TheOddOne

Thank you so much! :DDD

"Note: All solutions should be expressed in the form , where  and  are real numbers."

Could you perhaps fill in the blanks for me? Thank you! =^-^=

Thank you for helping!

A question though: would it also work if you split up the 6C3 into, say

6C1, 5C1, 4C1?

So the result would be:

4*4*6C1*5C1*4C1

or

4*4*6*5*4?

I'm not sure if this is an one in a million accidentally correct answer.

Thank you for your help once more =^-^=

Answer: 

44/3

Solution:

Hi Guest! Sorry for the late help 

Let's get  \(\mathrm{Line_1}\) into standard form first, yeah?

\(\mathrm{Line_1}\) = 

3x+4y=-14

      4y=-3x-14

       y=-3x/4 -7/2

So now that \(\mathrm{Line_1}\) is now happily in standard form, let's start looking for \(\mathrm{Line_2}\)'s equation.

First, let's find the slope.

To find a perpendicular line, you have to take the opposite reciprocal of \(\mathrm{Line_1}\)'s slope, which is -3/4.

So \(\mathrm{Line_2}\)'s new slope is 4/3. 

What we have so far for \(\mathrm{Line_2}\): y=4/3 x + b

Now we need to find b.

We can do that by plugging in (-5,7), a point on the line, into x and y in the partially done equation for  \(\mathrm{Line_2}\).

y = 4/3 x + b <-- before plugging in

7 = 4/3 * -5 + b <-- after plugging in

7 = -20/3 + b <-- simplifying

41/3 = b <-- even more simplifying

b = 41/3 <-- just flipping it nothing here to see

So we have the full equation for \(\mathrm{Line_2}\), or, y = 4/3 x + 41/3.

From here, we look at the question again. What is it asking for?

"find m+b"

m = 4/3, and b= 41/3. 

Hence, the answer is 44/3.

=^-^=

If you find a mistake, please let me know in the replies!

Final Answer: 

2880

Reasoning:

Odd numbers: 1,3,5,7,9

Even numbers: 2,4,6,8

So there are 5 odd numbers and 4 even numbers.

^ The number possibilities

For the first box, there are five possibilities, because there are five odd numbers.

For the second slot, there are four because there are four even numbers.

For the third, there are four possibilities, because there are four odd numbers left, since you can not use whatever was the first option.

For the fourth slot, there are three possibilities, because there are three even numbers remaining.

The pattern continues, until we are down to the ninth box, the unit digit, where there is only one possibility remaining.

Multiply what you get from the slots:

5*4*4*3*3*2*2*1*1 

= 2880

Please reply if you find a mistake lurking!

=^-^=

Oh, can I ask again in a bit? I think I got it.

I don't know how to reedit the question, which I would have if I could. It won't let me.

Ah, yeah! Thank you so much! :D

;D that would be nice

(I lost the email used-and i don't know how to recover that gmail account...)

Also, I kept flipping x and z. My fault... It's all supposed to be x so far. The question is what is z?

Hi catmg!

So if I'm reading this right:

( y - x ) = 2

( y + x ) = 172

- x = 2 - y

x = y - 2

Where did you get y+2?

Did I make another addition mistake... I shouldn't stay up late lol

I actually had another account on here-forgot the password... :facepalm:

I would like to talk to the friends I made on here again... Started the account in 2018!