The formula you need to know is that the side opposite of the 30° angle is always half the hypotheneus. For example in question 2 X should be 6 since 3 is opposite side of the angle 30°. In a 45 45 90 triangle, it is important to know that the straight sides are always the same length (since they are the same angle). For example in question 9, v is also 9√2.
When you have two sides, you can figure out the third side with a² + b² = c² since they are all right triangles. Good luck
This problem can be solved by the chicken rabbits method or you can just do simple algebra.
I.) Chicken and rabbits method
First assume all 110 coins are dimes and none are quarters.
We will have a total value of 11 dollars
Now for each dime we switch out for a quarter, we adds 15 cents to the total value.
18.50-11=7.50 dollars
There are 750/15=50 group of 15 cents in the 7 dollars and 50 cents.
This also meant that we need to switch out 50 dimes for 50 quarters.
So we have 50 quarters.
That first method is very good and very quick once you get the hang of it, now I'm going to show you the algebraic way to solve this.
Let's say there are x dimes and y quarters.
Set up equation
x+y=110
10x+25y=1850
Now solve multiply first equation by 10
10x+10y=1100
subtract
15y=750
y=50
Now we set the numbers of quarters to y so the answer is 50 quarters.
I personally recommend using algebra whenever you can because the practice is very important and you will eventually get really fast at setting up and solving equations. The first method is faster in this case but the second is more generalize, hope it helps.
Answer:
Velocity of the 24.6 g marble is 31 cm/s.
Step-by-step explanation:
Given:
Marble 1:
Mass of the marble 
= 12.3 gm
Velocity of 
before collision 
= 15.5 cm/s
Velocity of after collision 
= 77.5 cm/s
Marble 2:
Mass of the marble 
= 24.6 gm
Velocity of 
before collision 
= 62 cm/s
Velocity of after collision 
= ?
From the law of conservation of momentum, we know that momentum before equals the momentum after :
So,
⇒ 
⇒ 
⇒ Plugging the values.
⇒ 
⇒ 
⇒ 
⇒ 
...subtracting both sides 953.25
⇒ 
⇒ 
...dividing both sides with 24.6
⇒ 
⇒ 
cm/s
The velocity of the 24.6 g marble after the collision is 31 cm/s and it will move opposite to of the 12.3 g marbles that is towards left.
