gwenspooner85

Thank you guys.

I'm sure there's a more clever way than this. Anyways:

We write the prime factorization of 30! to get 2^26×3^14×5^7×7^4×11^2×13^2×17×19×23×29 (using Wolfram Alpha). The prime factors here are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. So there are 10 prime divisors of 30!.

Lol not geometry...it's geometric series.

Haha it's okay. :)

Congratulations on 1000+ likes!

s/t=14/12

Then s/t, where t is 7 must equal to 14/12.

s/7=14/12

12s=98

s=98/12

s=49/6

Let x be the number of crows and 15-x the number of groundhogs. Note that crows have 2 legs and groundhogs 4. We form an equation for the number of legs.

2x+4(15-x)=40

2x+60-4x=40

-2x=-20

x=10

There are 10 crows and 15-10=5 groundhogs.

Write 3x+4y=-14 in slope intercept form:

3x+4y=-14

4y=-3x-14

y=-3/4x-14/4

The line perpendicular to it must have slope of 4/3. So we have y=4/3x+b. We plug in the given point (-5, 7) to solve for b.

7=4/3(-5)+b

7=-20/3+b

b=41/3

m+b is 4/3+41/3=45/3=15.

\(3^x=243^4\\ 3^x=(3^5)^4\\\ 3^x=3^{20}\\ \boxed{x=20}\)