Saturday
April 19, 2014

Posts by Reiny


Total # Posts: 26,024

Math - Quart to Gallon Ratio
2.5 gallons = 320 oz punch : grape juice = 64 : 16 = 320 : g 64/16 = 320/g 4 = 320/g 4g = 320 g = 80 it would take 80 oz of grape juice number of quarts = 80/32 = 2.5 quarts (Editorial: Go metric to avoid such silly calculations)

math
original perimeter = 2L + 2w new length = 2L new width = 3W new perimeter = 4L + 6w 4L+6w - (2L+2w) = 92 2L + 4w = 92 L + 2w = 46 L = 46-2w area of original = lw = w(46-2w) = 46w - 2w^2

math
children tickets ---- x adult tickets ------- 3x 9x + 5.3(3x) = 872.10 take over from here

math
3hex + 4trap = 200 3hex = 200 - 4trap 1 hex = (200-4trap)/3 or 4trap = 200 - 3hex 1 trap = (200 - 3hex)/4

Math Pre-Cal
to know the "value" of the quadratic function, you must know the value of x simply plug in your given value of x and work it out.

Math Pre-Cal
Use the vertex form first y = a(x-h)^2 + k, where (h, k) is the vertex, so ... vertex is (1,-1) so f(x) = a(x-1)^1 - 1 but (2,2) lies on it, so 2 = a(2-1)^2 - 1 2 = a(1) - 1 3 = a so you have f(x) = 3(x-1)^2 - 1 now expand this ... f(x) = 3(x^2 - 2x + 1) - 1 = 3x^2 - 6x + 3 - ...

Math
let the height be h h^2 + 12^2 + 4^2 = 14^2 h^2 + 144 + 16 = 196 h^2= 36 h = √36 = 6

pre cal
mmmhhh? (0+3)^2 = 3^2 = 9

pre cal
Look back at my explanation in the previous post for vertex (h,k), we get y = a(x-h)^2 + k so for vertex (-3,5), we get y = a(x-(-3) )^2 + 5 or y = a(x + 3)^2 + 5 Now plug in the other point (0, -4) -4 = a(0+3)^2 + 5 -4 = a(9) + 5 -9 = 9a a = -1 y = -(x+3)^2 + 5

pre cal
Two points only is not enough to establish a quadratic, unless one of those points is the vertex. If one of the points is a vertex, use the method I just showed you in your previous post. Let me know what you think.

Math help
Well,you are told that y has a value of 3 so in the 2nd equation, simply replace y with that value and solve for x 4(3) = 2x + 18 12 - 18 = 2x -6 = 2x -3 = x so x=-3, y = 3 Done!

Math
taking a stab at .75

Pre cal
in your text or in your notes, you should have the usual form of the equation if you have the vertex if vertex is (h, k) then the equation of the quadratic is y = a(x-h)^2 + k compare the values of (h,k) with your vertex of (3,-13) the value of a govern which way the parabola ...

Pre cal
Since you are using the word "vertex" I will assume you might be talking about a quadratic function. with vertex (3,-13) the parabola would be y = a(x-3)^2 -13 but (0,-4) lies on it, so .... -4 = a(9) - 13 9a = 9 a = 1 f(x) = (x-3)^2 - 13

Algebra
yes, you are correct example of exponential growth graph http://www.wolframalpha.com/input/?i=plot+y+%3D+2%5Ex example of exponential decay graph http://www.wolframalpha.com/input/?i=plot+y+%3D+%281%2F2%29%5Ex

Math
Let the number be x 2(x-2) + 7 = 57 2x - 4 = 50 2x = 54 x = 27

math
MN = √( (11-3)^2 + (-2+4)^2 ) = √(64 + 4) = √68 or 2√17

Calculus
smaller number --- x larger number ----- x + 132 product=P=x(x+132) = x^2 + 132x dP/dx = 2x + 132 =0 for a min of P 2x = -132 x = -66 the smaller is -66 the larger -66+132 or +66 the two numbers are -66 and +66

Calculus
let the sides of the base be x cm each let the height be y V= x^2 y 4000/x^2 = y surface area = x^2 + 4xy = x^2 + 4x(4000/x^2 = x^2 + 16000/x d(surface area)/dx = 2x - 16000/x^2 = 0 for a min surface area 2x = 16000/x^2 x^3 = 16000 x = appr 25.2 cm y = 4000/25.2^2 = appr 6.3 cm

math
follow my method in your previous post, let me know what you got

math
The way you typed it .... multiply each term by 5x the LCD 8 + 4x = 12x^2 - 13x 12x^2 - 17x - 8 = 0 use the quadratic formula to find 2 answers what you probably meant: 8/(x+4) = 12/(5x-13) 40x - 104 = 12x + 48 28x = 152 x = 152/28 = 38/7

math
total number of fish --- x use a simple ratio: x/100 = 400/12 x = 100(400/12) = appr 3333 fish

math
How about 6 ?

math
Wow,, that must be some school! number of times around = 330/5.5 = 60 times

math
it usually takes two steps, 1. "move" all terms except the y term to the right side ---> -y = -7x + 7 2. divide each term by the coefficient of the y term ---> divide by -1 y = 7x - 7 #2. 15x + 3y + 2 = 9x + 14 - try it using my 2-step method

algebra 1
So he wants the area to be 4(12) or 48 inches^2 πr^2 = 48 r^2 = 48/π r = appr 3.9 inches

math
10 cm:1mm = 100 mm : 1 mm = 100 : 1

mAtHS
|4x-3| < 1 4x-3< 1 and -4x + 3< 1 4x < 4 and -4x< -2 x < 1 and x > 1/2 1/2 < x < 1 , that is, x has to be between 1/2 and 1

density and pressure
volume = (5)(8)(10) m^3 = 400 m^3 mass = (1.3 kg/m^3)(400 m^3) = 520 kg

maths
smaller ---- x larger ------x+5 x + x+5 = 39 continue...

maths
the number --- x its reciprocal --- 1/x x + 4(1/x) = 5 times x x^2 + 4 = 5x x^2-5x + 4 = 0 (x-1)(x-4) = 0 x = 1 or x = 4 I leave it up to you to check them out.

math
area of ||gm = base x height base (6 5/8) = 26.5 (53/8)base = 26.5 base = 26.5(8/53) = 4 chec: 4(6.625) = 26.5

Math
the complement of 55.1° is 34.9° the supplement of 55.1° is 124.9° I cannot comprehend your answer.

Algebra
yes

math
yes, You can always check your factored answer by simply expanding it. You must get back the original.

Algebra 1~ For Reiny or Steve, I only have 5 min.
#1 change 3x+12y=20 12y = -3x + 20 y = (-3/12) + 20/12 y = (-1/4)x + 5/3 same slope, but different y-intercepts, so 2 parallel lines, NO solution #2 Jack = 55 + 4x Emily = 28 + 13x when is 13x + 28 = 4x + 55 13x - 4x = 55 - 28 9x = 27 x = 3 you are right! #3 10x-2 = -7x + 3 17...

Writing and solving equations
Just translate the English to Math, after all, Math is just a language. let the number of green balls be g , as suggested "The number of red balls is 3 more than the number of green balls" ---> reds = g+3 "the number of blue balls is 7 more that the number of...

math
let the remaining two angles be 16x and 19x 16x+19x+88+62 = 360 ok, up to you...

Algebra Check
yup!

Math
22 > 2x by 14 22 = 2x + 14 8 = 2x x = 4

Algebra 1
slope of first line = -4/5 for the 2nd: -5y = -4x - 15 y = (-4/-5)x - 15/-5 y = (4/5)x + 3 ---> slope is +4/5 so they are neither parallel nor perpendicular. (to be perpendicular, they must be opposite in sign, and flips of each other, not true in your case) 2nd question: s...

math
sam would earn (60+89+83+99+95+60)/6 = ... And why would this not be "fair" ???

Algebra 1
no remember it is y - y1 = m(x-x1) so for (-4,6) y-6 = (2/4)(x - (-4) ) y - 6 = (3/4)(x + 4)

maths
number of 20 cent coins ---- 4x number of 50 cent coins ---- 3x (notice 4x : 3x = 4 : 3) 20 of the twenty cents coins were taken out so we have 4x - 20 left value of those 20 coins = 20(20) = 400 cents which would make 400/50 or 8 fifty cent pieces So number of 50 cent coins =...

Algebra 1
you got it

Algebra 1
-7-(-12) = 5 -2 - (-7) = 5 3 - (-2) = 5 yup, it is! you tell me what the common difference is.

Math help
I assume you have a typo, and the 2nd equation is -14x + 4y = 26 notice dividing by 2 will yield the first equation so you basically have ONE equation in TWO unknowns, which will yield an infinite number of solutions, e.g. (1, 10) is one, so is (13, 52) etc

Typo alert:math---help! 1 question
my first two lines should have said: 2x + 6 = 2(x+3) 2x+6 = 2x+6

math---help! 1 question
3x + 6 = 2(x+3) 3x+6 = 2x+6 0=0 The variable dropped out and we had a true statement. So there will be an infinite number of solutions since the equation is actually an identity, that is, the left side is equal to the right side If , however, the variable drops out, and you en...

Math
let the two unknown angles be 3x and 5x 3x + 5x + 100 = 180 ...... take over

Math - Ratio or Proportion (I think??)
6 lbs for 3 people for 5 days, then 2 lbs for 1 person for 5 days, or 2/5 lbs for 1 person for 1 day, or 2 lbs for 5 people for 1 day, or 14 lbs for 5 people for 7 days.

math
amount of 20% solution to be used: x ounce amound of 50% solution to be used : 60-x .2x + .5(60-x) = .3(60) time 10 2x + 5(60-x) = 3(60) 2x + 300 - 5x = 180 -3x = -120 x = 40 40 ounce of the 20% and 20 ounces of the 50% solution should be mixed.

Algebra
correct

Algebra, URGENT!! HELP!
(12x^9)^2 = 144x^18

Math
let number of miles be x when is .5x + 25 = .25x + 30 times 4 2x + 100 = x + 120 x = 20 equal at 20 miles

Calculus
I noticed the following ... A denominator, whose derivative shows up in the numberator... Ahhh, logs! ∫ sin t/(2-cost) dt = ln (2-cost) take it from there.

Calculus
by "inspection" I get (1/6)(1 - cos 3t)^2 | from 0 to π/6 = (1/6)(1 - 0)^2 - (1/6)(1 - 1)^2 = 1/6 - 0 = 1/6 I was assuming that your limit went from 0 to π/6

maths
x^1 + 1/4 ÷ x^1/4 or (x^1 +1)/4 ÷ x^(1/4) etc ?? must use brackets to establish correct order of operation.

MATH
Let the number of students be x number of nuggets = 5x + 30 or number of nuggets = 6x + 4 6x+4 = 5x+30 x = 26 There were 26 students, so she neede 26(5) + 30 or 160 nuggets.

Math
Let the side parallel to the house by y the each of the other two sides be x Make a sketch 2x + y = 50 y = 50-2x area = xy = x(50-2x) =50x - 2x^2 the x of the vertex of this parabola is -b/(2a) = -50/-4 = 12.5 so x = 12.5 and y = 50-25 = 25 The garden should be 25 m long and 1...

MATH
let number of Chinese books be 3x let the number of English books be 5x number of Malay books = (5/9)(3x) = (5/3)x Malay books : English books = (5/3)x : 5x = 5x : 15x = 5 : 15 = 1 : 3

algebra
S = k(T)^(2/5) when S = 8 , T = 32 8 = k (32)^(2/5) 8 = k(4) k = 2 when T = 243 S = 2(243)^(2/5) = 2(3^2) = 18

Math
let the number of $25 increases be n rent = 940 + 25n number rented = 218-5n income = (940+25n)(218-5n) = 204920 +750n - 125n^2 If you know Calculus: d(income) = 750 - 250n = 0 for a max of income 250n=750 n = 3 if you don't know Calc complete the square: -125(n^2 - 6n + 9...

Algebra
slope = (-9+3)/(-6+2) = -6/-4 = 3/2 y+3 = (3/2)(x+2) 2y + 6 = 3x + 6 3x - 2y = 0

math(CHECK ASNWERS)
all ok

maths
"Solving" implies you have an equation. You have no equation.

SAT prep help
x^4 = 10 x = 10^(1/4) then x^6 = (10^(1/4) )^6 = 10^(3/2) or appr 31.623

calculus
You are right, I subbed 10 into the wrong variable Good catch. when y = 10 x^2+ 6^2 = 10^2 x^2 =100-36= 64 x = √64 = 8 in my #1 from above post: 2(8) dx/dt = 2(10)(40) dx/dt = 50 mph

Algebra
Ford rental: cost = 35 + .14x, where x is the number of miles Chevy rental: cost = 34 + .16x when is 34 + .16x > 35 + .14x .02x > 1 x > 1/.02 x > 50

calculus
Let his horizontal distance over the high school be x let the distance between him and the school be y I see a right-angled triangle and x^2 + 6^2 = y^2 2x dx/dt + 0 = 2y dy/dt , #1 when x = 10, y^2 = 100 + 36, y = √136 in equation #1 2(10) dx/dt = 2(√136) (40) dx/...

Algebra 2
x^2 + x = -c x^2 + x + 1/4 = 1/4-c (x+1/2)^2 = (1-4c)/4 x+1/2 = ± √(1-4c)/2 x = -1/2 ± √(1-4c) = (-1 ± √(1-4c) )/2 -keep only the x^2 and x terms on the left - take half of the coefficient of the x term, then square it - add that result t...

Calc I
f ' (x) = e^x - 5x^4 f '' (x) = e^x - 20x^3

Math help
for all 3 , elimination looks like the easiest way 1. -7x-6y=-21 -x-6y=-3 subtract them to eliminate the y's -6x = -18 x = 3 back into the 2nd: -3-6y=-3 -6y=0 y = 0 ----------> x = 3, y = 0 2. -7x+2y=13 -14x+4y=26 Did you notice that the 2nd equation is simply twice the...

Calculus
area = ∫e^(-x/2) dx from x = -6 to ∞ = [-2 e^(-x/2) ] from -6 to ∞ = 0 - (-2e^3) = 2e^3 note: as x ---> ∞ , e^(-huge) = 1/e^huge ---> 0

PreCAL
You are right Bosnian, it is D Time to clean my glasses, lol

PreCAL
x = 9t+2 --> t = (x-2)/9 y = -6t+9 --> t = (9-y)/6 then : (x-2)/9 = (9-y)/6 6x-12 = 81-9y 9y = -6x + 93 y = (-2/3)x + 31/3 looks like B)

trig
forgot to mention that you cannot just skip the "angle" after a trig operator. What you typed would be like having an equation of the type ... √ = ∫ + ∑

trig
LS = (csc^2 Ø + cot^2 Ø)(csc^2 Ø - cot^2 Ø = (1 + cot^2 Ø + cot^2 Ø)(1+cot^2 Ø - cot^2 Ø = 1 + 2cot^2 Ø RS = (1 + cos^2 Ø)/sin^2 Ø = (sin^2 Ø + cos^2 Ø + cos^2 Ø)/sin^2 Ø =...

math
height after 1st bounce = 10(.6) height after 2nd bounce = (10(.6))(.6) = 10(.6^2) height after 3rd bounce = 10(.6^3) ... height after nth bounce = 10(.6^n)

MATH
MMMhhh? Both I and bobpursley answered you . http://www.jiskha.com/display.cgi?id=1390567139 Why are you reposting?

algebra
Both Steve and I both answered you in 2 different posts. Do you not look at your earlier posts?

math
You must learn to "translate" the English into Math "The product of a number and 2 has the same value as that number minus 2" - product means multiply - a number --- x so far: (x)(2) or 2x - has the same value ---> = so far: 2x = - that number minus 2 --...

math
do it the same way I just showed you in your last post Let me know what you think.

math
x+0 = x^2 x^2 - x = 0 x(x-1) = 0 x = 0 or x = 1, but x was to be a non-zero integer so x = 1

Math
Since no restriction in terms of being a smoker or non-smoker is required, we are simply choosing 5 people from 15 which is C(15,5) = 3003

Trig
of course

Trig
Why are you calling this trig ? x^2 - 4x + 2 = x+2 x^2 - 5x = 0 x(x-5) = 0 x = 0 or x = 5 sub in those x's in either of the two equations to find the y, then choose your answer. http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2+–+4x+%2B+2%2C++y+%3D+x+%2B+2

Math
PV = 1333.28(1 - 1.05375^-40)/.05375 = $21750.00 Balance after 8.5 year = 21750.00(1.05375)^17 - 1333.28(1.05375^17 - 1/.05375 = $17365.12 check my arithmetic

math
r^10 s^5

german
Wir haben geschlafen. (past tense)

math
length = 8-2x width = 2-2x height = x volume = x(8-2x)(2-2x)

8th grade math
volume = length x width x height = ....

To: Reiny
A very confusing question. Are the triangles right-angled? "The slope side of triangle A is double the slope of B" ---> a triangle has 3 sides, what does "slope side" mean? the slope of which side? What is triangle A and what is triangle B.

Algebra 2
7n = n - 5n^2 - 20n 5n^2 + 26n = 0 n(5n + 26) = 0 n = 0 or n = -26/5

To: Reiny
what question?

permutation and combination
so we only use 24 cards, of which 12 are red number of 5-card hands = C(24,5) = 42504 let's exclude number with no reds and only one red number with no reds = C(12,0) x C(12,5) = 792 number with 1 red = C(12,1) x C(12,4) = 5940 no number with at least two reds = 42504 - 79...

math
let the width be w length = 2w-5 w(2w-5) = 25 2w^2 - 5w - 25 = 0 (2w+5)(x-5) = 0 w = -5/2 or w = 5, but the width could not be negative, so the width is 5 and the length is 2(5)-5 or 5 your rectangle is a square.

math
done before, look back

Math!
35/26.25 = 8/h 35h = 8(26.5) h = .....

math
16^(1/3) e^4

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