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2,3,7,8  → 45

One way

7 (8 - 2)  + 3  =

7 (6)  + 3  =

42  + 3  =

45

That is a good question.

There is no divide by sign on your keyboard so / is used for division on a computer.

Also

fractions are often written sideways,  like   6/7   or 8/4

Fractions and division are the same thing.

so

$1/2=\frac{1}{2}=1\div2$

What are the rules? Can the numbers be used more than once.

Can you only use certain operators like + - ???  What operators can you use?

I acuallly understood, after the text started sayin' that my brain would start understanding.

There is no end of pi it goes  on forever

These are sometimes tricky...ones  !!!!

Going good....and you  ?????

x^2  - 36x +   ???

Take  (1/2)  of 36  = 18  ....square it.....=  324   and this is the number...

Proof.....the binomial is  ( x - 18)  ...so.....

(x - 18)^2  =  (x - 18) (x - 18)  =  x^2   - 18x - 18x + 324   =  x^2  - 36x + 324

EXCELLENT, ISmellGood    !!!!!

I think you got the hang of it.....!!!!!~~~~

BTW -  you can check your answers...put either one back into the original equation...if you come up with "0"....you have done it correctly.....!!!!

Thank you!

So first I find what sums to 5 and multiplies to 6.

2 3

-2 -3

1 6

-1 -6

2 and 3 equal to 5

 (x+2)(x+3)=0

x can be either -2 or -3

DID I DO THAT RIGHT??? I think I did but idk.

It is most likely the same one. I used to get on every day and message her and she would always respond back with some positive comment. Then one day it was like she dissapeared of the face of the earth. I later learned that he parents saw it and then forbidded her from logging back on. I was wondering if it was over now but ..... i guess not :/

When i searched for her name in the post this came up

No prob, rarinstraw.....!!!!

If it's the same "Hayley" that I'm thinking of, sadly, she left the forum about a year and a half ago and hasn't returned......I agree....she WAS a ray of sunshine....I always wondered what happened to her.......  

In a certain pentagon, the interior angles are  a,b,c,d   and e where  a,b,c,d,e are integers strictly less than 180 . ("Strictly less than 180" means they are "less than and not equal to" 180.)

If the median of the interior angles is  61  and there is only one mode, then what are the degree measures of all five angles?

-----------------------------------------------------------------------------------------------

The sum of all the interior angles of a pentagon  = 540°

Note that if we require integer solutions....we will have a problem

If the median angle is  61° and we have only a single mode....all the angles must be of  different measure....then..... the largest  possible integer values of the smallest two angles  are 59° and 60°

But note that the sum of the three smallest angles [ 59° + 60° + 61°] = 180°.....so....this means that the remainder of the angles must sum to  540 - 180  = 360°.....but  this would mean that one of the largest two angles will have to be > 180° [because of the single mode requirement] and this isn't allowed

Thank you CPhill!

What EXACTLY do you mean???

Example......

If we had a triangle  with the vertexes  (1,0), (0,1)  and ( 3,2)

Let us supose that we had a scale factor  of 2

This means that the new triangle will have the vertexes  2( 1,0),   2(0,1)   and 2(3,2)  =  (2,0),  (0,2) (6,4) 

Ah...thank you!!!   Well now I see what was wrong...my equation was this:

5 / (R + 2)  =  7 / (R - 2)      

A motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at​ 2mph, find the speed of the boat in still water.

Distance  / Rate  = Time

Let the rate of the boat in still water  = R

Against the current the rate of the boat  = R - 2

With the current the rate of the boat  = R + 2

So......equate the time

5 / ( R - 2)   = 7 / ( R + 2)      cross-multiply

5 ( R + 2)   = 7 (R  - 2)     simplify

5R + 10  = 7R - 14      rearrange as

24   =  2R

12  = R    =    12 mph      

The time it takes =   5 / [12- 2]  = 5 / 10   = 1/2 hr

(2*sqrt(2)*e^t)^2

Notice that   2sqrt(2)   = sqrt (4 * 2)   =  sqrt (8)

So we have

[ sqrt (8) * e^t ] ^2   =

[sqrt (8) ]² * [ e^t ]²  =

8 * e^2t

Assuming that you know the x and y coordinates of two points on the line ....the midpoint is given by :

Add  the x coordinates and divide by 2     =    x midpoint coordinate

Add the y coordinates and divide by  2  =  y midpoint coordinate

Example 

(5, 6)   and  ( 7, 8)

Midpoint  =   [  ( 5 + 7) / 2  ,  (6 + 8) / 2 ]  =  [ 12/ 2,  14/2 ]    =  [ 6, 7 ]

x^2 - x  - 12  = 0

Here's the way I do it .....this method applies only if the lead coefficient is an understood "1"...as in this case........

[ there are also other methods ]

Write this as

x^2  - 1x   - 12  = 0  

Now......   look  at  the term on  "x"   = -1

And look at the constant term  = -12

Ok....we  are looking for two integers that  multiply to  - 12   and  that  sum to - 1  

Possibilities

1   -12

-1   12

2    -6

-2    6

3   - 4

-3    4

Notice that the only thing that works is   3  and - 4

(3) + ( - 4)    =  -1        and

(3) * (-4)  = -12

So....we just factor with these...i.e.,

(x  - 4)  ( x + 3)  = 0

Now.....set each factor to 0 and solve for  x....so we have.....

x  - 4  = 0                          and                        x + 3  = 0

add 4 to both sides                                    subtract 3 from both sides

x  = 4                                                             x  = -3

And those are the two solutions

The "smaller" x  = -3

The "larger" x  = 4

Does that help  ????

Try this one for yourself :      x^2  + 5x + 6  = 0 

$({2}^{2}*{e}^{t})^2=16{e}^{2t}$