1x6x1x5 = 210 c - correct D - evens at front and end 4x?x?x?x3 , leaves 7 for the other places= 4x7x6x5x3 = 2520
March 21, 2016

Math
makes no difference, you can do both ways in your head, since (anything)^0 = 1 you will get 1
March 21, 2016

Math
1 : 24 ---> 1/2 : 12
March 21, 2016

Precal
LS = cosx/(1+sinx) + cosx/(1-sinx) = ( cosx(1 - sinx) + cosx(1+sinx) )/(1 - sin^2 x) = (cosx - sinxcosx + cosx + sinxcosx)/cos^2 x = 2cosx/cos^2 x = 2/cosx = 2secx = RS
March 21, 2016

Math
If 10 g is worth about $1 then 1 kg is worth about $100
March 21, 2016

Wrong - Math
We have 5 people If we treat Basil and Edna as a unit, we would be arranging only 4 which would be 4! or 24 But we could switch Basic and Edna around and they would still be together. So total number of ways = 2(24) or 48 ways
March 21, 2016

algebra
I am going to assume that the roof is 96 ft high, not 9696, and you want to know when the ball is 48 ft high, not 4848 so 48 = -16t^2 + 8t + 96 (the equation implies it was tossed upwards with a velocity of 8 ft/sec) 16t^2 - 8t - 48 = 0 2t^2 - t - 6 = 0 (2t + 3)(t - 2) = 0 t...
March 21, 2016

Math
You went for the most expensive oil. What made you decide it was A ? I am interested in your method.
March 21, 2016

Math
I can't seem to find your choice. Just divide the cost by the number of pints to get the unit cost. btw, the second case gives you the unit cost
March 21, 2016

maths
Let the distance for each section be x km time for the first leg = x/60 time for the 2nd leg = x/90 total time = x/60 + x/90 = (3x+ 2x)/180 = x/36 avg speed = total distance/total time = 2x/(x/36) = 2x(36/x) = 72 km/h notice it is not the average of the two speeds.
March 21, 2016

correction - Math
tanØ = 60/91 Ø = arctan(60/91) = 33.398° distance , using Pythagoras: d^2 = 60^2 + 91^2 = 11881 d= √11881 = 109 miles
March 21, 2016

Math
agree
March 21, 2016

Trigonometry
circumference = 24π inches so speed = 24π(620) inches/min = 14880π/(12(5280)) miles/min = 14880π/(12(5280)) miles/ (1/60) hrs = 44.27 mph check my arithmetic
March 21, 2016

geom
form the 100 ft into a circle.
March 21, 2016

oops - math
Never mind, ignore my reply. Did not notice the $ vs % symbols So If the price is $100 or less take the $10 off If over $100, then take the percentage discount
March 21, 2016

math
I don't understand. Doesn't the 10% coupon give you 10% off. What is the problem?
March 21, 2016

Trigonometry
sinacosa(sina/cosa + cosa/sin) = sin^2 a + cos^2 a = 1
March 21, 2016

Maths
slope = (4-3)/(-1-2) = -1/3 using that slope and the point (2,3) y-3 = (-1/3)(x-2) arrange into whatever version of line you learned. Sub (-1,4) into your equation to make sure it works
March 21, 2016

Math
No, Evan, I thought we had ruled out C Did you expand C before you decided? for C: (x+6)(x+5) = x^2 + 5x + 6x + 30 = x^2 + 11x + 30, not the given expression for B: (x+6)(x-5) = x^2 - 5x + 6x - 30 = x^2 + x - 30 , the given!!
March 21, 2016

Math
When I expand your choice of answer, I get x^2 - 11x + 30, so clearly not the right answer. you can tell from the -30, that the two constants must be of opposite sign, ruling out A and C Try expanding the other two
March 21, 2016

Classic case of homework dump - STATISTICS
I have just counted 14 questions all dealing with probability that you want us to answer. You have not indicated where your difficulty with these questions is, nor have you shown any effort or steps towards the solution of any of them. You really don't just want us to do ...
March 21, 2016

Math
at the lower end , that is, at x = 1 3^(1/3) = 1.44.. √2 = 1.414.. so ∛3x > √2x at x = 9/8 (27/8)^(1/3) = 3/2 = 1.5 √(18/8) = √(36/16) = 6/4 = 1.5 so for all values for 1 < x < 9/8 ∛3x > √2x They become equal at x = 9/8 as ...
March 21, 2016

Maths
So in effect the third of our circle becomes the curved surface area of the cone ( 120° = (1/3) of 360°) area = (1/3)π 42^2 = 588π cm^2
March 21, 2016

Math
Have you learned the binomial theroem? If not, follow this pattern (3-x)^7 = C(7,0) 3^7 (-x)^0 + C(7,1) 3^6 (-x)^1 + C(7,2) 3^5 (-x)^2 + .... + C(7,6) 3^1 (-x)^6 + C(7,7) 3^0 (-x)^7 = 1(3^7)(1) - 7(3^6)x + ... + 7(3)x^6 - x^7 You might also want to look into how Pascal's ...
March 20, 2016

Pre-Calc
recall that if we have an equation factored equal to zero, then roots can be obtained by setting each of the factors equal to zero e.g. if (x-6) is a factor, then x = 6 is a root so reverse your thinking. If the roots are 2 and 1, then the factors must have been (x-2) and (x-1...
March 20, 2016

Algebra
number = 2^t so 2^t = 1,000,000 take log of both sides and use log rules t log2 = log 1,000,000 t = 6/log2 = 19.9 minutes it would take appr 20 minutes
March 20, 2016

Math
you should be familiar with the "choose" notation. What is C(15,11) ?
March 20, 2016

Math
reds --- x greens -- 3x blue ---- x/2 yellow --- x/2 x+3x+x/2+x/2 = 10 5x = 10 x = 2 2 reds 6 greens 1 blue 1 yellow prob(red) = 2/10 = 1/5 etc
March 20, 2016

Maths
"I am between 400 and 500" ---> 4XX "My middle digit is a prime number" ---> 42X 43X 45X 47X "My digits are descending order" ---> 43X 42X "The sum of my digit is 9" ---> 432 "I am divisible by 6" Yup, redundant ...
March 20, 2016

math
x ∝ y^3 ---> x = ky^3 , where k is a constant given: y=2 when x=1 1 = 8k k = 1/8 x = (1/8)y^3 when y = 1 x = (1/8)(1^3) = 1/8 when x = 108 108 = (1/8)y^3 864 = y^3 y = appr 9.5244
March 20, 2016

Math
A 5 cent coin is called a nickel not a Nichol. 10 dimes 5 nickels 1 penny Prob(dime, then penny) = (10/16)(1/16) = 5/128 I recommend that you check your typing, spelling, and grammar in any future posting. e.g. bag --> back -->bad
March 19, 2016

math
3w + 2c = 11 5w + 6c = 23 first times 3: 9w + 6c = 33 2nd as is : 5w + 6c = 23 subtract them: 4w = 10 w = 2.50 sub back into first to find c
March 19, 2016

Math
There will be 13 terms, so the middle term is term #7 Term(7) = C(12,6)(2x)^6 (3y)^6 = 924(64x^6)(729y^6) = 43110144 x^6 y^6
March 19, 2016

Stupid Math School Math
let the distance covered by the slower car be x miles then the distance covered by the faster car be 750-x miles time for slower car = x/40 time for faster car = (750-x)/50 aren't those times the same ??? so ... x/40 = (750-x)/50 cross-multiply and solve for x Once you ...
March 19, 2016

math
Eli, if this were a 4 mark question on my test, I would give you 1 mark for the answer. proper method: let Pari's age be x then Finn's age is x-9 x = 2(x-9) x = 2x - 18 -x = -18 x = 18 So Pari is 18, and Finn is 9
March 19, 2016

calc
height ------- h base radius --- h/3 V = (1/3)π r^2 h = (1/3)π (h^2/9)(h) = (π/27) h^3 dV/dt = (π/9) h^2 dh/dt for the given data: 15 = π/9 (100)dh/dt dh/dt = 135/(100π) ft/hr
March 19, 2016

sir damon help on these as well co-ordinate
r = 3, Ø = 150° cos150 = x/3 x = 3(-√3/2) = -3√3/2 sin150 = y/3 y = 3sin150 = 3(1/2) = 3/2 the point is (-3√3/2 , 3/2)
March 19, 2016

Math
y-x = x-8 y = 2x-8 z-y = y-x z = 2y - x = 2(2x-8) - x = 3x - 16 20-z = z-y y = 2z - 20 2x - 8 = 2(3x-16)-20 2x-8 = 6x - 32-20 4x = 44 x = 11 y = 22-8 = 14 z = 33-16 = 17 or, simplest way: 4d = 20-8 d = 3 so the terms are 8, 11, 14, 17, and 20 match the x,y, and z
March 19, 2016

Math
With relatively small numbers like in your problem, we could just "grind out" the answer in the following way: numbers which leave a remainder of 1 when divided by 3: 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 .... numbers which leave a remainder of 2 when ...
March 19, 2016

another correction - math
You would first of all have to expand a(x+2)^2 + b(x+2) + c = a(x^2 + 4x + 4) + bx + 2b + c = ax^2 + 4ax + 4a + bx + 2b + c = ax^2 + (4a+b)x + (4a + 2b + c) now compare: 3x^2 <---> ax^2 ---- a = 3 4a+b)x <---> -x 4a + b = -1 12+b = -1 b = -13 4a+2b+c = -9 12 - 26...
March 19, 2016

another correction - math
area = LW , not 2(L+W) that would be perimeter area = (5 - √12)(4 + 6/√3) = 20 + 30/√3 - 4√12 - 6√4 = 20 + 30/√3 *√3/√3 - 8√3 - 12 = 23 + 10√3 - 8√3 = 8 + 2√3 D^2 = (5-√12)^2 + (4+6/√3)^2 = (5...
March 19, 2016

correction - mathematics-logarithm
or log3 x^2 = -8 2 log3 x = -8 3 x = -4 x = 3^-4 x = 1/81 not 1/27 check with calculator if x = 1/27 3 (1/27)^2 = 23 (1/27) = 2(-3) = -6 ≠ -8 1/81 does check out.
March 19, 2016

Maths
You have conflicting data, as I will explain at the end Make a Venn diagram, with two overlapping circles, label them C and T enter 35 in the intersection. Since the T circle must contain 45, but you have already 35 entered , the part with only tea must be 45-35 or 10 Check ...
March 19, 2016

Math
from 1-20 number of primes is 8 number of perfect squares = 4 with no overlap so prob(primes or perfect squares) = 12/20 = 3/5
March 19, 2016

Geometry
a/4 = b/7 multiply both sides by 4 a = 4b/7 divide both sides by b a/b = 4/7
March 18, 2016

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