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Posts by Reiny

Total # Posts: 38,777

pre calc
Both Scott and I did this for you here , and we both got the same answer http://www.jiskha.com/display.cgi?id=1489120237

math
We know that (a+b)^2 = a^2 + 2ab + b^2 = ...

Advanced Functions
I did this a few days ago http://www.jiskha.com/display.cgi?id=1488730046

Calculus
you have to integrate the velocity to get to distance let the distance be s(t) s(t) = (3/8)(t^2 - 1)^(4/3) + c s(0) = (3/8)(1) + c = c + 3/8 s(3) = (3/8)(8)^(4/3) +c = c + 81/8 distance = c+81/8 - (c + 3/8) = 39/4 ft

geometry
A(n)=-2+(n-1)(-2.2) = -2 - 2.2n + 2.2 = .2 - 2.2n since term numbers are labeled with whole numbers, n ? 1 and the first term is -2 and the common difference is -2.2 the fourth term = a + 3d = -2 + 3(-2.2) = -8.6 then tenth term = .....

further maths
Just use your formulas that you learned for this topic. sum of 8 terms = (8/2)(first + last) = 4(6 + 46) = 208 #2 sum(10) = (10/2)(2a + 9d) = 60 2a + 9d = 12 ** sum(15) = (15/2)(2a + 14d) = 165 2a + 14d = 22 *** subtract ** from *** 5d = 10 d = 2 sub into ** 2a + 18 = 12 a = -...

Work Ethics
Look at this post from last year. It contains all of your individual question all in one post http://www.jiskha.com/display.cgi?id=1472922204

Math,quadratic equation
I suppose you are solving ? x^2 - 5x - 5 = 0 It does not factor, so your other option are to complete the square or to use the quadratic equation. Your choice.

math
Use a Venn diagram with 3 overlapping circles named after the reason for failing, use C, H, T as suggested as their labels Place 8 in the intersection of all three. Now work on the intersection of two at a time. e.g. 14 would go in the intersection of C and T, but we already ...

Math
so the field is 300 by 200 m and the road would be 10 m by 300m Surely you can find the area of the road.

Math
width --- x length --- x+16 2x + 2(x+16) = 200 solve

mathematics steve
So you got your orange, leaving 14 fruits remaining. prob(mango) = 5/14

math
Ok, let's go with that So the number of boys is x , and so is the number of girls Total at the party = 2x boys with part-time jobs = x/4 girls with part time jobs = 2(x/4) = x/2 total part-timers = x/4 + x/2 = 3x/4 no part-time jobbers = 2x - 3x/4 = 5x/4 5x/4 = 30 x = 24 ...

Math
learly you are studying the quadratic function , which when graphed is a parabola. One of the first things you learn is how to find the vertex. Go to your text or you class notes to look at the example and do the same thing.

algebra
child's ticket --- x adult ticket ---- 3x 5x + 2(3x) = 98 take over

MATH
That would be an answer, since all we need is two numbers or expressions which when multiplied give us 6x^2-3x-3m^2. I have a suspicion that the middle term should be -3xm, then we could go further: 3(2x^2-x-m^2) = 3(2x + m)(x - m) but since we want only two factors, namely ...

Math
As you should know, Interest = Principal x Rate x Time in #1 and #2 question plug in the given values, and solve for the missing variable compound interest: Amount = Principal (1 + i)^n , where i is the interest per period, and n is the number of interest periods. Again, plug ...

algebra
Actually I made an error. I meant to say pick x = 4, which would result in 0 on the right side, so the point is (4,-5)

algebra
This is a straight line, so all you need is two points. Join them and you got your line. pick x's that result in nice values of y e.g. let x = 0, y+5 = 0 y -5 ----> point (0,-5) let x = 7 y+5 = -2/3(3) = -2 point (7,-2) go for it

Math
volume = ?(1.2)^2 (4) ft^3 rate = 1.7 thirds of a foot ???? once you have that one figured out, divide volume by rate

Math
Ab's rate --- 1/5 Bail's rate ---- 1/3 combined rate = 1/5 + 1/3 = 8/15 combined time = 1/(8/15) = 15/8 hrs = 1 7/8 hrs

math
simplify (8*10^7)(7*10^4) i think it's 5.6*10^10 < --- incorrect simplify (3*10^6)(8*10^-4) i think it's 2.4*10^3 < --- correct Astronomers measure large distances in light-years. One light-year 5.88*10^12 mi Star is 9.8*10^1 light years from Earth in ...

math
3 = 1 e^(10k) 10k = ln 3 k = ln3/10 so amount = 1000 e^( (ln3/10)t) 9000 =1000 e^( (ln3/10)t) 9 = e^( (ln3/10)t) ln 9 = (ln3/10)t ln9/(ln3/10)= t t = 10ln9/ln3 = 20 years

Algebra
ratio of 1800 : 2400 = 3 : 4 return ration = 3x : 4x 3x+4x = 1400 7x = 1400 x = 200 so they receive 600 and 800 respectively

math
look at numbers ending in 7, such as 7^1 = 7 7^2 = 49 7^3 = 343 7^4 = 2401 7^5 = 16807 7^6 = 117649 7^7 = 823543 notice that the unit digits forms a cyclic pattern: 7, 9, 3, 1, 7, 9 3, 1, .... the same would be true for something like 37^n try it. Also: 2017^1 = 2017 --- 4 ...

Algebra
let the original fraction be 3x/(2x) (3x+3)/(2x-2) = 9/4 , where x ? 1 18x-18 = 12x + 12 6x = 30 x = 5 the original fraction is 15/10 A poorly thought-out question. Fractions should be reduced to their lowest terms. We would of course reduce our fraction 15/10 to 3/2. In that ...

Pre calc
let the rate of decay be r, where r is a decimal so letting 2003 correspond with t = 0 , then 2005 corresponds with t = 2 900,000 r^2 = 800,000 r^2 = 8/9 r = ?(8/9) = appr .9428 So count = 9000(.0428)^t in 2008 , t = 5 count = 900,000(.9428)^5 = appr 670,442 or 670,000 rounded...

Fractions
(4y^-3/5x^-4)^2 = (16y^-6)/(25x^-8) = (16/25)(x^8)/(y^6) or = 16x^8/(25y^6)

Mat222
let f(y) = (y^2 + 11y + 30)/(y+5) <---- those brackets are needed or else we would have a term of 30/y sitting there all by itself = (y+5)(y+6)/(y+5) = y+6 That is, f(y) behaves just like a linear function of f(y) = y+6, EXCEPT when y = -5 in the original function we get f...

math
You are using Pythagoras x^2 + y^2 = h^2 8^2 + y^2 = 11^2 y^2 = 121 - 64 = ... y = ?... = ??

Math
Bearings are usually measured in degrees or radians. Kilometres are not a unit of "bearing", I will assume you meant degrees. I labeled my starting place C, the end of the first leg A, and the end of the second leg B. Let me know when you are done with your diagram, ...

Math help! Hurry Please~
Can't help since you did not supply your choices. How can I check your answers ?

math
Since the places are specific, number of ways = 6(5)(4) = 120

geometry
You will have to have more information, such as, what is the size of the angle, or, how far from the wall is the foot of the ladder.

MATH
How can I possible check your work if you don't supply the answers. use <----- to point to your choice at each question. That way I don't have to scroll back and forth in your post.

Math
Make a sketch. It is easy to see that the height of the triangle that is folded over is 1/4 of the diagonal of the square, so .... let the side of the square be x then its diagonal is ?2x and the height of the triangle bent over is ?2x/4 and the fold at which the bending takes...

Algebra2
If you meant (0,2) then you are correct

Math\
I will assume you mean : Find the smallest number which is greater than 4444 n divisible by 8 What's with the n after the 4444 ? No idea why you tagged the word "formulas" at the end. well, 4444/8 = 555.5 so 555(8) = 4440 too small no the next numbers which are ...

Math
The order of operation would force me to do the divisions in the order they come, so (3m/2)÷ 3 = 7 = (3m/2)(1/3) = 7 3m/6 = 7 3m = 42 m = 14 confirmation by Wolfram http://www.wolframalpha.com/input/?i=solve+3m%2F2%2F3%3D7

Math - Calculus
width of rectangle ---- x length of rectangle --- 3x radius of circle ----- r so 2x + 6x + 2?r = 16 4x + ?r = 8 ----> x = 2 - ?r/4 let S be the sum of the areas of the rectangle , (you had "square" , I assume that was an error) S = ?r^2 + 3x^2 = ?r^2 + 3(1 - ?r/4...

6th grade math
The symbol for multiplication used in this format is either the * sign or to use brackets, not a comma V = l*w*h or (l)(w)(h) or simply V = lwh so V = (4)(2)(8.5) = ..... inches^3

Math
I was hoping that you would correct the grammar and spelling from you last post to make your question clearer. That first part is not even needed, since you said in your second sentence that the camera takes two pictures in each rotation cycle. So to take 100 pictures would ...

math
The LCD is 6, so multiply each term by 6 to get 4x - 4 = x + 8 easy from here

math
5x - 15 + 6 = 4x + 3 Do the x's disappear ? You were told what to expect in your previous question relating to this. http://www.jiskha.com/display.cgi?id=1489016844

Math
C(X)= 10,000 + 20xeX/600 makes no sense to me, did you mean C(X)= 10,000 + 20xe^(x/600) ?? if so, just plug in x = 600 to get C(600) = 10000 + 600(e^1) = .... e^1 = 2.718281828...

Algebra2
If you make a sketch, you will see that the directrix must be y = 4 let P(x,y) be any point ?( (y-6)^2 + (x+2)^2 ) = ?((y-4)^2 + 0) square and expand y^2 - 12y + 36 + (x+2)^2 = y^2 - 8y + 16 (x+2)^2 = 4y - 20 (x+2)^2 = 4(y- 5) I agree

Algebra2
-3x^2+12y^=84 3x^2 - 12y^2 = -84 x^2 /28 - y^2 /7 = -1 You have a vertical hyperbola, with vertices (0,?7) and (0,-?7) your answer is correct

Algebra2
You are correct, you are looking at an ellipse with centre (0,0)

maths
Looks like I messed up for my x I multiplied 4x by 4 instead of dividing by 4 4x = 3.4 x = .85 see Steve's solution

maths
cost of pencil --- p cost of eraser --- e cost of pen ----- x 2e + 4p = 2.4 (1) 6e + p + 2x = 3.95 (2) e + p + 4x = 4.15 (3) I would not use a matrix method, the equations are much too "nice". from (1) : e = 1.2 - 2p sub into (2) 6(1.2 - 2p) + p + 2x = 3.95 -11p + 2x...

Math
4 cm ----> 9 ft 1 cm ----> 9/4 ft then 11 cm ----> ??? ft ( if 1 apple costs 30 cents, how much would 3 apples cost? What operation did you do ?)

MATH
yes, the formula they appear to follow is this: given: the slope m, and a point (a,b) equation of line: y-b = m(x-a) so the slope of the given line is 8/3 perpendicular lines have slopes that are negative reciprocals of each other. So the slope of the new perpendicular line ...

math
so you want the terms that contain x^0 In (2+x^2)^6 (1-3/x^2)^2 we have the following: = (2^6 + 6(2^5)x^2 + 15(2^4)x^4 + ...)(1 + 2(-3/x^2) + 9/x^4) so we only have to worry about: 2^6 (1) , 6(2^5)x^2 * (-6/x^2) and 15(2^4)x^4 * 9/x^4 their sum is 64 + (-1152) + 2160 = 1072

Math
The men positions can be filled in (5)(4) or 20 ways. The women position can be filled in (12)(11)(10)(9) or 11880 ways Which is exactly what Steve had in P(5,2) * P(12,4) = 20(11880) = 237600 ways So go with Steve's answer.

Math
let's get the equation of that straight line: y+1 = (-5/3)(x-6) 3y + 3 = -5x + 30 3y = -5x + 27 y = (-5/3)x + 9 f(x) = (-5/3)x + 9

FUR. MATHS
Is there a question?

maths trigonometry
No improvement over your last post of this ... http://www.jiskha.com/display.cgi?id=1488915415 No question was actually asked.

Finance
.07x = 100 x = 100/.07 = 1428.57 check: If you had $1428.57 then annual interest at 7% is $100. So you use that to pay your charity or scholarship or whatever, and the balance would remain at 1428.57, allowing you to do this forever. Interest = 1428.57(.07)(1) = 99.9999 or 100...

math
Just saw the domain part ... 0 < x ? 2 F^-1(0) = undefined, but F^-1(x) ----> negative infinity F^-1(2) = (1-10)/4 = -9/4 so the domain of F(x) is - infinity < x < -9/4

math
First of all, I will assume you meant: F^-1(x) = (1-5x)/(2x), or else I would have just reduced to F^-1(x) = 1 - 5/2 = -3/2 , a constant The inverse of the inverse of a function would be the function, that is, the inverse of F^-1(x) would be F(x) so we just need the inverse of...

Math
now: temp = 65 after 1 hour temp = 65 + 5(1) after 2 hours temp = 65 + 5(2) after 3 hours temp = 65 + 5(3) ... after x hours temp = 65 + 5x

Math
my reply is the same as it was in your last post The question cannot be answered. More information is needed, such as a diagram, which of course we cannot post here.

Math
The question cannot be answered. More information is needed, such as a diagram, which of course we cannot post here.

Math
Every even number is divisible by 2, but not necessarily divisible by 4 e.g. 6,10, and of course the 18 in your list would fall into that category. So the correct answer is 18 but is even, so Lisa's generalization is incorrect. 18 is NOT divisible by 4

Math
sister --- x you ----- x+6 5 years from now: sister ---- x+5 you ------x+11 x+5 = (5/6)(x+11) 6x + 30 = 5x + 55 carry on

Math
let the volume of the larger glass be x ounces so volume in the pitcher = x + 4 so .6(x+4) = 4 + .5x .6x + 2.4 = 4 + .5x .1x = 1.6 x = 16 ounces

Maths
correct

math
amount at 5% ---- x amount at 4% ---- x - 2400 .05x + .04(x-2400) = 165 solve for x

Math
Did you make a sketch? let the height of the flag pole be f let the height of the tower be t tan 57 = f/70 f = 70tan57 tan 69 = (f+t)/70 f+t = 70tan69 t = 70tan69 - f = 70tan69 - 70tan57 = ... you do the buttonpushing

Math
We only want 4 pies, the fact that they are 9 inches is irrelevant. each pie needs 1/2 cup of juice, so we need 2 cups = 32 tablespoons each lemon produces 2 tablespoons, so we need 16 lemons. cost = 16($.33)= $5.28

Math
4 pies each needing 1/2 cup of lemon juice ---> we need 2 cups of lemon juice. I have no idea how many "tablespoons" are in a cup, look that up, find out how many tablespoons you need. Remember, you would not be able to buy a partial lemon, so you have to go to ...

math
Make an effort to memorize the ratio of sides of both the 30-60-90 and the 45-45-90 right-angled triangles, those values will come up again and again in your study of trig. angles: 30-60-90 sides : 1 - ?3 - 2 angles : 45-45-90 sides : 1 - 1 - ?2 a) so set up a ratio: 1/41 = ?3...

math
trusting the way you typed it .... (13-2)squared + (14-12 divided by 3) = 121 + (14 - 4) <---- order of operation, division before subtraction = 121 + 10 = 131

Math Help
No, your exponent is incorrect i = .108/4 = .027 but n = 5(4) or 20 periods let the payment be P P (1.027^20 - 1)/.27 = 25,706.30 P(26.06525..) = 25,706.30 P = $986.23 Why wouldn't your answer of $135,662.14 sound totally illogical to you?? You only wanted to accumulate $...

mathematics
h = -4.9t^2 + vt + 0, where v = 30sin35° so solve 4.9t^ - 3sin35 t = 0 t(4.9t - 3sin35) = 0 t = 0 , at the start or t = 30sin35/4.9 = appr 3.5 seconds

math
John --- x Pam ----- x-8 in 5 years: John --- x+5 Pam --- x-8+5 = x-3 x+5 + x-3 = 40 2x = 38 x = 19 john is now 19 and Pam is 11 check: in 5 years: John is 24, Pam is 16 sum = 24+16 = 40 My answer is correct

Algebra I
yes, you are right, my mental error or senior moment.

Algebra I
Ignoring the fact that this equation would violate the laws of gravity on earth .... find the vertex in the form (t,h) the value of t is your a) answer, and the value of h is your b) answer. Use the method that was taught to you. c) set -8t^2 + 48t + 160 = 0 divide by -8 t^2...

Algebra
?.0064 = .08 ?-.0081 = ?-1?.0081 = i (.09) , which is not a real number which you asked for, so ?-.0081 does not have a real square root

math
Well, were you surprised when the result popped out, was it un-expected ??

math
Area = ? r^2 circumference = 2?r Area/circumference = ?r^2 /(2?r) = r/2 2(Area) = r(circumference) Area = (r/2)(circumference) as required to show

Math
Check Steve's solution for the same question. http://www.jiskha.com/display.cgi?id=1436351642

Math- Interest Rates
Assuming this is a simple interest and not a compound interest problem, we are missing the rate a) so she has $4960 b) since I = PRT 960 = 4000(R)(3) R = .08 so 8% interest c) if the rate had been 9% amount = 4000 + 4000(.09)(3) = 5080 So how much more ???

Calculus
Just do it term by term the way it stands, the only one to be careful with is the -3xy, since you have to use a product rule 5x^2 - 3xy + 58 = 2y^3 10x - 3x dy/dx -3y + 0 = 6y^2 dy/dx 10x - 3y = 6y^2 dy/dx + 3x dy/dx factor out the dy/dx and just flip the equation dy/dx(6y^2...

Math
What method have you learned? There are several.

Math
On my computer, I see no figure on the right, just a cup of coffee.

Algebra
-3 = x^2 + 4x + 1 x^2 + 4x + 4 = 0 , so a=1, b=4, and c=4 just plug it in.

Math
Done

Math
Please number your question, and use proper notation for powers 1. x^3 + 8x^2 + 6 = 0 , (I assumed the + sign at the end) Without any work, if we assume it does factor, then any factor CANNOT end in a number which is not a factor of 6, since the 6 can only arrive from the ...

Algebra
see my reply here: http://www.jiskha.com/display.cgi?id=1488737021 type 5x2^ as 5x^2 etc so I will read that as, assuming the middle term in the first bracket is 11x (5x^2 + 11x - 9)(-2x^2 -x + 17) = -10x^4 - 5x^3 + 85x^2 - 22x^3 - 11x^2 + 187x + 18x^2 + 9x - 153 = -10x^4 - 27...

Algebra
Look at my reply here: http://www.jiskha.com/display.cgi?id=1488737021 You have the same kind of gibberish, please stick to one "name".

Algebra
Your notation is not acceptable did you mean y^11 instead of 11^y ? is x a variable or a multiplication sign ? The way you typed it we are dividing by only 560, you will need brackets otherwise. in your answer, -2^ and -15^ are meaningless.

math
by our definitions: a + 4d = 21 ---> a = 21-4d ** a+ 9d = 3(a+d) a + 9d = 3a + 3d 2a = 6d a = 3d *** equate ** and *** 3d = 21-4d 7d = 21 carry on

Math
You will have 3 similar right-angled triangles. I will list them with matching vertices ABC DBA DAC You can now form any ratio e.g. BC/AB = BA/DB = AC/DA plug in your given values and you can find all sides

correction - Advanced Functions
I said: period = 2?/k = 20 min That should have been 20 seconds

Advanced Functions
first two bits of information max is 8, min is -8, so a = 8 period = 2?/k = 20 min 20k = 2? k = ?/10 so let's start with h = 8 sin (?/10)t so we have the "shape" of our curve (sketch this from 0 to 20) http://www.wolframalpha.com/input/?i=h+%3D+8+sin+((%CF%80%...

Maths
base --- 5x height --- 2x (5x)(2x) = 360 10x^2 = 360 continue, find x, then sub back into my definitions

Maths
choices: (1,1) (1,2) (2,1) prob( less than 3) = 3/36 = 1/12

math
I read that as y = (x^2 - 3)/?2 dy/dx = (1/?2)(2x) = 2x/?2 let that closest point be P(x,y) so the slope of the tangent at P = 2x/?2 slope of PO = y/x at the closest point, PO is perpendicular to the tangent at P then, y/x = -?2/(2x) y = - ?2/2 for the x: (x^2-3)/?2 = -?2/2 x^...

maths
What is (13)(9) - 8^2 ?

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