Saturday
July 26, 2014

Posts by Reiny


Total # Posts: 26,871

Math
first notice the common factor of x x^3 - 3x^2 - 28x = x(x^2 - 3x - 28) now do the quadratic = x(x-7)(x+4) (notice (-7)(+4) = -28 and -7+4 = -3 )

alegebra
In this forum we type powers using the ^ to show exponents e.g 4x^2 , not 4x2 anyway 1. 4x^2 + 12x + 5 = (2x+1)(2x+5) 2. 2x^2 + x - 3 = (x-1)(2x+3) 3. ok 4. 16x^2 - 16x - 12 = 4(4x^2 - 4x -3) = 4(2x+1)(2x - 3) which is D) 5. = 3(x^2 + 7x - 8) = 3(x+8)(x-1) which is A) looks li...

Math
no need to do FOIL, just sub in n=11 (n-3)^2 = (11-3)^2 = 8^2 = 64 now just put n=11 into the different choices for answers

Math
if n=11, then (n-3)^2 = 64 A) is 17(5) ≠64 B) is 16(4) = 64 ahhhh!!! I assume there is only one answer, but check the others anyway.

math
let the three pieces be x , 3x, and 6x 6x - x = 2.5 5x = 2.5 x = .5 three pieces are .5 , 1.5, and 3 ft the piece was x+3x+6x or 10 long so 10x = 10(.5) = 5 ft mmmhh, what about the wood lost due to the sawdust? You must have one of those fancy new laser saws.

Finance
I will do the first, you do the others in the same way Let me know what you get. PV = ? Amount = 5000 i = .05 n = 10 PV(1 + i)^n = Amount PV(1.05)^10 = 5000 PV = 5000/1.05^10 = 5000/1.628894627 = $3069.57

Algebra 2
Jane, from your wording it is not clear if the first card drawn is returned to the deck or not. Suppose it is not returned could be F4 or 4F = (12/52)(4/40) + (4/52)(12/40) = 3/130 + 3/130 = 3/65 Your answer suggests that the card is returned after it is drawn. Then it would b...

trig
Just supposing you meant what you typed cot^2x+csc=x cos^2 x/sin^2 x + 1 sinx = x wolfram shows 4 answers in your domain http://www.wolframalpha.com/input/?i=solve+cot%5E2%28x%29+%2B+csc%28x%29+%3D+x x = appr. 1.211, 2.343, 3.523 and 5.964 When substituted all are within an er...

math
Oscar is definitely out of line.

Math
draw in an altitude to the base , which would bisect the base. So now you have a right angled triangle, let the equal sides be x cm each sin 43° = 7/x x = 7/sin43 = appr 10.26 cm For the second, I will assume that the 170 yrds is measured along the ski run then sin42 = x/1...

Algebra
mmmh, have you tried substituting t = 4 into the equation and comparing that answer to your graph result when t = 4 on the horizontal axis ?

Algebra
in 5 hours , (from 1:00pm to 6:00pm), he did 5 driveways. (7-2) so he does 1 driveway per hour or he takes 1 hour per driveway.

Algebra
it is in that form

algebra
y-0 = (-2/3)(x-5)

math
treat it as having 2 ordered pairs (28, 8) and (47,17) in the form (m,g) slope = (17-8)/(47-28) = 9/19 using (28,8) g-8 = (9/19)(m-28) 19g - 152 =9m - 252 9m - 19g = 100 or -19g = -9m + 100 g =(9/19)m - 100/19

Math
Notice what happens when you state a problem in a misleading way? I interpreted that you wanted the cost after a 40% discount. Steve thought that the $99 was the cost after the 40% discount. Besides, "$99 watch with a 40% discount. ", is a statement, not a question.

Math
discount = $ 99(.4) = $39.60 So cost of watch = $ 59.40 (how can you get $ 247 ? . That is 2 1/2 times the original cost !! )

algebra
amount needed to rent 5 movies is 3(5) + 10 = $25 He already has $10, so he needs an extra $15

Math
The tens place can be filled in 4 ways for each of those, the unit place can be filled in 3 ways number of such numbers = 4 x 3 = 12 (count the numbers that Ms Sue gave you)

Math
done by Steve http://www.jiskha.com/display.cgi?id=1349250036

math
Are you preparing for a test or exam? The question that you have asked and I have answered for you are of an elementary nature in this topic. I have a feeling that you have some major studying to do.

math
solve -6x^2 + 4x + 7 = 0 6x^2 -4x - 7 = 0 use the quadratic formula, since it does not factor.

math
how about just adding 15 ?

math
f(x) = (x+2 - 12)^2 = (x-10)^2

math
it factors .... (x-8)(x+5) = 0 x = 8 or x = -5

Math
the first term would be S1 = (5/2)(1) + (7/2)(1) = 6 the sum of the first 2 terms is S2 = (5/2)(4) + (7/2)(2) = 17 so the 2nd term = S2 - S1 = 17-6 = 11 which means the common difference must be 5 (just checking: the first 4 terms would be : 6, 11, 16, 21 and the sum of the fi...

algebra
2x + 2(x-4) = 64 take it from there.

Trig
sin Ø = .6 = 6/10 = 3/5 you should recognize the famous 3-4-5 right-angled triangle. so in quadrant II, construct your right-angled triangle in quadrant II sinØ = opposite/hypotenuse = y/r y = 3, r = 5 and in II, x = -4 so ... sinØ = 3/5 , csc Ø = 5...

statistics
enter your data into http://davidmlane.com/hyperstat/z_table.html click on "below" you should get 0.2638 so 26.38 % are less than 38 inches tall

Statistics
number of subsets of 6 elements = 2^6 = 64 which includes the nullset (plain pizza) and all elements ("the works")

Math
number of small trucks --- x number of vans -----2x number of large trucks --- 320 - 3x 30000x + 35000(2x) + 80000(320-3x) = 13000000 divide by 10000 3x + 7x + 8(320-3x) = 1300 -14x = -1260 x = 90 so 90 small trucks 180 vans and 50 large trucks

math
speed of boat --- x mph time to go downstream = 39/(x+12) time to go upstream = 39/(x-12) , clearly x > 12 39/(x+12) + 39/(x-12) = 4 1/3 = 13/3 (39(x-12) + 39(x+12))/(x^ - 144) = 13/3 78x/(x^2 - 144) = 13/3 13x^2 - 1872 = 234x 13x^2 - 243x - 1872 = 0 x^2 - 18x - 144 = 0 com...

EASY Volume of shapes
area = area of base x heigh so the hard part is to find the area of the equilateral triangle with sides 5 1. easiest way: area = (1/2) side^2 x sin60 = (1/2)(25)*√3/2 = 25√3 2. draw in the height of the triangle, call it h h/5 = sin60 h = 5sin60 area = (1/2)(base x...

SICK
What post are you talking about? Looked back in search for "anna" and all seem to have been answered.

Math
You should be able to do this mentally area = (1/2)( 3 + 7)(12) = (1/2)(10)(12) = (1/2)(120) = 60 How did you ever get 81.6 ??

CALCULUS
noticed an error from line 2 to line 3 y^2 - y = x y^2 - y + 1/4 = x + 1/4 (y - 1/2)^2 =(4x+1)/4 y - 1/2 = ±√(4x+1)/2 y = 1/2 ± √(4x+1)/2 = (1 ± √(4x+1) )/2 , x ≥ -1/4

math
Is the relation supposed to be linear? If so, then you have two ordered pairs, (0,20) and (12.5 , 25) Find the equation of that line using your usual method.

algebra
The y-intercept, by definition, lies on the y-axis Any point on the y-axis has an x value of 0 (you haven't gone either left or right from the origin)

math
The steeper the line, the larger the slope since 5/3 is greater than 4/3, consider it explained

Ghana National Lotto game
Wow, are you under the impression that lottery number outcomes can be predicted??? Please let me know how.

Algebra 1 (Reiny)
t^-6 = 1/t^6 when t = 2 1/2^6 = 1/64 If this is in relation to your other post , notice that in that question you had #1 t^6 , when t = 2

Algebra 1 Answer Evaluation (Reiny)
I messed up in #3 and #4 #3, I looked at your answer and saw the y's, should have looked at the original question which had no y values. answer is x^10 , see Steve's #4. a^-3/b^-2 = b^2/a^3, see Steve's We have the same answers for the rest

Algebra 1 Answer Evaluation (Reiny)
1. 2^4 = 64 , not 1/64 2. ok 3. x^4 y^6 , your first choice is incorrect 4. a^-3/b^-2 = a^(-3 -(-2)) = a^-1 or 1/a 5. 0.5 = 5.0 x 10^-1 6. 3^2 = 9 , they probably want the actual answer 7. a^3 x a^-6 x a^-2 = a^-5 or 1/a^5 , notice 3-6-2=-5 8. ok 9. (-4d^7)^2 = +16 d^14 looks ...

GEOMETRY MIDPOINT FORMULA steve how did this hapn
looks like Steve was using vector geometry Perhaps the following approach might make sense to you: make a sketch. since AC = 4AB AB : BC = 1 : 3 for the x's : (2 - (-2))/(-2-x) = 1/3 12 = -2-x x = -14 for the y's: (3-0)/(0-y) = 1/3 9 = -y y = -9 so point C is (-14, -9)

Math
any equation of the simple form x = k , where k is a constant is a vertical line. All vertical lines have an undefined slope

Math
y-8 = -8(x-1) y -8 = -8x + 8 y = -8x + 16 or 8x + y = 16 or 8x + y - 16 = 0

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

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