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I just realized my answer is really wrong.. Nice answer guest! 

Any factorial greater than 10! will end in 00. This means we just need to find what 5! + 6! + 7! + 8! + 9! ends in. 

5! = 120

6! = 720

7! = 5040

8! = 40320

9! = 362880

Add up the last two digits of these numbers and you get 180, which means the last two digits of the sum is 80, which is your answer :)

The coordinates of the triangle are: (3, 0) (1, 3) and (6, 6).

To find the dimensions of this triangle, use the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²) 

Let's name the vertices for ease. A = (3, 0), B = (1, 3), and C = (6, 6)

AB = √((1 - 3)² + (3 - 0)²)
      = √((-2)² + 3²)

      = √13

BC = √((6 - 1)² + (6 - 3)²)

      = √(5² + 3²)
      = √34 

AC = √((6 - 3)² + (6 - 0)²)

      = √(3² + 6²)

      = 3√5

Now that we know the dimensions, we can use Heron's Formula for that. 

s = semi perimeter = (√13 + √34 + 3√5) ÷ 2 ≈ 8.07

A = √s(s-a)(s-b)(s-c)

   = √8.07(8.07 - √13)(8.07 - √34)(8.07 - 3√5)

   = 10.5 units², which is your answer :)

Since we know ∠BAG ≈ ∠DEF, and AC ≈ EC, △ABG and △ACF, and △EDF and △ECG are similar triangles. This means the angles ∠ACF ≈ ∠ECG. All we need to know now is CF ≈ CG, which is your answer :)

Since the total is less than a dollar, dimes < 7, quarters < 4
 

--> 4P + 2N + 1D + 3Q
--> 5P + 1N + 1D + 3Q
--> 3P + 1N + 4D + 2Q            There are 6 combinations for when there is 1 < Q < 4
--> 4P + 1N + 3D + 2Q

--> 3P + 2N + 3D + 2Q

--> 2P + 3N + 3D + 2Q

--> 2P + 1N + 6D + 1Q

--> 1P + 2N + 6D + 1Q
--> 3P + 1N + 5D + 1Q
--> 2P + 2N + 5D + 1Q

--> 1P + 3N + 5D + 1Q           

--> 4P + 1N + 4D + 1Q

--> 3P + 2N + 4D + 1Q.            There are 2 + 3 + 4 + 5 + 6 + 7 = 27 combinations when there is 1 quarter
--> 2P + 3N + 4D + 1Q
--> 1P + 4N + 4D + 1Q
...

--> 7P + 1N + 1D + 1Q          
--> 6P + 2N + 1D + 1Q
--> 5P + 3N + 1D + 1Q

--> 4P + 4N + 1D + 1Q          
--> 3P + 5N + 1D + 1Q

--> 2P + 6N + 1D + 1Q

--> 1P + 7N + 1D + 1Q

This means the total combination is 6 + 27 = 33 combinations, which is your answer :)

First, factor the second term:

x² - 9 is a difference in squares so it equals (x + 3)(x - 3)

This means the terms are now:

(x - 3)² , (x + 3)(x - 3) , (x + 3)² , and (x - 1)²

Now the factors of these terms are: (x - 3) , (x + 3) , and (x - 1)

The least common multiple (LCM) is just the term with the largest power that holds these factors. 
This means the LCM is (x - 3)²(x + 3)²(x - 1)², which is also your answer :)

We can use the binomial theorem, which is explained here --> https://www.mathsisfun.com/algebra/binomial-theorem.html
 

Since we're only finding the coefficient of y⁴, the exponent of the y is, well 4, while the exponent of the 7 is 1 (5-4). 

This means the y⁴ term is 5C1 * (2y)⁴-7¹

= 5(2y)⁴-7

= -35(2y)⁴

= -560y⁴

Which means the coefficient of y⁴ is -560, which is also your answer :)

Using Heron's formula: √s(s-a)(s-b)(s-c), we can calculate this easily :)

s = semiperimeter = (3 + 4 + 5) / 2 = 6

√s(s-a)(s-b)(s-c) 

= √6(6-3)(6-4)(6-5)

= 6 units², which is your answer :)