# Posts by Reiny

Total # Posts: 39,548

Math
Nothing to solve, just multiply the two numbers. (Do 3 x 67, you should be able to do that in your head, then move the decimal 3 places to the left.) Of course you could also use your calculator.

Math
The way you typed it : 5^x + 2•5^x+1 = 3*5^x + 1 it does not factor over the rational numbers Secondly you did not say what type of number x is, let's assume x is a whole number, that is x = 0, 1, 2, 3, ... if you meant: 5^x + 2*5^(x+1) = 5^x( 1 + 2(5^1) ) = 5^x ( 11...

Math
first term --- a second term ---- ar a - ar = 2 a(1-r) = 2 sum to infinity = 15 a/(1-r) = 15 [a(1-r)][a/(1-r)] = 2(15) a^2 = 30 a = ± ?30 from a = ar+2 ?30 = ?30r + 2 r = (?30 - 2)/?30 = 1 - 2/?30 so we have ?30, ?30 + 2 , .... sum(5) = a (r^5 - 1)/(r-1) = .... = ..... ...

math
when it hits the ground, h = 0 0 = -4.9x^2 + 21.3x 4.9x^2 - 21.3x = 0 x(4.9x - 21.3) = 0 x = 0 , which corresponds to the moment she kicks the ball or x = 21.3/4.9 = appr 4.4 seconds

Math
I guess you could form columns for "n" and "left side" n ... LS 0 3 1 9 2 15 --- getting too big, looking for 2 on RS -1 -3 ---- too low, so n is between 0 and -1 1/2 6 ---- too high -1/2 -3 --- too low so between 0 and -1/2 -1/4 3/2 ----- too low so ...

math
notice that each new term is -3 times its previous, or tn = -3t(n-1) so we have -4, 12, -36, 108, -324

Algenra 1
both correct

math
This is the same type as your other post. Only this time you don't add anybody not belonging to either set.

Calculus
Do you actually expect somebody to do this assignment for you?

MATH
No, the 5 that do both are counted in the 16 geography students, AND the 18 chemistry students, so you are counting them twice number of students = 16+18 - 5 + 3 = .... make a Venn diagram to see.

Math
10(x+27) ? 26

Math
You will have to count the number of days from Feb 12 to June 23, I will leave that up to you and label it 'days' in I = PRT, your I = 40, R = ??, T = days/365 , P = 2000 40 = 2000(R)(days/365) R = 40(365)/(2000(days)) = your R will be a decimal, I will assume you know...

pre-calculus math
a zero of 3 gives us a factor of (x-3) complex zeros always come in conjugate pairs, so if -3-2i is one of them, -3+2i must be another. factors are (x - (-3-2i)) and (x - (-3+2i)) or (x + 3 + 2i) and (x + 3 - 2i) multiply the last two to get a quadratic factor (......) your f(...

Math
Thanks Steve, how sloppy of me

Math
amount of the 1% stuff to be added ---- x ounces .1x + .4(100) = .16(x + 100) solve for x

Algebra
f(2) = 21 , you had that f(a) = 6a^2 - 3 all you had to do is find the average rate of change, or more commonly known as the slope average rate of change = (6a^2 - 3 - 21)/(a - 2) = (6a^2 - 24)/(a-2) = 6(a^2 - 4)/(a-2) = 6(a+2)(a-2)/(a-2) = 6(a+2) , a ? 2

Math
1.6666666667 is NOT an irrational number. (1.6666666667 = 16666666667/10000000000 , there! I wrote it as a rational number)

Calculus
Your equation should have been h = -16t^2 - 6t + 130 When it hits the ground, h = 0 so, 16t^2 + 6t - 130 = 0 I would use the quadratic equation formula to solve for t (to be able to handle this topic, you MUST know that formula) make sure to reject any negative value of t.

Math
PV = 30,000 + 30,000( 1 - 1.0593^-12)/.0593 = ....

alg
y = 3x - 1 for (2,5) LS = 5 RS = 3(2) - 1 = 5

Algebra
I just googled : graph of a quadratic function, and guess what ? replace "quadratic" with the other two words

I agree, but then pay this off as quickly as possible with such a high interest rate. Notice the payment of \$25 wouldn't even pay the interest. (first months interest after introductory period = 1800(.2399)(1/12) = \$35.99

1 Out Of 100 Math Trick HELP PLEASE!!!
1. Choose a number between 1 and 100. ------> x 2. Multiply the number by 5. -------> 5x 3. Add 15 to the number. -------> 5x+15 4. Divide the number by 5. ------> x+3 5. Subtract the original number. ------> 3 try it with any number: 1. ----- 12 2. ------ 60 3...

Pre-calc
Use brackets to write the fractions, such as 1/(2x) + 6/2 , <---- that was a guess, I can't tell what you meant

Pre-calc
I will assume that these are the zeros or the solutions to your function = 0 if 3-i is a zero, then 3+i is a zero, since complex solutions always appear in conjugate pairs sum of those roots = 6 product of those roots = 9 - i^2 = 10 so the quadratic producing those two complex...

Algebra
your formula is interpreted this way f(3) = f(2) + f(1) f(4) = f(3) + f(2) f(5) = f(4) + f(3) etc so f(3) = 3 + 2 = 5 f(4) = ....... notice we already eliminated b) continue .... btw, this is a famous sequence called the Fibonacci sequence, one of my favourite topics in Math.

Math
How did you possible get those answers ???

Algebra
What problem? Are you switching names ??

Algebra
No How did you get that ????

Math
remember , Perimeter = 2 x width + 2 x length area = length x width Perimeter = 2(5x-4) + 2(5x) = .... area = 5x(5x-4) = ... in each case simplify my expression

Pre-Calculus
To prove an identity, we usually start with one side and using basic identities show that it is equal to the other side LS = cosx - sex = cosx - 1/cosx = (cos^2 x - 1)/cosx = - sin^2 x / cosx = -sinx(sinx/cosx) = -sinx tanx = RS

Math
Didn't you want to make at least \$200 ? So it should be 15h ? 200 h ? 40/3 , not less than like you had However, your conclusion that the painter must work a minimum of 13 and 1/3 hours to earn at least \$200, is correct

Math
correct,

Algebra 2
depends on the transformation. e.g. suppose we have f: (x,y) ----> (x,-y) , a reflection in the x-axis , and g: (x,y) ---> (-x,-y) , a reflection in the origin if we do fg (x,y) ---> (x,-y) ---> (-x,y) and if we do gf (x,y) = (-x,-y) ---> (-x,y) , we get the ...

math
explain the meaning of 127nine

algebra
| 4x - 5 | > 4 4x - 5 > 4 OR -4x + 5 > 4 4x > 9 or -4x > -1 x > 9/4 or x < 1/4 change into the notation you learned and graph on a number line

algebra 2
6x-8 = 4 or -6x+8 = 4 6x = 12 or -6x = -4 x = 2 or x = 2/3

algebra
follow the same steps and procedure as in https://www.jiskha.com/display.cgi?id=1506548306 except use AND between the two inequations

algebra 2
width --- x length --- 2x perimeter = 2width + 2 lengths = 54 continue

algebra
Both conditions are referenced in terms of nickels, so let the number of nickels be x number of dimes = x+1 number of pennies = x+6 Value equation: 5x + 10(x+1) + x+6 = 480 continue ....

Algebra 2 A
correct make sure your equation is 26.00+3.25x=24.00+3.50x

maths
Ummmhh, if you are half as old as your sister, wouldn't your sister be twice as old?? . I defined it the way I did to avoid fractions. What does 6(x-20) mean? Does it not say 6 times (the son's age) ?? 2x-20 = 6(x-20) 2x-20 = 6x - 120 -4x = -100 x = 25 So the son is ...

maths
So the father is now twice as old as his son son's age ---- x father's age ---- 2x Twenty years ago : son's age = x-20 father's age = 2x-20 2x-20 = 6(x-20) solve for x, etc

math
first of all , you have a typo in g(x)=x^2=7x I think you meant: g(x)=x^2+7x , since the + and the = are on the same key you are given that g(x) = x^2 + 7x so you want g(3). As Philip stated, wherever you had an x , now put in a 3 g(3) = 3^2 + 7(3) = 9 + 21 = 90 so since f(x...

f(x)=4x^2+3x+5 and g(x)=3x^2+2x+2 I will do A and C, you do the rest a) (f+g)----> 7x^2 + 5x + 7 (f+g)(3) = 7(3)^2 + 5(3) + 7 = 63 + 15 + 7 = 85 c) (f-g)(x) = 4x^2+3x+5 - (3x^2+2x+2) = x^2 + x + 3

Math
a) h = 8 + 6t 6t = h-8 t = (h-8)/6 c) when t = 6 h = 8 + 6(6) = .... d) when h = 29 29 = 8 + 6t 21 = 6t t = 21/6 = 3.5 it would take 3.5 months

PRE-CALC
you are given that x = i is a solution Complex roots, just like irrational roots, always come in conjugate pairs, so x = -i is another solution so you know (x+i) and (x-i) are factors (x+1)(x-1) = x^2 + 1 which means x^2 + 1 is factor of your given polynomial now do a long ...

#5 25 is a perfect square ---- 5^2 = 25 , but 27 is a perfect cube --- 3^3 = 27 #6 is incorrect ?9 - 7 = 3-7 = -4, which is an integer Whole numbers are positive integers I agree with the others.

Math
24.4 trillion = 24,400,000,000,000 cost per person = 24,400,000,000,000/325,000,000 = 24,400,000/325 = \$62,769 At \$62 it could be paid off in 1 year by everybody chipping in a bit, unfortunately .....

Math
number dogs = 135(.365)(1.6) = appr 78.8 million dogs

math
-8y+3(g+h) - -5y-4(g+h) = -8y + 3g + 3h + 5y - 4g - 4h = ..... btw, - - 5 is considered "poor mathematical form"

Maths
I drew a horizontal flight path 400 m above the ground. On that path, I labeled the first position of the plane as A and the 2nd position as B, and the location of Melbourne on the ground as M I also labeled C on the flight path as the point directly above M. Let the speed of ...

math
3150 = 9*25*14 you take it from here

none are correct A typical equation of a straight line, other than vertical or horizontal lines, need an x and a y variable. I will do one of them , say #4, you do the others slope of line = (-10-2)/(15-5) = -12/10 = -6/5 using the point (5,2), y - 2 = (-6/5)(x-5) multiply ...

Calculus
Let the vertex on the line 3x + 4y = 12 be (x,y) then y = (12-3x)/4 = 3- 3x/4 area = xy = x(3 - 3x/4) = 3x - 3x^2 /4 d(area)/dx = 3 - (3/2)x = 0 for a max of area (3/2)x = 3 3x = 6 x = 2 , y = 3 - 6/4 = 3/2 max area = xy = 2(3/2) = 3 units^2

look at your list of properties, which pattern do you see?

one has square brackets around it, and the other one doesn't. I would consider both to be -3

algebra
each of the equal angles ---- x third angle = 2x - 4 so : x + x + 2x-4 = 180 continue

Algebra
now: son's age --- x man's age --- 3x 5 years ago: son's age = x-5 man's age = 3x-5 3x-5 = 4(x-5) solve and the mystery will be unravelled.

math
just solve the two equations. I would use y = 20-x from the first and sub it into the 2nd let me know what you get

math
Here is just one such worksheet http://www.bearsdenacademy.e-dunbarton.sch.uk/_includes/attachments/P1283/Unit2_TrigonometricEquations.pdf That should keep you busy for a while. Try the questions before looking at the solutions.

math
Your first source would be your textbook. Perhaps your teacher gave you a handout of such equations. You can always google "trig equations" or "trig equations worksheet" There would be an infinite number of such equations.

maths
time in car ---- t hrs time on motorcycle --- 1 - t hrs 30t + 18(1 - t) = 22 solve for t, sub into 30t to get the distance in km

Math
width --- w length --- 3w 2(w+3w) = 96 4w = 48 w = 12 m or 1200 cm 3w = 36 m or 3600 cm area of flower bed = 1200(3600) cm^2 area of rectangle including path = (1280)(3680) cm^2 area of walkway = the difference or 390400 cm^2 volume of concrete needed for walk = 390400(15) cm^...

algebra
5x - 3y = 0 5x = 3y or 3y = 5x y = (5/3)x , which is in the form of y = mx, a direct variation.

Math
The areas of two similar figures area proportional to the square of their corresponding sides, so w^2/18^2 = 52/117 w^2 = 144 w = ?144 = 12

Physics/Math
You must be studying vectors in 3-D and cos ?, cos ?, and cos ? must be the direction cosines of a vector <a, b, c> you will recall that cos ? = a/?(a^2 + b^2 + c^2) cos ? = b/?(a^2 + b^2 + c^2) cos ? = c/?(a^2 + b^2 + c^2) Here is a great youtube which uses a specific ...

maths
What happened to the 100 ml that were split ? If they were given as part of the share , why not just do 2500 ml ÷ 4 = 625 ml per child or 100 ml ÷4 = 25 ml remaining 2400 ml ÷ 4 = 600 ml, and of course 600 ml + 25 ml = 625 ml , same as above

Math
Where are points a and b on the pond? What is a mosese ?

Further maths
Let x be the number who passed both. x + 31-x + 29-x + 3 = 50 -x = -13 x = 13 number who passed Chemistry only = 31-x = 31-13 = 18

Math
In most languages, there are special words for very common numerical values, as well as mathematical concepts e.g. almost every language has a special word for 12 besides the numerical name. That is, in English we use "dozen" meaning 12, in German "Dutzend"...

math
translating your conditions: W = k * w* h^2 / l given: w = 3in, h = 4in, l = 6 ft or 72 in , W = 28 tons 28 = k(3)(16)/72 k = 42 W = 42 * w* h^2 / l plugging in the second case: W = 42(5)(16)/240 = 14 tons

Algebra 2
6|6-4x|=8x+4 divide by 6 |6-4x|=(8x+4)/6 ---- I wanted to isolate the absolute value expression 6-4x = (8x+4)/6 OR 6-4x = -(8x+4)/6 36-24x = 8x+4 or 36-24x = -8x - 4 -32x = -32 or -16x = -40 x = 1 or x = 40/16 = 5/2 I will leave it up to you to verify my answers

Math
can you think of a number which divides into 42 as well as 49 ???

Math
Just add and subtract in base 2 x + 1011 + 1101 = 11101 x + 11000 = 11101 = 101 or , copping out and changing to base 10 10112 = 1110 11012 = 1310 111012 = 2910 y + 11 + 13 = 29 y = 5 and 510 = 1012 , as above

Algebra 2
#3, you list no choices, but the question itself is your answer: r ? 1/5 the rest are correct up to #7

Math
draw a dotted line y = 4x+2, (your line is to be excluded) and shade in the region below the line 2x - y ? 2 -y ? -2x + 2 y ? 2x - 2 draw a solid line y = 2x-2, and shade in the regions below it your solution is the intersection of the 2 regions

algebra
correct, how did you get that? I am more interested in your method and thinking than the actual answer.

Algebra
I don't see where it wants the number of hours only. I see "how long will it take ....." your answer of 55.3846... is correct so that would be 55 hours and .3846... of an hour so .3846..(60) = 23.0769... minutes if you wanted it broken down into seconds, use the ...

Algebra
I answered this for you 4 days ago. Why are you asking the same question again ?? https://www.jiskha.com/display.cgi?id=1505894047

stats
one letter variable ---- 26 two character variable ----- 26x36 three character variable --- 26 x 36 x 36 four character variable ---- 26 x 36 x 36 x 36 = 26(36)^3 ... eight character variable ---- 26(36)^7 Possible characters = sum of the above = 26(1 + 36 + 36^2 + ... + 36^7...

Math
larger --- x smaller = (1/2)x middle = (3/4)x x + x/2 + 3x/4 = 126 times 4 4x + 2x + 3x = 504 x = 56 larger is 56, smallest is 28 , middle is 42

Math
number of advanced tickets ---- x number of at door tickets ----- 480-x 4x + 5(480-x) = 2100 solve for x

math
Is the "discount" confusing you ? I believe most textbooks would handle it like this: Let the annual discount rate be i 1-i = (1 - .005)^12 = .995^12 = .94162 i = .058377 or a discount of 5.8377% Had it been just plain old interest ..... let the nominal rate be i (1+...

Algebra
f(x)={x^2, if x ? -4 {x^3, if -4 < x ? 1 {?x, if x > 1 so if x = -4, it belongs to the first function f(-4) = (-4)^2 = 16 if x = 4, we have the last function f(4) = ?4 = 2

Mathematics
"where t is the time in hours from....." is incomplete Did you mean from noon ? Let's assume it is after noon, else make the necessary adjustments at 9:45 pm , t = 9.75 set your calculator to radians d = 3.163 metres The min of 3cos 30t is -3 and its max is +3 So...

Math
cost of gift ---- x cost for each of the nine originals = x/9 cost per student with 13 paying = x/13 x/9 - x/13 = 33.32/9 times 117 13x - 9x = 3898.44 4x = 3898.44 x = 974.61 check: original share = 974.61/9 = 108.29 new share = 974.61/13 = 74.97 saving per share = 33.32 , as ...

Math
number of skiers --- x number of boarders ---- 2x , notice x : 2x = 1 : 2 2x - x = 1250 etc

math
Han's starting number ------ x , counts backwards by 100 Sally's starting number ----- 300 counts forward by 10 after 6 counts, Sally is 360 after 6 counts, Han's is at x - 600 x - 600 = 360 x = 960

Algebra
let the number of 50 notes be 3x let the number of 20 notes be 5x , notice they are in 3:5 ratio number of 10 notes = 25 - 3x - 5x or 25 - 8x value of notes equation: 50(3x) + 20(5x) + 10(25-8x) = 590 150x + 100x + 250 - 80x = 590 170x = 340 x = 2 sub back into my definitions

Algebra
let the amount of aluminum added be x kg .55(160) + x = .7(160+x) 88 + .55x + x = 112 + .7x .85x = 24 x = appr 28.24 kg

Math
a+2d = -1 a+6d = 11 subtract them: 4d = 12 d = 3 from a+2d = -1 , a = -7 term(n) = a+(n-1)d = -7 + 3(n-1) = -7 + 3n - 3 = 3n - 10 "the numbers of which must be added to get a sum of 430" I will assume you mean, "how many terms are needed to have sum of 430"...

Algebra
follow the same steps I showed you in your previous question.

Algebra
speed of jet in still air ---- x mph speed of wind ---- y mph 4(x+y) = 1008 ---> x+y = 252 4(x-y) = 832 ----> x-y = 208 add them: 2x = 460 x = 230 from x+y = 252 , y = 22

College Algebra
let the time taken to catch up be t hours distance covered by the sister be 65t distance covered by Sarah is 60(t+2) but the went the same distance, so ... 65t = 60(t+2) solve for t

Algebra
let the smallest angle be x then the next smallest angle is 3x+26 You know in a right-angled triangle the two smaller angles must add up to 90° , so x + 3x+26 = 90 solve for x ....

Math medication problems
One confusion that could arise is to use cc vs ml http://thecompounder.com/2015/04/13/cc-vs-ml-whats-the-difference/ the ordered rate was 600 cc/8 hours = 75 cc/hour The pharmacist erroneously calculated this to be 200 ml/hr or 200 cc/hr

Algrebra
your slope for BD should have been 9/1 or 9 To be a rhombus, the slopes of the diagonals should have been negative reciprocals of each other the negative reciprocal of -1/5 would be +5 which it isn't. so ABCD is not a rhombus Another way to check: The sides are not equal ...

math
Just translate into Math "three consecutive numbers" ---> x, x+1, x+2 "the sum of the second and the third numbers " --- x+1 + x+2 "exceeds the first by 14" ---> x+1 + x+2 - x = 14 now just solve for x, and sub back into my definitions