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Posts by Reiny

Total # Posts: 38,760

Calc
length of pool --- x width of pool -----y cost = 10x + 5y = 1000 2x + y = 200 y = 200-2x area = xy = x(200-2x) = 200x - 2x^2 d(area)/dx = 200 - 4x = 0 for a max of area 4x=200 x=50 then y = 200-100 = 100 state your conclusion

math
Snowball was in the air as long as h > 0 let's see when h = 0 0 = -16t^2 + 48t + 28 divide by -4 4t^2 - 12t - 7 = 0 (2t + 1)(2t - 7) = 0 so t = -1/2 or t = 7/2 but t ? 0 so the ball was in the air for 7/2 or 3.5 seconds

algerbra
Are you saying: 11?(37x) = 44?37 ???? if so, then ?(37x) = 4?37 square both sides: 37x = 16(37) x = 16

math
number of 2-pointers ---- x number of 3-pointers ----- 16-x 2x + 3(16-x) = 38 solve for x

algebra word problem
lower rate ---- r higher rate ---- r+.015 1100r + 1800(r+.015) = 288 1100r + 1800r + 27 = 288 2900r = 261 r = .09 the one rate was 9% , the other 10.5% check: 1100(.09) + 1800(.105) = 288

Math
2.52 cm = .0252 m

Maths
So, one is chose, leaving 14 others to those from. Number of ways = C(14,3) = 364

math
the volume of similar objects is proportional to the cube of their corresponding sides, so V1 : V2 = 1^3 : 3^3 V1 / 162 = 1/27 V1 = 162/27 = 6 the new volume is 6 cm^3

Algebra
let the first be x let the second be y the third is x-45 x+y > x-45 by 80 ---> x+y = x-45 + 80 x + y = x + 35 y = 35 x + y + x-45 = 194 2x + 35 - 45 = 194 2x = 204 x = 102 the first is 102 the 2nd is 35 the 3rd is 57

Algebra
9|r-2|-10<-73 9|r-2| < -63 |r - 2| < -7 BUT, the absolute value of anything has to be ? 0, so it certainly cannot be ? -7 Your inequation has no solution. Just try some numbers in your solution, they don't work. e.g. for r < 9 , let r = 4 LS = 9|4-2) - 10 = 8 ...

geometry
compare the two lengths of the corresponding dimenstions: lengths: 14.7/4.2 = 3.5 widths : 20.3/5.8 = 3.5 heights: 33.6/9.6 = 3.5 well, how about that ??

Algebra
Something not right here. According to your equation, it is not launched from ground level, but from a height of 4 units. Furthermore it is launched with a downwards velocity of 1 unit of distance/ 1 unit of time domain: t ? 0 check for a typo

Algebra
see my comment at your repeat posting of the same question above.

Algebra
First of all , don't switch to decimals ( 7/6 ? 1.16, it is 1.1666.... ) So you have two points (-7/6 , 0) and (0,7) slope = (7-0)/(0+7/6) = 7/(7/6) = 6 equation of first line : y = 6x + 7 slope of 2nd line = 12 <----- it said twice the first y-intercept of 2nd line = 7...

Algebra
First of all , define your variables 3x + 7y = $46.00 8x + 4y = $75.00 <----- notice correction 3x + 7y = $46.00 (times 8): 24x + 56y = 368 8x + 4y = $75.00 (times 3): 24x + 12y = 225 subtract them: 44y = 143 y = 3.25 go back into one of the original equations to find x, ...

Algebra
equation #1: x - y = 47 equation #2: deals with the number of legs 4x + 2y = 938, or 2x + y = 469 add our two equations: 3x = 516 take over....

Maths
now: Mona ---- x Dad ----- 3x in 12 years: Mona = x+12 Dad = 3x+12 3x+12 = 2(x+12) take over

Algebra
Why do you have L's, W's and x's in your equation ? width ---- w length ---- l equation #1: 2w + 2l = 84 w+l = 42 ** equation #2: "The length of a rectangle is 91 less than six times the width of the rectangle" ---> l = 6w - 91 sub that back into ** w...

MATH
so a point on it is (4,0) y-0 = 3(x-4) y = 3x - 12

math
so it must be a vertical line All vertical lines have equation of the form x = c, where c is a constant look at the point (3,-1) , its x value is 3 so : x = 3 is the equation.

V.i.p. Maths
Bob, I always thought that happened in Indiana. https://en.wikipedia.org/wiki/Indiana_Pi_Bill 22/7 is the best approximation to ? using at most 2 digits as the numerator of the fraction. If you allow 3 digits, the best fraction is 355/113 which differs from ? by only ....

Maths
Make a sketch, drawing the right-angled triangle formed by the chord and the two radii. Find the area of that triangle, very easy find the area of the 1/4 of the circle, very easy subtract those two to get the minor segment Find the area of the whole circle and subtract the ...

Algebra
first of all just divide the 2nd equation by 5 to get n + 2d = 86, the other is n + d = 59 <<---- you had 430 here. subtract them: d = 27 then in n+d = 59 , n+27 = 59 n = 32 She has 27 dimes and 32 nickels check: is 27+32 = 59 for the sum of coins? YES for the value of ...

math
The height creates a right-angled triangle with angles of 30° and 60° so if the base of that triangle is x, then using the ratios of the 30-60-90 triangle, x/1 = 12/?3 x = 12/?3 or 12/?3 *?3/?3 = 4?3 So the base of the equilateral triangle is 8?3 giving you an area of...

Math
Not really familiar with the formulas relating demand function, cost functions and profit, but here is an example of your question. http://math.stackexchange.com/questions/758620/maximized-profit-w-a-cost-demand-function

Business Math ( Future ordinary Annuities)
You should get into the habit of making a time graph on a straight line for these kind of questions. Think of the whole thing as being in two accounts. 1000(1.025^48)/.025 would be amount you would have at the end of 4 years, sitting at time 4 But you want that amount at time ...

Business Math ( Future ordinary Annuities)
Think of it as 48 payments of 1000 at 2.5%, then that sum riding along for 72 periods at 3% plus 72 payments of 1000 for the next 72 periods amount = 1000(1.025^48 - 1)/.025 (1.03)^72 + 1000(1.03^72 - 1)/.03 = 1,009,889.30

triangles
Using the standard notation of listing similar triangles by listing the order of matching vertices, triangle ADE is similar to ABC (i.e. angle A matches with angle A, angle D matches with angle B, angle E matches with angle C, that way all ratios can be easily stated) AE/AD = ...

math
For the first one, the perimeter is 428 cm so each side is 428/4 or 107 cm so its area is 107^2 or 11449 cm^2 Do the second square the same way.

alg 2 first final study guide
f (x) =2X^3 + 2x^2 - 3x + 2 try values of x = ±1, ±2 f(1) = 2 + 2 - 3 + 2 ?0 f(-1) = -2 + 2 + 3 + 2 ? 0 f(2) = 16 + 8 - 6 + 2 ? 0 f(-2) = -16 + 8 + 6 + 2 = 0 , yeahhh x+2 is a factor Using synthetic division I got (x+2)(2x^2 - 2x + 1) = 0 x = -2 or x = (2 ±...

Math
sum(9) = (9/2)(2a + 8d) = 153 times 2 9(2a + 8d) = 306 18a + 72d = 306 divide by 18 a + 4d = 17 term(5) = a+4d = 17 from above

Algebra
the slope of the given line is 5 so the slope of the perpendicular line must be -1/5 So immediately you know your choice is wrong. the new line must be y-3 = (-1/5)(x+10) y = (-1/5)x - 2 + 3 y = (-1/5)x + 1 <-------- C what reasoning do you have to choose A ?

Math
I am not an American, but I was able to Google this and found out the answer in about 2 minutes. Surely you can do that also.

Annuities
amount = 4000( 1.06^30 - 1)/.06 = ....

Calculus
let the equation of the parabola be y = ax^2 , with (-100,100) on it 100 = a(-100)^2 100 = 10,000a a = 100/10000 = 1/100 so y = (1/100)x^2 The car's headlights will hit the point (100,50) when the light-line is tangent to the parabola at the point (a,b) dy/dx = (1/50)x at...

Physics. I'd appreciate your help.
"..acting at 30 degrees" is not clear. Which way does the 30° go, east of north ?, west of north ?, I will solve it as if it was 30° east of north. If not just make the necessary adjustments. the resultant of our two forces, I will consider north to be 90°...

precalculus
We know sinØ = y/r so r sinØ = 2 r(y/r) = 2 y = 2 <------- the horizontal line y = 2

math help
< says "less than" > says "greater than"

Algebra
speed of plane in still air ---- x mph speed of wind ------------ y mph 1575/(x+y) = 7 7x+7y = 1575 x+y = 225 1575(x-y) = 9 9x - 9y = 1575 x - y = 175 add them: 2x = 400 x = 200 back-sub: 200+y = 225 y = 25 state your conclusion

Maths
I will assume that 41/4 is to mean 4 1/4 or 17/4 weight of box C ---- x weight of box B -----(17/4)x weight of box A ---- (5/2)(17/4)x or (75/8)x total weight : 19 5/4 kg or 195/4 kg ??? , the way you typed it. I was going to make the same assumption as above, but why would it...

Algebra
2b + s = 770 ---> s = 770-2b 3b + 2s = 1260 use substitution: 3b + 2(770-2b) = 1260 solve this for b to get burgers sub back into s = ... to get soda

Area of a figure
As you probably noticed, your figure did not come out as you intended. I read that as a rectangle 4 by 10 with an attached triangle of base 6 and height 4 so total area = rectangle + triangle = 4x10 + (1/2)(6x4) = 40 + 12 = 52 btw, "triangular point" makes no sense. ...

Algebra
You don't say what kind of a figure you have, but since you only mentioned three sides, I will assume you have a triangle. middle side ---- x shortest side ---- x-14 longest side ----- x+2 x + x-14 + x+2 = 60 solve for x, sub back into my definitions. Check if your answers...

Math solving for x
4x^2 + 7 is a second degree expression Had it been 4x^3, it would have been a third degree expression. The term with the highest degree determines the degree of the whole expression. If the equation had been 4x^2 + 7 = 0 4x^2 = -7 x^2 = -7/4 which is not a real number, so the ...

Math Word Problem
total number of students on the bus = 46 so what is the percentage equivalent of 20/46 ? You just want an approximation. If it had been 20/50 it would have been 40% you the denominator is a bit less than 50, so your percentage is a bit more than 40%, How about 43% or 44% ?

Math Word Problem
let the amount blueberry juice be x cups let the amount of raspberry cups be 3x cups (notice x : 3x = 1 : 3 , as needed) x + 3x = 48 4x = 48 x = 12 So she needs 12 cups of blueberry and 36 cups of raspberry notice 12 : 36 = 1 : 3 as required.

math
let the angles be 3x, 5x, and 7x you know they have to add up to 180° Solve 3x + 5x + 7x = 180 for x, the sub back into my definitions.

Math
My suggestion is to just learn the proper way to multiply. For relatively small numbers I might use the distributive property mentally. e.g. 14 x 6 ----> 10x6 + 4x6 = 60+24 = 84 or in cases like 18 x 6 , you could do 20x6 - 2x6 , .... (18 = 20-2) = 120 - 12 = 108 For larger...

math
Look at the question that Steve answered 3 years ago http://www.jiskha.com/display.cgi?id=1372679603 It is identical to yours except there were 7 children instead of your 10 BUT, in your question it seems that they changed the 7 to 10 but failed to change the associated ...

algebra
3x + 6y = 12 or even better ... x + 2y = 4

Math
h(x) = x^2 - 8x + 1 h(-1) = (-1)^2 - 8(-1) + 1 = 1 + 8 + 1 = 10

Geometry
that answer cannot possibly be correct let C(-2,-3) be the centre of rotation. then CA = <-5+2, -40+3> , where <...> is a vector = <-3,-37> using the rotation matrix cosØ -sinØ sinØ cosØ times <-3,-37> = 0 -1 1 0 times -3 -37...

Math
more than likely Lucy meant 4 x 10^5 and 4 x 10^7 as the two distances difference = 4(10^7) - 4(10^5) = 4(10^5) (10^2 - 1) = 4(99)(100,000) km farther = 39,600,000 km more or simply 40,000,000 - 400,000 = 39,600,000 km more

Math
1 slurp = (2/5)gulps 1 sip = (2/7) slurps 35 sips = 35(1/7)slurps = 5 slurps = 5(2/5) gulps = 2 gulps

Math
If your equation is x = -2 you have a vertical line where all points have the x-value of -2 e.g. (1,-2), (4,-2), (-2,-2), (0,-2) etc In general if you have an equation where the y term is missing you have a vertical line If you have an equation where the x term is missing , ...

Math (optimization) really confused
Make a sketch of a rectangle with a line parallel to the width dividing the rectangle into two equal parts. Let the length of the smaller rectangle be x and its width equal to y. (the whole rectangle would be 2x by y) given: 2xy = 225 y = 225/(2x) length of fence = L L = 4x + ...

Probability
your data is perfectly suited for this applet http://davidmlane.com/normal.html Just enter you data and enjoy

Math (related rates) help?
let the height of the ladder against the wall be y ft and let the base of the ladder be x ft from the wall we know x^2 + y^2= 13^ 2x dx/dt + 2y dy/dt = 0 when y = 12, x = 5 by above Pythagoras, and dy/dt = -2 ft/s 2(5)(dx/dt) + 2(12)(-2) = 0 dx/dt = 24/10 = 2.4 ft/s

Math
When dividing powers with the same base, keep the base and subtract the exponents, so 100^12 / 100^8 = 100^4 , which is C check the second one in the same way

h.p.
No response or indication that you even looked at the answers I gave you to your previous questions in this topic. What are your thoughts on this question?

h.p.
so term(6) = 1/(a+5d) = 1 a+5d = 1 ** term(10) = 1/(a+9d) = 5 5a + 45d = 1 *** ** times 5 ---> 5a + 25d = 5 subtract from *** 20d = -4 d = -1/5 in ** a - 1 = 1 a = 2 so the HP is 1/2 , 5/9 5/8, 27/20, ... term(15) = 1/(a+14d) = 1/(2 - 14/5) = -5/4

ALGEBRA PLEASE HELP
for a given point (p,q) and slope m the equation is y - q = m(x - p) Which of the choices matches this pattern for your given data

harmonic progression
Just like in your previous problem, the corresponding AS is 2/5 + 13/20 + 9/10 + 23/20 + ... = 8/20 + 13/20 + 18/20 + 23/20 + ... looks like a = 8/20, and d = 5/20 or a = 2/5 and d = 1/4 so term(n) of this AS = a + (n-1)d = 2/5 +(1/4)(n-1) = 2/5 + n/4 - 1/4 = n/4 + 3/20 = (5n...

harmonic progression.
If 1/3+8/23+4/11..... is a harmonic series, then the corresponding arithmetic series is 3 + 23/8 + 11/4 + ... = 24/8 + 23/8 + 22/8 so a = 3 and d = -1/8 term(7) = a + 6d = 3 -6/8 = 9/4 so the 7th term of the HS is 4/9

Inequality test
Wrong "guess", Jason why did you pick D ?

Geometry
#1, correct #2. you have a reflection in a horizontal line, so the x value does not change. P(4,11) was 8 units above y = 3, so the new point has to be 8 unites below y = 3 that is we want (4,-5) or D #3. reflection across the y-axis, leaves the y alone but switches the x to ...

calculus
if s(t) = (t+3)/(t-1)^3 v(t) = ( (t-1)^3 - (t+3)(3)(t-1)^2 )/(t-1)^6 , using the quotient rule v(t) = (t-1)^2 (t-1 - 3t - 9)/(t-1)^6 = (-2t - 10)/(t-1)^4 = -2(t+5)/(t-1)^4 I will leave it up to you to show that a(t) = 6(t+7)/(t-1)^5 so the velocity is decreasing for a(t) < ...

g.p.
Assuming g.m. stands for geometric mean the terms are 2, a, and 1/4 and a/2 = (1/4)/a a^2 = 1/2 a = ± 1/?2 or ± ?2/2

g.p.
the terms would be 8/27, (8/27)r, (8/27)r^2, (8/27)r^3, (8/27)r^4, (8/27)r^5, (8/27)r^6 , -81/6 (8/27)r / (8/27) = (-81/16) / ((8/27)r^5) r^7 = (-81/16)(27/8) r^7 = (-3)^7 / 2^7 r = -3/2 I will let you find the terms to be inserted

calculus need help studying now
a) I suggest expanding this rather than using the product rule y = (x^2 - 4x + 4)(x-7) = x^3 - 11x^2 +32x - 28 y ' = 3x^2 - 22x +32 y '' = 6x - 22 = 0 for a point of inflection x = 22/6 = 11/3 <------ there is your error y = (11/3-2)^2 (11/3-7) = (25/9)(-10/3...

Math Question
x^2+y^2-7x=12-4y x^2 - 7x + 49/4 + y^2 + 4y + 4 = 12 + 49/4 + 4 (x - 7/2)^2 + (y+2)^2 = 113/4 = ?113/2 you had that so the centre is (7/2 , -2) and the radius is ?113/2 which is appr 5.315 set you compass at appr 5.3 units, and with the above centre, draw your circle

Math
looks like you are just dividing your input by 10 y = x/10

math
Usually the "length" of a rectangle is greater than its "width", but anyway..... let the length be x yds then the width is x+15 yds x(x+15) = 100 x^2 + 15x - 100 = 0 (x - 5)(x + 20) = 0 x = 5 or x = -20, the latter is not possible the length is 5 and the ...

Math (please check my answer)
2 angles and the contained side of one triangle are the same as 2 angles and the same contained side of another, so ASA makes them congruent.

MATH @Damon @ms. Sue
The assumption we have to make is that the velocity is a linear function of the time .... So we have two ordered pairs (3,53) and (6,62) slope = (62-53)/(6-3) = 3 using the point (3,53) v-53 = 3(t-3) v-53 = 3t - 9 3t - v = - 44 or y = 3t + 44 should be easy to plot for 3 < ...

Math
younger brother --- x years Martha ----------- 2x years x + 2x = 36 carry on

Math
speed of current ---- x mph distance traveled each way ---- d miles time with the current = d/(6+x) time against the current = d/(6-x) d/(6-x) = 2d/(6+x) divide by d 1/(6-x) = 2(6+x) 6+x = 12 - 2x 3x = 6 x = 2 state your conclusion.

Math
salmon's rate of swimming --- x mph let rate of current be y mph 15/(x+y) = 3 3x+3y=15 ---> x+y=5 15/(x-y)=5 5x - 5y = 15 ----> x - y = 3 add those two equations: 2x = 8 x = 4 , then y = 1 state your conclusion

algebra
typo error in 90 c + 180 + 130 c = 4 c^2 + 80 c should be : 90 c + 1800 + 130 c = 4 c^2 + 80 c ---> c^2 - 35c - 450 = 0 (c - 45)(c + 10) = 0 c = 45 or a negative city speed was 45 mph

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Bro subscribe to the alex jones channel my man!

Business Math
i = .06/12 = .005 n = 20(12) = 240 PV = 50,000 paym = ?? paym( 1 - 1.005^-240)/.005 = 50,000 payment = $358.22 after 7 years: balance of mortgage = 50000(1.005)^84 - 358.22(1.005^84 - 1)/.005 = $38,737.12 Since the current value is 90,000 but they still owe 38,737.12 the ...

Math
"Determine the initial amount of the substance to the nearest 10th of an hour" HUH, since when is an amount of something measured in units of time?? (I will just ignore that part of the question) N = 8 e^(-6t) initial --- t=0 N = 8 e^0 = 8 mg <----- the initial ...

Math
let each of the equal sides be x cm A = (1/2)x^2 dA/dt = x dx/dt we know dA/dx = -5 cm^2 /s dx/dt = -5/x H^2 = x^2 + x^2 = 2x^2 H = ?2 x dH/dt = ?2 dx/dt = ?2(-5/x) so when x = 10 dH/dt = -5?2 /10 = -(1/2)?2 cm/s or appr -.707 cm/s

Algebra
number of dimes ---- x number of nickels ---- 2x + 1 value of coins: 10x + 5(2x+1) = 165 10x + 10x + 5 = 165 take over

math
http://www.jiskha.com/display.cgi?id=1480267024

Math
the way you typed it .... -5 + ?-50/10 = -5 + 5?2 i/10 = -5 + (?2/2) i what you probably meant: (-5 + ?-50)/10 = (-5 + 5?2 i)/10 = -1/2 + (?2/2) i

Emma
We solve equations, you don't have an equation if you meant: evaluate (?6+i)(?6-1) = 6 - ?6 + ?6i - i I have a strong feeling you meant: (?6+i)(?6-i) = 6 - i^2 , but i^2 = -1 = 6+1 = 7

Algebra
y = kx given: x=3, y=10 10 = k(3) k = 10/3 so y = (10/3)x when x = 6 y = (10/3)(6) = 20

precalcalculus
I assume you are familiar with the tradional way of identifying the information given about a triangle, such as ASA, SAS, SSS and SSA use "cosine law" for SAS and SSS use "sine law" for ASA and SSA #1 - a case of ASA --> a side contained between two ...

precalculus
There are several question of your type in the Related Questions section below

precalculus
Vague question. are you converting an equation or a point with rectangular coordinates?

Maths
For any number, there are 10 possible digits for the unit place, one of those is the 2. so prob(your event) = 1/10

Algebra
compare: http://www.jiskha.com/display.cgi?id=1480210517

Algebra
find the vertex of the parabola. The t of the vertex tells you when it reached the maximum height, the h tells you what that height is.

Math
equation: y = 100 (2)^(t/3.2) .. .. to get 450 bacteria 450 = 100 (2)^(x/3.2) 4.5 = 2^(x/3.2) take log of both sides and use log rules (x/3.2)log 2 = log 4.5 x/3.2 = log 4.5/log2 x = 6.944 hrs. or appr 7 hours

precalculus
How does this post differ from this one? http://www.jiskha.com/display.cgi?id=1480198638

PreCalc
let f(x) = 2x^3+x^2-8x+3 f(1) ? 0 f(-1) = -2+1+8+3 ? 0 f(3) ? 0 f(-3) ? 0 f(3/2) = 0 , yeahhhh, 2x-3 is a factor by long division, 2x^3+x^2-8x+3 = (2x-3)(x^2 + 2x -1) the quadratic has roots of x = -1 ± ?2 looking at the graph of y = 2x^3+x^2-8x+3 -1-?2 < x < -1+?...

Algebra
let the distance from Seattle to wilderness be x miles x/420 + x/300 = 6 times 2100 the LCM 5x + 7x = 12600 x = 1050 miles

Trigonometry
look at the cos^-1 (x/3) construct a triangle with base of x and hypotenuse of 3 by Pythagoras: r^2 = x^2 + y^2 3^2 = x^2 + y^2 y^2 = 9 - x^2 y = ?(9-x^2) so we want the tangent tan (cos^-1 x/3) = opposite/adjacent = ?(9-x^2)/3

precalculus
(3(cos(5pi/4)+i sin (5pi/4) ) )^8 = 3^8(cos 8(5?/4) + i sin 8(5?/4)) = 6561( cos 10? + i sin 10?) = 6561( 1 + i(0) ) = 6561 B (3-3i)^6 let z = 3-3i, so we want z^6 r = ?(9 + 9) = ?18 = 3?2 plot (3,-3) which is in IV, so Ø = 315° or 7?/4 z = 3?2(cos 7?/4 + i sin 7?/4...

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