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notice how 2x^2-7x+2=x^2-9x+1 is equivalent to x^2+2x+1. This factors to (x+1)^2

a = b, so 1/(-1-1)*2= -1/2*2= -1

What is the smallest positive multiple of $13$ that is greater than $500?$  

Divide 500 by 13 to find your starting point.   500 / 13  =  38.46  

So the mulitplier you want will be the next whole number, i.e. 39   

The answer is 13 • 39  =  507  

_.

Brenden wants to make a shed that is a copy of his office building. The roof of the office building is
18.5 m wide and 5.4 m higher at the center than the edges. If the shed is 3 m wide, what will be the
rise of the roof?   c

In proportion:  x is to 3.0  as  5.4 is to 18.5  

                       x / 3.0 = 5.4 / 18.5      

                               x = (3.0)(5.4) / 18.5  

                               x = 16.2 / 18.5 = 0.876 which rounds to 0.9 meter   

Check answer:  5.4 is a little less than 1/3 of 18.5   

                         0.9 is a little less than 1/3 of 3.0      ballpark, so probably right  

_.

Thanks alot

Angle BAC = 150 degrees          (60º + 90º)

Richard spent 2/7 of his money on 4 bags and 4 pencil cases. The cost of a bag

is twice that of a pencil case. With 5/6 of his remaining money, he bought more

pencil cases. How many pencil cases did he buy in all?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Cost of 4 pencil cases = 1/3(2/7) = 2/21    or     4/42

Cost of "more pencil cases" = 5/6(5/7) = 25/42

Proportion:        (4/42) / 4 = (25/42) / x          x = 25

Richard bought 29 pencil cases.

a = 21

b = 21 + d

c = 21 + 2d       d is the common difference       Summed, a + b + c = 180

21    +   21+d      +   21 + 2d   = 180

d = 39       

so   angle c = 21 + 2d = 99^o

How to delete this question?

I don't I alr know the solution.

Straight

What is the height of the tower to the nearest degree METER?

Draw yourself a picture to see that

  tan 72 = height / shadow

  tan 72 = height / 55

55 tan 72  = height      in meters  

The smallest possible value of x + y + z is 14.

The answer is 511.  Hope this helps!

The largest integer n is 13.

The area of the fourth region is 32.

a has at most 12 divisors.

1/3    + 3/8    

      for adding or subtracting fraactions, you must have a common denominator ( you do not have to do this for multiplication or division)

1/3 = 8/24        3/8 = 9/24

8/24   + 9/24   =   (8+9) / 24  = 17/24 mile

Yesterday, (5)/(6) of the 180 students in a contest gave their speeches. How many students gave their speeches?Write your answer in simplest form.    

 5     180  

—  •  —–  =  150 

 6       1 

ohh thank you for your help! i knew t = 0 but kept calculating as -4 for some reason. thanks (i cant give you plus 1 for some reason)

I do not understand Straight.

Do you actually need help on this problem or not?

How about

\(3(3.\bar3)=10\)

I have not used any numbers other than three threes.

Note: I have not looked at any answers.

I know there was a mistake but I alr know it.

Straight

Hello Guest,

I'm so sorry, this isn't possible, you cannot change the the solution but do something by the 3s and get the solution 10.

Still this is very clever! Have you already seen the video?

Straight

All the pronumerals I introduce represent integers

N=9t+5    (1)

N=7m+2   (2)

N=5g+1     (3)

Looking at 2 and 3

7m+2=5g+1

5g=7m+1

5g=5m+(2m+1)

g=m+(2m+1)/5

Let a=(2m+1)/5

5a-1=2m

2m=4a+(a-1)

m=2a+(a-1)/2

let b=(a-1)/2

2b+1=a

so   m=2(2b+1)+b = 4b+2+b = 5b+2

and so     g=(5b+2)+a = 5b+2+2b+1 = 7b+3

Equation 3 becomes     N=5(7b+3)+1 = 35b+16

So now we have only 2  Diophantine equations to solve simultaneously

N=35b+16   and

N=9t+5

You can try solving those 2.

They are actually a little easier than the two I just did.  :)

Some of your questions are quite interesting unaza.

If you had made a positive impression here you would have at least a few more quality answers.

BUT

You have had some answers.

Some have been good ones.

You have not responded in any way.

I have even said this to you before...  AND what was your response?  NONE.

Well, you are consistent, I will give you that!

I saw another answerer chastize you as well.  Your response.  Nothing, just more questions.

You post a multitude of difficult questions.  Probably all of your homework. This is not encouraged.

I like this particular question.  Normally I would give your my thoughts or my solution.

But I am very reluctant to do so.  Shame!

"Real numbers x, y are randomly chosen from the interval [0, 1]. what is the probability of 
3x + y ≤ 1."

The area of the triangle divided by the area of the square gives the probability: