# Posts by Reiny

Total # Posts: 38,372

**Maths**

first of the numbers ---- x the next odd number ---- x+2 x(x+2) = 195 x^2 + 2x - 195 = 0 (x+15)(x-13) = 0 carry on

**Algebra**

Assuming that your "new math" follows the traditional order of operation, just do it. a ? b = 2a ? 3b then: (1 ? 2) ? 7 = (2 - 6) ? 7 = -4 ? 7 = -8 - 21 = -29

**Maths**

let the sides be 3x, 4x, and 5x solve for x and sub into my definitions 3x+4x+5x = 12 you should be able to do it in your head. Did you notice that your triangle is also right-angled?

**Math**

Just make the changes to my solution I gave you before you found the typo http://www.jiskha.com/display.cgi?id=1485954263

**Maths**

length of base = 50-10 = 40 cm width of box = 40-10 = 30 cm height of box = 5 cm volume = length x width x height = ...... cm^3

**Kevin ? - Math**

The first part I already answered in your previous post. If the gradiant is 34, the diameter is quite steep. Lets find its equation: y = 34x + b but (1,2) lies on it, so 2 = 34(1) + b b = -32 y = 34b - 32 the equation of the circle I described in the earlier post is (x-1)^2...

**math**

nope .... amount = 500 (1.25)^m , where is the number of minutes (an increase of 25% results in what you started with plus the increase or 1 + .25 = 1.25 e.g. suppose an article costs $100 a 25% increase would be $25 so the cost is $125 that is: 100(1.25) = 125 )

**Math**

The line AB would be the horizontal diameter of a circle with centre (1,2) and radius 5 So just go 5 units to the left and to the right of (1,2) A could be (-4,2) and B could be (6,2) or B(-4,2) and A(6,2) notice AB = ?(6+4)^2 + 0^2) = 10

**Math**

what is (26.5+31)/2 ?

**Math**

Follow the same steps I just showed you here http://www.jiskha.com/display.cgi?id=1485922261

**Math**

Follow the same steps as I just showed you when you were Bobby

**Math**

f'(x) = lim (f(x+h)?f(x))/h , as h ---> 0 =lim (4hx?1h+5h^2)/h , as h ---> 0 = Lim (4x - 1 + 5h) , as h ---> 0 = 4x - 1

**Math**

4 inches ---> 6 ft 1 inch -----> 6/4 ft or 1.5 ft

**maths**

"4th term is 7" ---> a+3d = 7 "7th term is 13" ---> a+6d = 13 subtract them: 3d = 6 d = 2 sub back into my first equation to find a, then use the Sum of Terms formula to find sum(20)

**math**

The previous one is (2n-2) the next one after 2n is (2n+2

**Math**

8 bananas at 50 g each is 400 g what is 400/1000 times $6.50 ?

**Math**

x- 4/5 = 12/15 x = 4/5 + 12/15 x = 12/15 + 12/15 = 24/15 = 8/5

**Math**

(x-3)^2 + sin(x-3) + 7

**sequence help plz**

clearly an arithmetic series with a = 5 and d = 6 sum(2n) = (2n/2)(10 + (2n-1)(6)) = n(10 + 12n - 6) = 4n + 12n^2

**math**

so your chord is also 3 cm from the centre. construct the right-angles triangle look at the angle it makes at the centre, cosØ = 3/6 = 1/2 Ø = 60° the chord subtends an angle of 120°

**MATH @Damon @ms. Sue**

notice for Option 1: 1100 1210 1331 1210 / 1100 = 1331 / 1210 = 1.1 so we have a geometric progression, making the function exponentinal term(n) = 1100 (1.1)^(n-1) , where n is the number of years in Option 2: 1100 1200 1300 we have 1200 - 1100 = 1300 - 1200 = 100 we have a ...

**maths**

16 2/3% = 50/300 = 1/6 check: on my calculator 1/6 = .166666... or 16 2/3%

**Math**

500 (2^(t/12)) = 800 , where t is in hours 2^(t/12) = 1.6 take logs of both sides, and use the rules of logs t/12 log2 = log 1.6 t/12 = log 1.6/log 2 t = 12(log 1.6/log 2) = appr 8.1 hours

**Algebra**

John1 meant to say 3(-3x) = -9x , not -6x then 2x - 9x = 6 -7x = 6 x = -6/7 ---> not found in any of the answers, so I suspect a typo somewhere y = -3(-6/7) = 18/7 (-6/6 , 18/7) is the correct solution This answer works in both equations

**Algebra**

rate last year = 1300/1250 = 1.04 if rate is the same, next year: 1300(1.04) = 1352

**Math**

what is 8 ÷ (2/3) ?

**Math**

In the second term, I counted 6 of "(" and 7 of ")", so mismatched brackets. I will assume you meant: cos(x)/(1-tan(x)) + (sin (x))* cos(x))/ (sin (x)- cos(x)) then: = cosx/( 1 - sinx/cosx) + sinx cosx/(sinx - cosx) = cosx/( (cosx - sinx)/cosx) - sinxcosx/(...

**Math**

I usually change everything to sines and cosines (tan(x) +cot(x))/ (tan(x)*cot(x)) = (sinx/cosx + cosx/sinx) / (sinx/cosx * cosx/sinx) = (sin^2 x + cos^2 x)/(sinxcosx) / 1 = 1/(sinxcosx) ----> I know 2sinxcosx = sin 2x so sinxcosx = (1/2)sin2x = 2/sin 2x or 2 csc 2x or from...

**Math**

(1+tan(x))* (1+cot(-x)) = (1 + sinx/cosx)(1 + cosx/sinx) = [ (cosx + sinx)/cosx][ (sinx + cosx)/sinx] = (sin^2 x + cos^2 x + 2sinxcosx) / (sinxcosx) = (1 + 2sinxcosx)/(sinxcos) = 1/(sinxcosx) + 2 or = secs cscx + 2

**math**

solve these equations: 1. 20-x = 10 2. 10x - 12 = 18 at the end you say "what is the number 7" ?????

**Math**

greater --- x lesser --- x-1 x+x-1 = 15 solve and sub into my definitions

**Geometry**

clearly the ellipse has a vertical major axis centre is (2,1) , b = 3 For this ellipse: e = c/b 1/3 = c/3 c = 1 a^2 + c^2 = b^2 a^1 + 1 = 9 a^2 = 8 (x-2)^2/8 + (y-1)^2/9 = 1

**Geometry**

"Angle D is nine less than twice the measure of Angle C" D = 2C - 9 and we know C+D = 180 , so .....

**Coordinates**

Show that two of the three line segments have slopes that are negative reciprocals of each other.

**Math**

c(x) = 8 + 1.5x

**Maths**

a = 120000 m/s^2 v = 120000t + c when t=0, v = 0 , so c = 0 s = 60000t^2 + k , where s is the distance, k a constant when t=0, the plane hasn't gone anywhere so 0 = 0 + k, k = 0 s = 60000(t^2) when t = 4, s = 60000(4) = ...

**Maths**

draw a perpendicular from the centre to the chord. draw the radius to the end of the chord. You have a right-angled triangle with one leg of 6 and a hypotenuse of 10. Use Pythagoras

**Math**

That is some wind!!! I think you have a typo and meant that the plane's speed is 650 mph. however, taking it as is: let the plane's speed be x mph from city x to city y: distance = 8(x-650) from city y to city x: distance = 5(x+650) 8(x-650) = 5(x+650) solve for x , ...

**Mathematics**

draw the science circle totally within the math circle enter 56 in the science circle, put 17 in the science only circle 82-73 or 9 take neither science nor math.

**Maths**

x(1.8)(r) = x 1.8r = 1 r = 1/1.8 = .555.. so the discount rate should be .444... or appr 44.4% e.g. suppose the item cost $100 after markup, selling price = 180 to end up with $100, we have to discount it $80 80/180 = .44444 notice 1 - .4444... = .555...

**Geometry**

This makes no sense to me. If the octagon is equiangular (all angles are equal) , how can the side be of different lengths ?

**math**

Join the centres and you will have an equilateral triangle with sides 1 m Also the band will form 3 arcs , each of 120°. So the band covers the entire distance around the circle, that is, its circumference. Notice that if you complete the rectangle, we know the long side ...

**math**

let the time be t minutes distance covered by Ali = 48t distance covered by Tina = 62t 48t + 62t = 1320 solve for t

**statistics**

cutting through the chase .... prob(your stated event) = C(10,7)(1/5)^7 (4/5)^3 = 120(1/78125)(64/125) = appr .0008

**Maths**

from the second: 4x + 10y = 50 4x = 50-10y into the first: 50-10y - 3y = 11 -13y = -39 y = 3 then 4x = 50 - 30 x = 5

**Math**

sheets left after 1st week = 4/5 of 500 = 400 after 2 more weeks 3/5 of those are left = 240 or, long way: papers used in 1st week = (1/5)(500) = 100 left: 400 he uses 2/5 of those: (2/5)(400) = 160 leaving him 400 - 160 or 240 at the end of 3rd week

**Algebra**

|4-6|^3 - |5-9| / |3(6-5)| + |35-7)| = 8 - 4/3 + 28 = 104/3

**math**

The order of these items does not matter so I will use combinations Size -- C(3,1) = 3 meats --C(7,1) = 7 veggies --C(5,2) = 10 cheese -- C(4,1) = 4 number of pizzas = 3x7x10x4 = 840

**Math**

number of erasers ---- x number of pencils ----- x+10 22x + 14(x+10) = 446 solve for x

**maths**

1. Show that two of the three line segments have slopes that are negative reciprocals of each other. 2. let the fourth point be (x,y) Make a sketch to see which lines would be parallel. You will have 2 equations in 2 unknowns

**math**

Let the 3 numbers in GP be a , ar, and ar^2 after first change: a , ar+2, ar^2 are now in AP that is, ar+2 - a = ar^2 - (ar+2) ar^2 - 2ar + a -4 = 0 ** after 2nd change: a, ar+2 , ar^2 + 9 , are now in GP again, (ar+2)/a = (ar^2 + 9)/(ar+2) (ar+2)^2 = a(ar^2 + 9) a^2 r^2 + 4ar...

**Geometry and shape**

Thanks Steve, e.g. a regular hexagon or octogon , etc

**Geometry and shape**

Only the rhombus, equilateral means equal, a parallelogram does not necessarily have 4 equal sides

**Math**

No idea what you are saying.

**math**

First of all your third angle is 68° , not 132° You are not asked to state the lengths of the sides, simply list them in order of size. The property to use is: In any triangle , the longest side is opposite the largest angle, the smallest side is opposite the smallest ...

**math**

Sketch is the big thing!! On mine , I extended AC to M so that angle BMC = 60° Also you can see that angle MCB = 60° (external angle) So triangle CBM is equilater, and since CM = 12 CB = MB = 12 Also, since ABC is isosceles and CA = CB CA = 12 now by the sine law: AB/...

**maths**

Use you sum(n) terms formula (11/2)(2a + 10d) = 891 but d = 15 (11/2)(2a + 150) = 891 11(2a + 150) = 1782 2a + 150 = 162 continue once you have a, just use your formula term(28) = a + 27d = .... etc

**pre-algerabra**

But you didn't double. but, yes, if the drawing is to scale, then you must multiply each dimension by the same scale factor for yours: 10/12.5 = 4/x 10x = 50 x = 5 so a room 10 ft by 12.5 ft ----> 4 units by 5 units in your drawing.

**calculus**

you should know that using the metric system, a = -4.9 m/s^2 distance = -4.9t^2 + 48t + c, where c is the initial height velocity = -9.8t + 48 given: v = -50 -50 = -9.8t + 48 9.8t = 98 t = 10 When t=0 , distance = 0+0+c = c when t = 10, distance = -4.9(100) + 48(10) + c = c - ...

**Math**

let the other angles be 7x and 10x so : 7x + 10x + 95 = 180 solve for x, and sub into my definitions

**Math**

Just did this for you in your earlier post http://www.jiskha.com/display.cgi?id=1485495789

**Mathematics**

original amount in A ---- x original amount in C ---- x-20 after the pouring: A has x-15-10 B doesn't matter C has x-20 + 10 = x - 10 difference between C and A = x-10 - (x-20) = x-10 -x + 20 = 10

**Math (Advanced probability)**

expected wins: .15(1) = .15 .05(5) = .25 .01(50) = .50 1/10000(500) = .05 total expected wins on one ticket = .95 That is, if they charged 95 cents for a ticket , everybody would break even in the long run. So to make a 40% profit, they should charge .95(1.4) or $ 1.33

**Math**

Looks like a binomial distribution question. I read your question to say that exactly 5 are to respond. prob(response) = .15 prob(no response) = .85 prob(5 of 15 respond) = C(15,5) (.15)^5 (.85)^10 = appr .0449

**Math**

You are missing the fact that they could be ordered according to increasing or according to decreasing age. Each would be ordered by age. so prob = 2/120 = 1/60 = appr .0167

**Math**

What is 5! ?

**Math**

your post is incomplete. You did not state the rate of exchange, without it any of the answers are possible

**Math**

The y-intercepts are of great help. It also helps to have an idea what the general shape of different polynomials are. e.g. A fourth degree generally has the shape of a W , etc Also a reasonable number of ordered pairs can be calculate and plotted to show the shape of the ...

**Math**

plan 1: cost = 14 + .06n , where n is the number of minutes plan 2: cost = 22 solve: 14 + .06n= 22

**Pre Cal 12**

Square to be cut out : x cm by x cm then the height of the box is x, and the base is 12-2x by 8-2x, where 0 < x < 4 volume = x(12-2x)(8-2x) = 36 x(6-x)(4-x) = 9 x(24 - 10x + x^2) = 9 x^3 - 10x^2 + 24x - 9 = 0 I tried x = ±1, ±3 and x = 3 was a solution. by ...

**Algreba**

easiest way: since your new line is perpendicular to x+2y = -7 this new line must look like 2x - y = c but (2,3) lies on it, so 2(2) -3 = c = 1 new line: 2x - y = 1

**Algebra**

Their normals are <3,-2,0> and <1,2,4> The only way that the two planes could not intersect is if they are parallel or plane equation is a multiple of the other. Since their normals are not parallel, neither are the planes

**mathematics**

for the AS" first term --- a third term -- a+2d ninth term -- a+8d but those terms form a GP (a+2d)/a = (a+8d)/(a+2d) (a+2d)^2 = a(a+8d) a^2 + 4ad + 4d^2 = a^2 + 8ad 4d^2 - 4ad = 0 d^2 - ad = 9 d(d-a) = 0 d = 0 ---> not too interesting or a = d but term 7 of the AS = ...

**math**

Since these are special positions, the order counts, so what is 15x14x13 ?

**HELLO CAN ANYONE HELP ????!!!!!!!**

I think you have a typo and you wanted to compare y = 2^x with y = log2 x They are inverses of each other. Proof: start with y = 2^x the inverse is formed by interchanging the x and y's ----> x = 2^y which in log form would be : y = y = log2 x

**I'm stuck on math plz help!!**

see your other post above when you posted as "R"

**Statistics**

The first friend will have the birthday on some given day, doesn't matter when. The prob that the second friend will have a different birthday = 364/365 the prob that the third friend will have a birthday from the other two = 363/365 prob that all three have different ...

**Pre-Cal**

SW is a direction. Make a sketch on the N-S-E-W grid SW is in the third quadrant, dividing it into two parts of 45° each. Draw such a line OP, marking its length as 400 mph, and O at the origin. Draw a line PR horizontally to the right and mark it 50. So now you have a ...

**algebra**

What about it?

**Math**

It says the other two angles are equal, so your triangle must be isosceles. Let each of those equal angles be x x + x + 110 = 180 solve for x

**math**

only the 2 or 3 can be used at the front without the odd restriction: number of such number = 2x2x1 = 4 we can actually list them: 345, 354, 435, 453 notice that 1 of them is even so there are only 3 of them or suppose it starts with the 4: only the two odds are left, so ...

**Maths**

Steve did this http://www.jiskha.com/display.cgi?id=1394768509 See other variations of the same question in the Related Questions below

**Math**

the ratio of sides of your triangle are 1:?3:2 or x : ?3x : 2x given x = 16 other sides are 16?3 and 32 perimeter = .... just add them up

**Math Pre-Calc 12**

let the base be x by x cm let the height be y given: 4x + y = 120 y = 120 - 4x V = x^2 y = x^2(120-4x) = 120x^2 - 4x^3 dV/dx = 240x - 12x^2 = 0 for a max of V 12x^2 - 240x = 0 12x(x- 20) = 0 x = 0 ----> yields a minimum volume or x = 20 so the box is 20 cm by 20 cm by 40 cm...

**Algebra**

direction vector of P1P2 = <2 , -2, 0> so the equation of the plane which had <2, -2, 0> as its normal is 2x - 2y + 0z = c but A(1,3,-2) lies on it, so 2(1) - 2(3) + 0 = c c = -4 plane equation: 2x - 2y = -4 or x - y = -2 equation of line through P1P2: x = 2 + 2t y...

**Math/Algerbra**

87 mg needs 4 mL 1 mg needs 4/87 mL 173 mg needs (4/87)(173) mL or appr 7.954 mL or just use a ratio: 87/4 = 173/x 87x = 4(173) x = 4(173)/87 ----> same as above

**Ap algebra**

you can't use the quadratic formula on 2+3X^2-X^3=0 , since it is not a quadratic, it is a cubic Do you have a typo? Assuming it is correct, lets see if it factors: let f(x) = 2 + 3x^2 - x^3 f(1) = 2 + 3 - 1 ? 0 f(-1) = 2 + 3 - (-1) ?0 f(2) = 2 + 12 - 8 ? 0 f(-2) = 2 + 12...

**Math**

Are you using the US gallon or the Imperial gallon? (one of the many problems in not using metric!) I will assume US, so 1 US gallon = 3.97 litres and 1 mile = 1.61 km I will do the 2nd question, you do the first one. 1 gallons ---> 107 miles 3.97 l -----> 107 miles 1 l...

**Math**

number of gallons for each ginger --- 3x cranberry -- 2x orange -- x cost: 2(3x) + 4(2x) + 5x ? 38 19x ? 38 x ? 2 take it from there, remember I said ? .

**maths**

of the 30 fruits, how many are "either grape or banana" ? How many are "not bananas" ?

**Math**

let the width of the lawn be x yds field --- 25 yds by 100 yds area = 2500 yds^2 field including the lawn around it: (25+2x) by (100+2x) yds area = (25+2x)(100+2x) yds^2 area of lawn = (25+2x)(100+2x) - 2500 you said: (25+2x)(100+2x) - 2500 = 2(2500) 2500 + 250x + 4x^2 - 2500...

**mat**

You are given the time it took for the first car to go 599.5 miles in 5.5 hours. Using rate = distance/time the rate of the first car is 599.5/5.5 = 109 mph So the slower car went at 102 mph And the slower car would take 599.5/102 hrs or 5.87745 hrs or 5 hrs and 53 minutes 5:...

**Math 11**

speed of ferry ---- x km/h speed of car ----- x+60 km/h time for ferry = 175/x time by car = 175/(x+60) What are you told about these times? Form your equation from that fact.

**Math 11**

length of squares to be cut out ---- x base ----- 15-2x by 20-2x (15-2x)(20-2x) = 104 solve for x and you have the size of the cut-out The rest is easy

**Math 11 Foundations**

each of the two equal sides ---- x the single side ------- y given: 2x + y = 60 y = 60-2x area = xy = x(60-2x) x(60-2x) = 400 expand, and solve the quadratic

**Math**

3+1/4*cos(theta)=13/4 1/4*cos(theta)=13/4 - 3 = 1/4 cos(theta)= 1 we know cos 0 = 1 so Ø = 0

**Find the equation of the perpendicular line**

steps: - find the midpoint for the given points - find the slope of the line passing through those points - the slope of the line you want is the negative reciprocal of that slope - find the equation using the method you learned.

**Standard Form**

steps: - find the slope of the line passing through the given points - find the equation using the method you learned.

**Specify a Period on the graph**

for y = cos(kx), the period is 2?/k apply this to your question

**Trig**

the way you typed it: 2+1/3tan(theta)=2 1/3tanØ = 0 tanØ = 0 then Ø = 0, 180°, 360°, ... since the period of tanØ = 180°, you can obtain a new answer by simply adding or subtracting multiples of 180° to any answer. did you mean 2 + 1...