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happy belated anniversary, CPhill !!! i'm still quite an on-and-off member here, but your work is really great ! 

thanks for everything you have done!

Oh wait never mind it's a "nickname" for me, funny!

Wait who's Triple V and did I get the date right? Also, I said one of the best, not the best. (No one is the best everyone is great!)

Thanks,    TripleV    !!!!!

I really appreciate  that     .......I'm not the best on here....but, I try  hard   ......

Hey there!

Here I am assuming that Barry is cutting it across the width of the board, and that you are looking for 1 foot long peices. If this is the case then Barry will end with 9 peices altogether after cutting the board.

Hope this helped :)

Hey there!

To find the equivalence you can just expand the initial expression. The correct response is D.

I am feeling lazy today xD. If you want me to show you there working just reply and i will be happy to do so

Hope this helped :)

this is a hexagon (six sides). so the sum of all the interior angles would be \((6-2)*180 = 720\).

since all of the angles given are on straight angles, we can just subtract that angle measure from 180, to get the interior angle measure.

180 - 95 = 85

180 - 62 = 118

180 - 47 = 133

180 - 45 = 135

180 - 33 = 147

now let's sum all of these together. 

85 + 118 + 133 + 132 + 147 = 615

to find the missing angle measure, let's subtract 615 from 720 (the total sum of all the interior angles). 

720 - 615 = 105.

so now we know 180 - (2x + 4) = 105.

180 - 2x - 4 = 105

176 - 2x = 105

-2x = -71

x = 71/2 = 35.5

hope this helped! please let me know if you are confused about anything i did 

tan 18° =   800 / H          rearrange as

H =  800  / tan 18 °  ≈  2462.15 m

D

84

E     13        C

arctan  ( 84 / 13)  = C   ≈  81.2°

it says the answer is in the form of a square root

Let's  see if we  can find a pattern

Note  that  :

3^1 mod 23  = 3            3^12 mod 23   = 3       3^23 mod 23  =   3         3^34 mod 23 = 3

....

So...it  appears  that      3^(1 + 11n)  mod 23  =  3

Then

3^(1 + 11 * 9) mod 23  =  

3^(1 + 99) mod 23  = 

3^100 mod 23   =   3 

i'm not sure if i should take this seriously, but...

7 * 7 = 49.

a good way to envision this is to draw 7 groups of 7, or x groups of y (whichever numbers you're multiplying).

o o o o o o o

o o o o o o o

o o o o o o o

o o o o o o o

o o o o o o o

o o o o o o o

o o o o o o o

now, you can count these, i guess, though it may be tedious.

this site also helps teach you more about basic multiplication, feel free to check it out:

https://www.ducksters.com/kidsmath/multiplication_basics.php

in a way, multiplication is very similar to addition. i'd recommend you to try and memorize the basic multiplication tables. you'll quickly notice a pattern with most of them. 

hope this helped! feel free to ask any further questions you may have.

thank you! :)

Good job, Idyllic    !!!!

let's define two variables: l and w, to represent the length and width of this rectangle. 

we'll have a system of equations.

l = 7 + 5w

w * l = 6

now let's use substitution.

(7 + 5w) * w = 6

5w^2 + 7w = 6

5w^2 + 7w - 6 = 0

now let's solve the quadratic by using the quadratic formula.

\(x = {-7 \pm \sqrt{7^2-4 \cdot 5 \cdot -6} \over 2 \cdot 5} \)

\(x = \frac{-7 \pm \sqrt{49 + 120}}{10}\) 

\(x = \frac{-7 \pm \sqrt{169}}{10}\)(oops, i meant to do w, not x for the variable in these three; sorry about that!)

\(w = \frac{-7 + 30}{10}, \frac{-7-30}{10}\)

\(w = \frac{23}{10}, \frac{-37}{10}\)

i doubt that the width can be negative, so i believe your answer is 23/10.

hope this helped! please let me know if you are confused about anything i did 

i'm pretty sure that angle ROS is 2 times angle RTS (correct me if i am wrong).

so, we can craft an equation that looks like this:

16x - 4 = 2(7x + 5)

16x - 4 = 14x + 10

2x = 14

x = 7

now we plug x back into our expression for angle RTS.

7(7) + 5 = 49 + 5 = 54 

hope this helped! if you are confused on how i did anything, please let me know! :)

The  equation  is

x^2  +  ( y - 5)^2  =  36

(6,5)  is on the  crcle

( sqrt (35)  , 4 )  is on the  circle

sin x  =12/15

arcsin (12/15)  = x   ⇒  53.1 °

y  changes  by -5  when x changes  by 2 and  we have a  y intercept  of  -5

slope = -5/2       y intercept =  -5

"B"  is  the  one that fits   the bill

(2x - 7)^2  = 25   take  both roots

2x - 7  = 5               2x  - 7  =  -5

2x  =  5 + 7             2x   =  7 - 5         

2x  =12                  2x =  2

x  = 6                       x   =  1

w= pup

x= pooch

y = mutt

z = bird dog

w =  x + y            (1)  

z =  w + x      ⇒   (2/3) z = (2/3) w  + (2/3)x       (2)

2z  = 3y        (3)            

Relate  w  and  x

Manipulate (3)

y  = (2/3)z

Put  this  into  (1)  for y

w = x + (2/3)z

Sub (2)  into (1) 

w = x  + [ (2/3)w  + (2/3)x  ]        rearrange as

w - (2/3)w  = x + (2/3) x

(1/3)w  =  (5/3)x

w   =  5x

1 pup  =   5 pooches

sin(x) = 12/15

x = 53.1 degrees

That answer is wrong...

There are 10 values of a that work.