Pangolin14

I'm sorry, that doesn't prove it.

I love these problems!

1) N=11 when divided by 12

So if you are familiar with modular arithmetic, we will write some equations. 

N==2 (mod 3)

N==3 (mod 4)

N==x(mod 12)

Let's solve for N. 

3a+2=4b+3

a and b are integers

take the whole thing modulo 3

b=2(mod 3)

so inputting for a new quotient integer c,

N=3a+2=4(3c+2)+3

N=3a+2=12c+11

N= 11 (mod 12)

or the remainder is 11 when divided by 12

2) D=102

482-74=408

992-74=918

1094-74=1020

The GCF is 102. 

D=102

!!!

3) N=311

Again, use modular arithmetic with integer variable quotients. Solving the way I did before, N=311 (mod 315) so N>=311+315n, and n can't be negative thus N=311.

4) 38 candies

lol, same modular arithmetic.

Solving equations and writing them, we have for the # of candies=x

x=3(mod7)

x=6(mod8)

x=3(mod5)

so x=3(mod 35)

and x=6(mod 8)

therefore x= 38 mod 280, and x=38 

(because 318 would obviously be too many candies for >8 people to eat.)

Celsius: -273

Fahrenheit: -459

for #1

And second one all I know is the mass of a hydrogen atom is 1.67 x 10-27 kg and Boltzmann's constant is k = 1.38 × 10-23 Joule/Kelvin. But I don't know how to solve! SOrry!!

Yay, I love rate problems!

Noon is 12:00 PM. 

So train A leaves at 12:00 PM and drives at 90 mph (I know right? CLASS 5 PASSENGER THAT'S LUXURY). And train B leaves from the same place and drives from the same direction at 10 mph greater than 90mph. In 30 minutes 12-12;30, Train A will go 45 miles and Train B will go 0 miles (Not left yet). In another 30 minutes, a total of 1 hour, Train A will have went 90 miles and train B will go 50. 2 hours, 180 miles VS 150 miles. 4 hours, 360 miles VS 350 miles. And 5 hours will add a total of 10 miles difference, which is 450 vs 450!!! Therefore 12:00+5:00=

17:00 in 24 hour clock

and 5:00 PM in 12 hour clock!

I'm sorry, I don't really understand; the problem is already completed.

Pepperoni=P

Mushrooms=M

Sausage= S

Green Peppers=G

Onions= O

C=cheese

Note that all of these pizzas have cheese.

1.P+M+C=14.67

2.P+M+S+G+C=17.85

3.P+M+S+G+O+C=19.44

Subtract equations 2 from 3 and get Onions=$1.59.

Then you can't find out any more, as this is a pizza estimation problem that has too many variables and I don't eat pizza soooooo...

b=10-a

c=a+90

when simplified

a+2b+c=110

a+2b+c=110

a+3b+2c=110+10-a+a+90

That's 210.

Square root 90 is 3 * sqrt 10. It is irrational and therefore not rational.

It is real because it is not a letter, it is a number.

It is not whole obviously,

natural is whole except no 0s so not natural.

Not an integer= all negative and positive and 0 counting numbers.

It is only irrational and Real.

Hmmmmmmmmmmm well, we graph functions.

And when we shift things to the right we do positive of x. So it is the third choice.