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4r^3 - 8r^2  -5r + 10

Factor by grouping

4r^2 (r - 2) - 5(r - 2)       take out the common factor (r - 2)  and write back the rest

(r - 2) ( 4r^2 - 5)

3u + 9 -11u = -23   combine like terms on the left side

-2u + 9  =   -23       subtract  from both sides

-2u = -32           divide both sides by -2

u = 16

yep thanks

I'm assuming this might be

-11y -8 + 3y = 24       combine like terms

-8y - 8   =  24         add 8 to both sides

-8y =  32         divide both sides by -8

y = -4

thanks

Here you go :

https://web2.0calc.com/questions/7w-17-12w-38#r1

 cos2x -  sinx = 0

(1 - 2sin^2 x) - sin x  = 0             multiply through by -1

2sin^2 (x)  +  sin x - 1   =  0       factor

(2sin x - 1) (sin x + 1) = 0

Set each factor to 0   and solve for  x

2sinx - 1 = 0

2sin x = 1

sin x = 1/2

And this happens at  x =   pi/6 + 2pi*n       and     x =   5pi/6 + 2pi*n       where n is an integer

Also

sinx + 1  = 0

sin x = -1

And this happens at     x  =   3pi/2 + 2pi*n    where n is an integer  

OK....I  find the Sate of Confusion is one I occupy quite often...LOL!!!

Thank you so much for your help! I was so confused.

in an equilateral triangle where the height is the root of 6 as we find the side having no more data

The side is given as

√6 / [ √3 / 2 ]  =

√6 * 2 / √3 =

√[6/3] * 2  =

√2 * 2  =

2 √2   =   the side

I’m just peachy. I’m listening to a wonderful song:

So long, farewell, auf wiedersehen, goodbye. 

It’s topped-off with a swooshing sound similar to an Atomic Flush. 

A very novel ending and the best part of the song, for sure. 

BTW, when I loaded this page, I noticed there is a countdown display with a hexadecimal number on it. It hasn’t started counting.

Below the display is a dimmed button with the label: Activate.

This is kinda odd. Don’t you think so?

21) 

4x + 8y  = -16      (1)   

-8x + 10y = -20    divide through by 2  ⇒  -4x + 5y = -10     (2)

Add (1) and (2)    and we get that

13y = -26             divide both sides by 13

y = - 2

And using (2) to find x, we have

-4x + 5(-2) = -10

-4x  - 10 = - 10       add 10 to both sides

-4x = 0

x = 0

20)     x - 2y  = 18   ⇒  x = 18 + 2y

Sub the into the second equation for x    and we have

-6(18 + 2y) - 4y = 4      simplify

-108 - 12y - 4y = 4      

-108 - 16y = 4            add 108 to both sides

-16y = 112            divide both sides by -16

y  =  -7 

And

x  =  18 + 2(-7)   =   18 - 14    =    4

 sin2x / [1-cos2x ]  =  cotx           work with the left side

sin 2x  /  [ 1 - (1 - 2sin ^2 x ) ]  

sin 2x / [ 2 sin^2 x ] [ 2sin x cosx] / [ 2 sin ^2 x ]

sin x cos x  / [ sin ^2 x]

sin x cos x / [ sin x * sin x ] =

cos x / sin x      =

cot x

Thanks! You were right!

Yup 

There are

9 1 digit numbers

90 2 digit numbers

252 3 digit numbers

257 4 digit numbers 

for a total of 608

the 3 digit number breakdown is as follows, n and m are distinct non-zero digits

9 nnn

9*8=72 nnm

9*8=72 nmn

9*8=72 nmm

9 nn0

9 n0n

9 n00

I leave working out the 4 digit breakdown to you.

Thats good!

I’m good, thanks

Welcome to the site YNH! I am good you?

We have the following set of moves

(right, right, right, right, right, up, up, up ,up)

So.....we have 9 possible moves  and we want all the ordered sets where any  4 of them are  "up" or any 5 of them are "right"

So....the total pathways are  = C(9,4) = C(9,5)   = 126 paths

YAY! Not anymore!