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In the expansion of \(ax+b)^{2000}, where a and b are relatively prime positive integers, the coefficients of x^2 and x^3 are equal.   Find a and b. 

Consider the set S=1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,23,24,. . . . ,123456789\}, which consists of all positive integers whose digits strictly increase from left to right. This set is finite. What is the median of the set?

The median here is given by (123456789 + 1)/2  

Daniel had 80 more stickers than Elle. He gave 1/4 of his stickers to Elle. She then gave 3/5 of her stickers to Daniel. In the end, Daniel had 92 more stickers than Elle. How many stickers did Daniel have at first?

In a triangle, all of the angles must add to 180^o

^soooo

x    +    4x-5      +    55      =   180     you should be able to solve for 'x' now.....

I mean, as you can see he did almost the same approach as you, gwenspooner85, so I think you should be able to decipher his thinking

-5x^3    + (-5x^2 -x^2) x (-7x-6x) + 1 + 1        complete the red part to find coefficient of x^2

What is this, "A for Effort" day?  The answer is wrong and somebody gave it a "plus heart"?

(3m+5)(n-2)           expand to find the missing number in your Q 

29/4

Incorrect 

Thank you so much for your help!!!

Thanks guest,  this is a great contribution!

why not simplify the problem and let the 2 polynomials both be linear

m,n are both non zero and real.

\(f(x) = mx-4\\ g(x)= nx+k\\ \\~\\ h(x)= (mx-4)(nx+k) = ( some\; number)x^2 + ( some \;number )x   -4k\\ but\\ -4k=3\\ so\\ k=-\frac{3}{4}\)

So      g(0) = -3/4

Since the train passed the first walker in 15 seconds walking at 6 km/h, it therefore follows that the second walker, who was passed in 1/2 the time of the first walker, must be walking at Twice the speed of the first walker, or: 2 x 6 km/h =12 km/h

that was wrong, thank you though

This is one of the BEST videos that I have seen on the explanation of Extended Euclidean Algorithm, Watch it step by step very slowly and view it several times. I think you will evetually understand it. Good luck.

https://www.youtube.com/watch?v=6KmhCKxFWOs

Find the Prime Factors of each:

1 - 9 = 3^2   and   27 =3^3    and    128  =2^7

2 - By taking an infinite number of Square Roots, The exponents will eventually converge to 1 for each Prime Factor.

3 - Then, will be left with the factors themselves multiplied by each other.

4 - Therefore: 3  x  3  x  2 = 18

B = Boys
G =Girls
(B - 3) / G = 4,   B / (G - 3)=9, solve for B, G
B = 27   and    G = 6
27 - 3 = 24   and   6 - 3 = 3
24 / 3 = 8 - Ratio of Boys to Girls

Since you are only being given information about the horizontal distance, I suspect the 1m refers to the point (-1, 0).

So you would have \(D(0) = a*cos(b*0)+d \text{ or }D(0)=a+d\)

The pi/6 refers to a time, not a distance, so \(D(\frac{\pi}{6})=a*cos(b*\frac{\pi}{6})+d\) and because this is the centre where D = 0 this becomes \(0=a*cos(b*\frac{\pi}{6})+d\)

Does this answer your questions?

Nice answer!~

Hello, ElitBabbi!~

Hope your day was fine!~

Back to the maths.

1a) Graphing is useful in many ways. Graphing was invented by Rene Descartes, where we get the name, "Cartesian Plane" from.

Graphs are a common method to visually illustrate relationships in the data. The purpose of a graph is to present data that are too numerous or complicated to be described adequately in the text and in less space. 

Thus, the graph has many useful purposes. For some neatly built cities, with perfect square-blocks, you could, theoretically, plot your home and places of interest, and figure out how many blocks you would have to travel, based on the number of blocks on the map you have to cover-unless you can fly. Then... Yeah... I don't know.

You can use all sorts of graphs, as well. You can use a line graph to measure how much money is going toward things you don't need each month and work to get a negative slope on the graph-thereby saving money. There are loads of practical applications for graphs, and I can't think of anything incredibly useful right now, unfortunately.

1b) https://www.desmos.com/calculator/41eqoeuaub You can do the rest!

-TheLovely1

Hello, Guest!~

I'm going to elaborate on Electric Pavlov's excellent answer.

So, basically, the Law of Sines says that, according to Khanacademy, a side labeled, "A" over the sine * opposite of it, which is, angle "a", is equal to a side labeled, "B", over the sine * opposite of that side, which is the angle "b".

In short, you end up with, \(\frac{Side\ A}{Angle\ a}=\frac{Side\ B}{Angle\ b}\), and you can add the third side the same way: \(\frac{Side\ A}{Angle\ a}=\frac{Side\ B}{Angle\ b}=​​\frac{Side\ C}{Angle\ c}\)

For your case, we get:

 \(\frac{sin(70)}{5.7}=\frac{x}{5} \\ \\ sin(x)*5.7=sin(70)*5 \\ \\sin(x)=\frac{5sin(70)}{5.7} \\ \\x=sin^{-1}(\frac{5sin(70)}{5.7})\)

I do hope the math is correct.

From here, you can just plug it in!

I hope you did take away something from my answer!

-TheLovely1

1 - There are 27 boys and  6 girls in Classroom

2 - 3 boys leave =24 boys and 6 girls left =ratio of 4 boys to 1 girl

3 - 3 girls leave =27 boys and 3 girls left =ratio of 9 boys to 1 girl

4 - 3 boys and 3 girls leave =24 boys and 3 girls left =ratio of 8 boys to 1 girl.

m = 67.5º

n = 56.25º

Law of sines

sin 70^o  / 5.7 = sin x^o / 5       solve for 'x'