Thursday
April 24, 2014

Posts by Reiny


Total # Posts: 26,130

Precal
If AS , then 3x-1 - (-8x-3) = 2x+49 - (3x-1) 3x - 1 + 8x + 3 = 2x + 49 - 3x + 1 12x = 48 x = 4 check: if x = 4, the terms are -35, 11, and 57 and yes, there is a common difference of 46

math
distance for 1st bounce = 729 distance for 2nd bounce = 2(1/3)(729) = 2(243) distance for 3rd bounce = 2(1/3)(243) = 2(81) distance for 4th bounce = 2(1/3)(81) = 2(27) distance for 5th bounce = 2(1/3)(27) = 2(9) total distance = 729 + 2(243+81+27+9) = 1449

MATH
so this an arithmetic sequence with a = 8000 d = 600 n = 27 term (27) = a + 26d = 8000 + 26(600) = $23,600

Math
check your typing Is that supposed to say $8,000 ?

Math
P(x) =(2x+1)(x+3)(x-3)/((x-3)(x+2) = (2x+1)(x+3)/(x+2) When x = 3 , in new P(3) = 7(6)/5 = 42/5 so there is a hole at (3, 42/5) using P(x) = (2x+1)(x+3)/(x+2) = (2x^2 + 7x + 3)/(x+2) = 2x+3 - 3/(x+2) so we have an oblique asymptote y = 2x +3 see graph http://www.wolframalpha.c...

Geometry
It depends. Are the dimensions increased by 136% or is the area increased by 136% ?

math
-5x^2 + 400x - 2550 > 4000 5x^2 - 400x + 6550 < 0 x^2 - 80x + 1310 < 0 what are the x-intercepts? x^2 - 80x + 1310 = 0 x^2 - 80x + 1600 = -1310 + 1600 (x-40)^2 = 290 x-40 = ± √290 x = 40±√290 = appr 57.029 or 22.97 They must spend between $22...

algebra 1
I thought this looked familiar Here is an extended version of your question http://www.jiskha.com/display.cgi?id=1384866716

Math
"simplest " form would be 82944 , namely the answer if you want to write it as a power? (2^6)(6^4) or (2^4)(4)(6^4) = 4(12^4) or 4^5(3^4) or (3^4)(2^10) or ....

College alerbra
ok, then take log of both sides log (4^(x+2) ) = log (9^x) (x+2)log4 = xlog9 xlog4 + 2log4= xlog9 2log4 = xlog9 - xlog4 x(log9-log4) = 2log4 x = 2log4/(log9-log4) button-pushing time .... x = appr 3.419

College alerbra
A rough sketch of y = 4^(x+2) and y = 9x shows that the two can never meet. So, there is no solution Did you mean: 4^(x+2) = 9^x ?

math
In any reciprocal function or rational function, the possibility exists that the denominator could be zero. This would make the expression undefined, since we cannot divide by zero. So set the denominator equal to zero, solve for the variable, and the solution becomes the rest...

math
reciprocal of a linear function? I suppose we could say: f(x) = 1/(mx + b) e.g. y = 1/(3x -5) reciprocal of a quadratic function? How about f(x) = 1/(ax^2 + bx+ c) rational functions could have many different forms (there has to be an independent variable in the denominator) e...

Math
first one: a = 1.25 period = 6 2π/k = 6 6k = 2π k= π/3 so we have y = 1.25 cos ((π/3)(t + d) + 0.75 we have to know the height at the beginning (t=0) it was not given. That is, where is the swing at the "start" ? 2. circumference = 2π(3) = 6&...

PreCal
No, there is no solution, since log(any negative) is undefined. For the equation to be true, you correctly stated that 3^x = -27 I suggest you look at the graph of y = 3^x and see where the y value is -27. http://www.wolframalpha.com/input/?i=plot+y+%3D+3%5Ex

math ergent please please...
Ok, so all the algebra work has been done x^3-5x^2+2x+8<0 (x+1)(x-4)(x-2)<0 Quickest way: I would look at the graph of y = x^3-5x^2+2x+8 = (x+1)(x-4)(x-2) I know that this is standard cubic function opening up in quadrant I and having x-intercepts of -1, 2, and 4 So a ve...

Trigonometry
If cot Ø = =√15/7 then tan Ø = -7/√15 you want tangent to be negative and cosine to be positive, ---> must be in IV construct you triangle in quad IV by Pythagoras, the hypotenuse is 8 and cos Ø = √15/8

Trigonometry
You have received many replies to your numerous trig questions, and have not responded to a single one of them. How do we know that you are even reading the responses, and if so, if they are of any help to you. What is your main difficulty with these questions? What are you as...

Simple Math
present: daughter ---- x Mr. Yen ----- 61 -x 10 years from now: daughter -- x+10 Mr. Yesn -- 61-x +10 = 71-x at that time, he will be twice as old as she 71-x = 2(x+10) 71-x = 2x + 20 -3x = -51 x = 51/3 = 17 right now she is 17 and he is 44 check: 17+44 = 61 , checks in 10 yea...

Trigonometry functions
David, really now ! After getting help for so many trig question, don't you think it is time that you try some of these yourself? Especially the rather simple ones, like your last two? Let us know what you get and we'll check them

Trigonometry
This is the second time you have posted this same question since Steve answered it for you. Please look back to your previous posts before reposting it .

Steve - Trigonometry
Steve, you are right, should have looked at that original restriction more carefully. ( must have automatically assumed the usual 0 ≤ Ø ≤ 2π ) So you will find my other solution comical, where I assumed that domain and got solutions in all 4 quadrants :...

Trigonometry
if cot 2Ø = 5/12 then tan 2Ø = 12/5 recognizing the familar 5-12-13 right-angled triangle, we would say sin 2Ø/cos 2Ø = 12/5 = (12/13) / (5/13) so sin 2Ø = 12/13 ----> 2sinØcosØ = 12/13 and cos 2Ø = 2cos^ Ø -1 =...

trigonometry
If cot(2Ø) = 5/12 , then tan(2Ø) = 12/5 and 2Ø is in either I or III tan 2Ø = 2tanØ/(1 - tan^2 Ø) let tanØ = u then 12/5 = 2u/(1 - u^2) , (for easier typing) 10u = 12 - 12u^2 12u^2 + 10u - 12 = 0 6u^2 + 5u - 6 = 0 (2u + 3)(3u - ...

pre-calc help
(9√2 , -π/4 or (9√2, 7π/4 or (-9√2, 3π/4)

pre-calc help
factor it (5sinx - 1)(sinx - 4) = 0 sinx = 1/5 or sinx = 4 the latter is not possible, so sinx = 1/5 x must be in I or II x = 11.537° or 168.463° if you need the answer in radians , set your calculator to RAD (DRG button) and repeat the inverse sin operation.

Math
LS = (1-cosx)/(sinx)+(sinx)/(1-cosx) = ( (1-cosx)(1-cosx) + sinx(sinx) )/(sinx(1-cosx)) = (1 - 2cosx + cos^2 x + sin^2 x)/(sinx(1-cosx)) = (1 - 2cosx + 1)/(sinx(1-cosx) = 2(1-cosx)/(sinx(1-cosx)) = 2/sinx = 2 cscx = RS

math
check if ratio of 48: 272 = 3:17 Is it? If yes, you are right.

math
I am sure that you can push buttons on a calculator as well as I can change the percents to decimals first .... e.g. 67.95% = .6795 5% = .05 etc

math
I will read it as 31,760,000 / (1 - 0.0781 ) = 34450591.17

Pre-Calc
check your typing, is this the way you wanted it to look like ? Don't try to form fractions instead place numerator and denominatr within brackets and use / to show the division bar. e.g. (4x -9)/(x^2+6x-7)

geometry
If by vertical angles you mean opposite angles when 2 lines intersect, then they must be equal, so ... 4x- 34 = 3x + 17 x = 51 and angle1 = 3(51) + 17 = 170

math help
I will assume you want an equation which is parallel to the given line and passing through (-3,12) Then new line will have the same slope, so it will differ from the given line only in its y-intercept: new line: y = 4x + b but (-3,12) lies on it, so 12 = 4(-3) + b b = 24 y = 4...

german
Ich muss mit den anderen Lehrern mitstimmen. Sie haben dir die richtige Antwort gegeben. (notice that in both sentences, the verb is at the end)

Math
Had that first equation not mysteriously changed we would have; 1st times 3 ---> 12x - 9y = 15 2nd times 4 ---> 12 - 20y = 28 subtract: 11y = -13 y = -13/11 into 1st: 4x -3(-13/11) = 5 4x = 5 - 39/11 = 16/11 x = 4/11

Trigonometry
Do you not have a calculator? if cotØ = .791 then tanØ = 1/.791 = appr 1.264 Ø = 51.656° secØ = 1/cosØ = 1.612 2. sin^2 Ø + cos^2 Ø = 1 , one of the major trig identities, which you MUST know.

math
First of all the equation should say: h = -16t^2 + 140t + 40 you want h = 30 30 = -16t^2 + 140t + 40 16t^2 - 140t - 10 = 0 t = (140 ± √20240)/32 = 8.8 or a negative, which we will reject it would take about 8.8 seconds to reach a height of 30 ft (on its way down)

Precalc
Egg on face (intentions were honourable)

However ..... Precalc
But in log (7-4x) since we can only take logs of positives, 7-4x > 0 -4x > -7 x< 7/4 or x < 1.75 since 7400/401 > 1.75 there is no solution to this equation.

Math help, anyone?
12. 7x =24 x = 24/7 13. 22:36 = 11:18 14. 24/20 = 6/5 15. 4:12 = 4/12 = 1/3 16. 46:54 = 23:27 = 23/27

algebra
one obvious solution: d = 0 then 1/3t + 1/4.5(t+1.5) = 1 multiply each term by 9 3t + 2(t+1.5) = 9 3t + 2t + 3 = 9 5t = 6 t = 6/5 d = 0, t = 6/5

math ergent please
http://www.jiskha.com/display.cgi?id=1385391935

math
Again, I answered this question for you yesterday, when you posted it as Kevin http://www.jiskha.com/display.cgi?id=1385420924

math ergent please
I did this same question when it was posted under the name of "Kevin" now it is "kavi", mmmhhhh? http://www.jiskha.com/display.cgi?id=1385421276

analytic
so (7,3) is the midpoint remember how to find the midpoint between (a,b) and (c,d) midpoint = ( (a+c)/2 , (b+d)/2 ) so if the endpoints are (x,6) and (9,y) then ( (x+9)/2 , (6+y)/2 ) = (7,3) (x+9)/2 = 7 x+9 = 14 x = 5 and (6+y)/2 = 3 6+y = 6 y = 0 x = 5 , y = 0 check: what is ...

math
A's rate = 1/16 B's rate = 1/12 combined rate = 1/16+1/12 = 7/48 let the total time taken be t days so ... 2(1/16) + (t-2)(7/48) = 1 1/8 + (7/48)t - 7/24 = 1 , ----- 1 for whole job 7t/48 = 1 - 1/8 + 7/24 7t/48 = 7/6 7t = 56 t = 8 days So it took 8 days, with A working...

Algebra 1`
so you want to write the equation in the form y = ....... This usually requires two steps: 1. move everybody except the y term to the right side 3y = 12x + 15 2. divide each term by the coefficient of the y term y = 4x + 5 you can do this with every linear equation in x and y.

College Algebra
since the zeros of the quadratic are -4 and 3 we can say: f(x) = a(x+4)(x-3) so the only thing we don't know is a possible coefficient. but f(1) = - 30 -30 = a(1+4)(1-3) -30 = -10a a = 3 f(x) = 3(x+4)(x-3) expand if so needed

Algebra 1
let's look again at the third if you had √-47 there would be no answer but if you had - √47 then it would be -6 to the nearest integer.

Algebra 1
The first two are correct to the nearest integer. The third is a trick question, you cannot take the square root of a negative number

math
6 = 2x3 9 = 3x3 so the LCM of 6 and 9 is 18 so how many multiple so 18 are there from 1 to 1000 ? ...18 ....36 ... etc ... 990 term 1 = 18 term 2 = 36 ... term ? = 990 can you determine which term ? is equal to 990 ?

math
depends on what arithmetic operation you perform the "equation" of two negative fractions is not an operation. Please clarify your problem.

algebra
height of penny = -16t^2 + 5t + 4 to reach bottom of well, h = -100 -16t^2 + 5t + 4 = -100 16^2 - 5t -104 = 0 using the formula: t = appr 2.7 or a negative, which we'll reject

math ergent please
"the remainder is -2 when f(x) is divided by x+1" --> f(-1) = -2 and similarly f(1) = -4 yielding you two equations: f(-1) = -k - m - 3 + 7 = -2 k+m = 6 f(1) = k-m+3+7=-4 k - m = -14 solve these two equations for k and m

math
PM(x)=-x^3+7x^2-10x = -x(x^2 - 7x + 10) = -x(x-5)(x-2) so the x-intercepts of this function are 0, 5, and 2 and it is a cubic with a negative cubic term Make a sketch and you should be able to answer all your questions quite readily.

math
I use synthetic division for this type of question -2 | 1 -3 1 2 ........ -2 10 -22 ....... 1 -5 11 -20 (hard to line up nicely) x^3-3x^2+x+2 = (x+2)(x^2 - 5x + 11) - 20

math
first try, x=1, turns out to be a zero So ... synthetic division 3x^3+x^2-8x+4 > 0 (x-1)(3x^2 + 4x - 4) > 0 (x-1)(x+2)(3x - 2) > 0 so the corresponding function y = 3x^3 + x^2 - 8x + 4 has x-intercepts of -2, 1 and 2/3 and knowing the shape of this standard cubic to o...

math
How do you propose we show a "graphing calculator" solution on here ? since choices of x+ ±1, ±2 are the obvious first guesses and x = 2 can be found to be a solution in a few seconds, I then did a synthetic division to get 6x^3-13x^2+x+2=0 (x-2)(6x^2 -...

Calculus - Volume By Integration
I also checked my calculation in our previous post http://www.jiskha.com/display.cgi?id=1385311297 I carelessly dropped the π in my last 3 lines, and should have used my calculator to add up the terms in my last line. My last line should have been 500π which then als...

math
using the factor theorem, I tried x = ±1, ±2, ±5 I found x=1 and x=-1 to work as well as x=-2 so factors would be (x+1)(x-1)(x+2)(........) I can reason that the first term of the missing factor is x and it must end in -5 so x^4-3x^3-11x^2+3x+10 = (x-1)(x+...

math
let rate of the stream be x km/h So speed with the current = 5+x speed against the current = 5-x 2/(5-x) - 2/(5+x) = 10/60 times ((5-x)(5+x) 2(5+x) - 2(5-x) = (1/6)(25 - x^2) 4x = (1/6)(25-x^2) 24x = 25-x^2 x^2 + 24x - 25 = 0 (x+25)(x-1) = 0 x = 1 or x = a negative, which we w...

Math Word Problem
1. common sense solution: if it takes 10 carpenters to do a house in 8 days, then 1 carpenter would take 80 days, and 4 carpenters would take 20 days. 2. by the "constant" method number of days = k/number of carpenters given: 8 = k/10 k = 80 so number of days = 80/nu...

Calculus Area between curves
Here is a sketch of the region http://www.wolframalpha.com/input/?i=solve+x%2B6y%3D8+%2C+x%2B8%3Dy%5E2 I will do it the easiest way. The intersection points are (-4,2) and (56,-8) I would take horizontal slices effective width of a horizontal slice = 8-6y - (y^2 - 8 = 16 - 6y ...

math
prob = C(30,2) x C(13,1)/C(43,3) = 435(13)/12341 = .4582..

compound interest
do it the same way I just showed you in your previous post.

compound interest
time = 77-21 = 50 years amount = 1000(1.1)^50 = $ 117,390.85

Math
Use Pythagoras ... shorter side = x longer side = x+5 diagonal = 32 x^2 + (x+5)^2 = 32^2 x^2 + x^2 + 10x + 25 - 1024 = 0 2x^2 + 10x - 999 = 0 by formula: x = 19.99 or appr 20 or a negative so the two sides are appr 20 inches by 25 inches

cv
7n−(9n+1)>5 7n - 9n - 9 > 5 -2n > 14 n < -7

Algebra 2
#3 - #1 y - z = 0 or y = z 2x#1: 2x + 4y + 4z = 12 #2 : -2x + 4y + 6z = -3 add them, 8y + 10z = 9 sub in z=z 8z + 10z = 15 z = 9/18 = 1/2 y = 1/2 in #3 x + 3/2 + 1/2 = 6 x = 6-4/2 = 4 x=4, y=1/2, z = 1/2

college problem solving
let the tens digit be x and the unit digit be y then the number is 10x + y 10x+y = (x+7y) - 6 9x - 6y = -6 3x - 2y = -2 , #1 the number reversed would be 10y + x so 10y+x = 10x+y + 27 9x - 9y = -27 3x - 3y = -9 , #2 #1 - #2 y = 7 then from #1, x = 4 the number is 47 check: rev...

Calculus - Volume by Integration
A quick look at the region bounded by y=(x-2)^3-2, x=0, y=25 http://www.wolframalpha.com/input/?i=plot+y%3D%28x-2%29%5E3-2%2C+x%3D0%2C+y%3D25 shows me that I should scan horizontally from y = -10 to y = 25 using V = π∫ x^2 dy from y = -10 to 25 I need x^2 y = (x-2)^...

Geometry
make a sketch and reflect the point (4,6) in the vertical line x = 1 to get (-2,6)

math
Huh? What previous question ?

Calc
At a time of t hrs, let the position of ship A be P and let the position of ship B be Q Join PQ, and complete the large righ-angled triangle having a base of 100 and a height of 15t + 30t or 45t (the horizontal distance between them is always 100 km PQ^2 = 100^2 + (45t)^2 2 PQ...

Math
One of the popular questions in Calculus texts. Let the radius of the circle be x then the width of the rectangle = 2x let the height of the rectangle be y 2x + 2y + halfcircle = 30 2x + 2y + (1/2)(2πx) = 30 2x + 2y + πx = 30 2y = 30 - 2x - πx y = 15 - x - π...

math problem grade 8!!
14 saves, 1 goal let in ----> 15 shots probability of letting in a goal = 1/15 so for 90 shots, prob of likely goals = (1/15)(90) = 6

math
it isn't. prob of drawing a queen = 4/52 = 1/13 prob of not drawing a queen = 12/13 so the odds in favour of drawing a queen = (1/13) / (12/13) = 1/12 or 1 : 12

math
Ricardo ----- x Miriam ------ x+4 10 years ago: Ricardo -- x-10 Miriam --- x+4-10 = x-6 at that time she was 3 times as old as Ricardo x-6 = 3(x-10 x-6 = 3x - 30 -2x = -24 x = 12 Ricardo IS now 12 and Miriam is now 16 You check the answers to make sure the conditions fit.

Math
mmmh, let's see - I don't see any absolute value symbols - I don't see any fractions with variables in the denominator - I see a cubic term, so it is not quadratic. well , by the process of elimination......

Math
If you increase the radius of a circle, does its diameter increase or does it decrease?

Algerbra
from the 2nd ---> y = x+4 sub into the 1st x^2 + (x+4)^2 = 58 2x^2 + 8x+16-58 = 0 x^2 + 4x - 21 = 0 (x+7)(x-3) = 0 x = -7 or x = 3 if x = -7, y = -7+4 = -3 if x = 3 , y = 3+4 = 7 x=3, y=7 or x=-7, y = -3

finance charges
very vague question the way it is presented m, r, and t are not defined Do you want Present Value or Future amount the formulas should be in your text or are easily looked up.

finance
Let P be the semiannual payment P(1.065^30 - 1)/.065 = 50000 P = 578.87

math
???? check your typing.

Algebra
If your variables disappear after performing valid algebraic operations, and -you end up with true statement, there are an infinite number of solutions -you end up with a false statement, there are no solutions. so in your case the statement 0 = 0 is true, so .....

Calculus
Let the point be P(x,y) , point (-4,1) be A Since the shortest distance must be where AP is perpendicular to the given line. slope of given line = 6/5 so slope of AP is - 5/6 equation of AP: y-1 = (-5/6)(x+4) times 6 6y - 6 = -5x- 20 5x + 6y = -14 , #2 6x - 5y = -1 , #1, the g...

Math help plz check my answers!
1. 10:2 is not in lowest terms, both numbers divide by 2 10:2 = 5:1 2. r/5= 9/21 r = 45/21 = 15/7 which is appr 2.143 They should have given 15/7 as the correct choice, the rounded off number is not exact. 3. puzzled by your choice. it takes 3 cups to make 9 dozen so it takes ...

Math-Algebra 1
Different texts use slightly different names for the form of the linear equation. e.g 4x + 3y -12 = 0 -----> I would call general form 4x + 3y = 12 -------> standard form y = (-4/3)x + 4 ---- > slope-y intercept form point-slope form is a starting equation, usually en...

math
you have to do in in two parts we need the x-intercept: 0 = √x-3 √x = 3 x = 9 area from 0 to 9 + area from 9 to 16 (If you do it in one calculation from 0 to 16, the area which is below the x-axis will work its way into the answer as a negative area) y = √x -...

algebra 2
2(x-5)>6(x-3) 2x - 10 > 6x - 18 2x - 6x > -18+10 -4x > -8 x < 2

math
A very common formula for the area of a triangle with sides A and B with Ø the contained or included angle between them is Area = (1/2)(A)(B)sinØ then (1/2)(12)(9)sinØ = 48 sinØ = .88888.. Ø = appr 62.7° or 117.3° make a sketch to see...

math
monthly rate = .04/12 = .003333... time from 23rd to 65th birthday = 504 months amount = 100( 1.003333..^504 - 1)/.003333.. = $130,517.61

algebra 1
w = -3 is a "reasonable" answer because it satisfies the original inequation, and it falls within the domain of my solution. There are an infinite number of reasonable answers. check: if w = -3 LS = |4 - 3(-3)| = |4+9| = 13 Is 13 > 8 ??? YES, so w = -3 is one of t...

algebra 1
Here would be the correct solution ... 4-3w > 8 OR -4 + 3w > 8 -3w > 4 OR 3w > 12 w < -4/3 OR w > 4 You didn't state what Paul had said.

algebra 1
10 ???? How much spread is there between 10 and 14 ?? So , are you malik or nicki? don't switch names.

algebra 1
The domain is -40 < x<40 which I interpret at 40 days before Sept 21 and 40 days after Sept 21 (you do the counting) the range would be .... well if x = -40 y = -.05(-40) + 12 = 2+12 = 14 and if x = +40 y = -.05(40)+12 = -2+12 = 10 The numbers 14 and 10 would be the numb...

algebra 1
Here is a graph of the situation. http://www.wolframalpha.com/input/?i=plot+y%3D-0.05x+%2B+12+%2C+-40%3Cx%3C40 The way it is stated the equation makes little sense to me. Is x the time relative to Sept 21 ? Is -40<*<40 supposed to mean -40 < x <40 ? that is, are yo...

algebra 1
Last night , I had given you a full explanation, set-up and even the solution for this problem, even though it only asked for the two inequations at the beginning of my solution. http://www.jiskha.com/display.cgi?id=1385177236 and you responded with, I am confused. What part d...

cal
I think you meant: f(x) = x/(x^2 + 1) (or else why not just reduce it to f(x) = 1/x + 1 ? ) for concave upwards, f ''(x) > 0 f'(x) = (1 - x^2)/(x^2 + 1)^2 using the quotient rule and again f''(x) = 2x(x^2-3)/(x^2+1)^3 so when is f''(x) positive ?...

math
Huh ? What question above ?

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