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Posts by Reiny

Total # Posts: 38,325

math
speed of boat in still water ---- x km/h speed of current ------ y km/h distance with the current = 4(x+y) distance against the current = 5(x-y) we know that 3.5(x+y) = 70 x+y = 20 but 4(x+y) = 4(20) = 80 then 5(x-y) = 80 x-y = 16 x+y=20 x-y=16 add them 2x = 36 x = 18 , then y...

math
number of books on first shelf ---- x number of books on 2nd shelf ---- 55-x after re-location first shelf --- (55-x)/2 + x 2nd shelf ---- (55-x)/2 (55-x)/2 + x = 4(55-x)/2 times 2 55-x + 2x = 220 - 4x 5x = 165 x = 33 before the shift: 1st shelf ---- 33 books 2nd shelf ---- 22...

Math - Trigonometry
Did you make your sketch. After I filled in the angles I found angle A to be 90° so you have a right-angled triangle. Yeahhh, Pythagoras! I can find the other angles! tanB = 800/280 = ... angle B = appr 70.7° then angle C = 90-70.7 = 19.3° state the result as a &...

Math - Trigonometry
Like I pointed, as did writeacher, the ' here means minutes of angle, the seconds of angle would be '' so 30° 45' 4'' would be 30° + 45/60° + 4/3600° = 30 + .75 + .001111.. = 30.75111..°

Math - Trigonometry
Suggestion: Sketch a rectangle ABCD, with A at the topleft corner. AB as the width of 3.8 and AD as the length. Draw the diagonal BD. Now look at the right-angled triangle BCD angle DBC = 32° 15' The unit measure of and angle in common notation is the degree. There are...

Algebra
I think the key wording is "exactly one pair of parallel sides" That rules out square, rectangle, rhombus, parallogram, since those have opposite sides parallel, thus 2 paris of parallel sides. That leaves you with "trapezoid", sometimes called trapezium. ...

Math
smaller ---- x larger ----- x+21 2x + (1/2)(x+21) = 38 each term times 2 4x + (x+21) = 76 should be easy to solve for x

Mink high school MatheMatics
Ahh, now you are going to use a different formula amount = Principal (1 + i)^n , where i is the interest rate per interest period, and n is the number of periods for yours , i = .0625, and n = 6 plug in and work that calculator.

Maths
same stuff as before, show your steps so I can see if you are doing it correctly.

Maths
Use the same formula I showed you before

Maths
.9375x = 7.5

Maths
Done, when you were Regina

Maths
Interest = principal x rate x time rate = 6 1/4% = .0625 plug in the values

algebra
speed of passenger train ---- x km/h speed of express ------ x+20 km/h Time = distance/rate 360/x - 360/(x+20) = 3 , saying the difference in their times is 3 hours multiply each term by x(x+20), the LCD 360(x+20) - 360x = 3x(x+20) 3x^2 + 60x - 7200 = 0 x^2 + 20x - 2400 = 0 (x...

math
If 1 cm -----> 15 cm 5 cm -----> 5(15) or 75 cm 3 cm -----> .........

pre-Calculus
Use the Remainder theorem let f(x) = x^40 - 3 if f(x) is divided by x+1 , the f(-1) is the remainder, so f(-1) = ......

Math
I will assume you want to prove the identity to be true. The way you typed , the statement is NOT an identity You must have meant: (secx+tanx)/(secx- tanx) = (1+2sinx+sin^2x)/ cos^2x LS = (1/cosx + sinx/cosx) / (1/cosx - sinx/cosx) = ( (1+sinx)/cosx)/( (1-sinx)/cosx) = (1+sinx...

Algebra HELP ASAP!!!
You MUST know how to find the equation in the form y = mx + b, if given a point and the slope let's start with y = (3/5)x + b but (-3,-1) lies on it, so replace the x and y of the equation and solve for b PLug it back in and you are done!

Math
More information is needed. e.g. is the rectangle 55 by 100 or how about 50 by 110 , or how about 44 by 125 ? Each case would have a different semicircle at the ends.

Math
number of dogs --- 2x number of cats ---- 3x (notice 2x : 3x = 2 : 3 ) given: 2x + 3x = 15 5x = 15 x = 3 number of cats = 2x = 2(3) = 6 number of dogs = 3x = 3(3) = 9

Algebra
How many different riders could come in first ? 6 That leaves how many to come in second? 5 what is 6x5 ??

math
Number of $3 tickets ---- x number of $8 tickets ---- 4-x 3x + 8(4-x) = 22 solve for x and interpret or Number of $3 tickets ---- x number of $8 tickets ---- y then x+y = 4 3x + 8y = 22 solve for x and y and interpret

Algebra Help ASAP PLEASE!
" I *think* it might be C but I'm not sure." Unacceptable in mathematics. If you know your material there is no such thing as "I'm not sure" Your lessons, text or notes will show the following steps to find the inverse: let y = 2x+4 step1: ...

5 grade math
number of ounces = 60(2.5) ounces = 150 ounces As I recall, there are 16 ounces in a pound, so .....

Calculus
I will assume that you are finding the derivative with respect to x. let u = x^2/35 or u = (1/35)x^2 let y = sin u dy/du = cos u , and du/dx = (2/35)x dy/dx = (dy/du)(du/dx) = (cos u)(2/35)x = (2x/35)cos (x^2/35) your aim will be to reach that final line directly.

Math Algebra
Steve's "big hint" applies to all 3 of your questions. I will use it on #3 comparing: y = ax^2 + bx + c , and y = -3x^2 - 12x + 3, ---> a=-3, b=-12, c=3 the x of the vertex is -b/(2a) = -(-12)/-6 = -2 which also means that the axis of symmetry is x = -2 to get...

maths
I assume you made a sketch. I sketched a right-angled triangle by letting the radius of the circular base of the cylinder to be r and the distance to the centre of the sphere to be be h then h^2 + r^2 = 18^2 ----> r^2 = 324 - h^2 volume of cylinder = ? r^2 (2h) = ?(324 - h^...

Math
I will use the sum and product of roots properties. for the given : sum of roots = p + q = 1/2 product of roots = pq = -4/2 = -2 new roots are p- q/p and q - p/q sum of new roots = p - q/p + q - p/q = p^2q + q^2p - q^2 - p^2 = pq(pq + qp) - ( (p+q)^2 - 2pq) = -2(-4) - (1/4 + 4...

math
sketch your triangle, I called BC = 21 , AB = 17 By the cosine law we can find angle B then sinB = altitude/17 altitude = 17sin B

math
number of dimes ---- x number of quarters ---- x+10 x + x+10 = 52 continue please

math
prob(2boys of 3 children) = C(3,2)(1/2)^2 (1/2) = 3/8 or, you could list them: BBB BBG BGB BGG GBB GBG GGB GGG There are 3 with 2 boys, 1 girl prob(your event) = 3/8

scrap my solution , go with Steve - calculus
messed up in 4th step.

calculus
I will assume that y3 is y^3 1/(y+x+3) * (dy/dx + 1) = x dy/dx + y + 3y^2 dy/dx plug in the point (-4,2) : 1/(2-4+3) * (dy/dx + 1) = -4dy/dx + 2 + 12 dy/dx 1/ln1 * (dy/dx + 1) = 2 + 8dy/dx arggghhh , 1/ln1 = 1/0, which is undefined so we have a vertical tangent at (-4,2) ...

Algebra 1
I assume you want to simplify the first two 1. (3?6 + 5?10)^2 - 286 + 60?15 You must know how to square a binomial ... = 54 + 30?60 + 250 - 286 + 60?15 = 18 + 60?15 + 60?15 = 18 + 120?15 2. the first part is the expansion of a difference of squares pattern, you must know that ...

Geometry
let the length, the width and the height be a , b, and c respectively make a sketch to see that 4a + 4b + 4c = 76 ---> a+b+c = 19 or c = 19 - a - b 2ab + 2ac + 2bc = 206 ---> ab + ac + bc = 103 abc = 165 or c = 165/(ab) 19-a-b = 165/ab 19ab - a^2 b - ab^2 = 165 ab(19 - a...

College statistics- SCWK450
You will find this most useful for these type of questions http://davidmlane.com/normal.html enter 78 and 4 for the mean and sd click on below and enter 80 you should get .6915 so appr the 69 percentile

@ Lily - Advanced Functions
sorry about the confusion , I just look back at my solution, that should have been 20 seconds (at 3 rotations per minute --> 1 rotation in 20 seconds) the math stays the same, t is in seconds

Please Help
(?6)?(a+2b?3c?4d)?(?2)?(?4a?3b+2c+d) = -6a - 12b + 18c + 24d - (8a + 6b - 4c - 2d) = -6a - 12b + 18c + 24d - 8a - 6b + 4c + 2d = .....

math
A simple ratio will do it: h/16 = 2.5/4 solve for h

Maths
5 days : 20 hours = 120 days : 20 days = 120 : 20 = 6 : 1

Math (Sinking fund)
i = .078/12 = .0065 n = 25 payment --- P P( 1.0065^25) - 1)/.0065 = 16000 on my calculator ... P = 591.48

Math
i = .08/12 = .00666... don't round off, carry answer in your calculator's memory n = 72 amount accumulated = 255( 1.00666...^72 - 1)/.0066.... = 23,466.46

Algebra
x square-2(7x+16)=0 x^2 - 14x - 32 = 0 if = 16 is a root, then (x-16) is a factor so (x-16)(x + ?) = 0 to get a final product of -32 at the end of the quadratic, we need +2 in the second bracket (x-16)(x+2) = 0 so the other root is x = -2

Calculus
You need the intersection of y = e^x and y = e^2 e^x = e^2 so x = 2 then area = ? e^2 - e^x from 0 to 2 = [e^2 x - e^x] from 0 to 2 = 2e^2 - e^2 - (0 - e^0) = e^2 + 1

@Henry - pre calc
It said exponentially. You made it a linear decay.

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

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