Given that (-7,-9) is on the graph of f(x), find the corresponding point for the function 2/3 f(x)

y coordinate is the only one affected so... 
(-7, -6) 

:)

The denominator of a fraction is 3 more than its numerator. If the numerator is multiplied by 3, the resulting fraction is 5/2 of the original fraction. Find the Original fraction.

3(n/(n+3))=5/2 

6n=5(n+3) 
n=15 

fraction: 15/18

Apply the distributive law to write an equivalent form of the follows: 1.x+nx+2x 2.(x+3)(5)+(x+3)(n) 3.(x+5)(n)+(x+5)

 1.x+nx+2x = 3+n)x



 2.(x+3)(5)+(x+3)(n) = (x+3)(n+5)


 3.(x+5)(n)+(x+5) = (x+5)(n+1)


:)

Find all integers m for which y^2+my+50 can be factored.

factors of 50:
1, 50
2, 25
5, 10 
So m can be 
{51, -51, 27, -27, 15, -15} 

:)

The difference between two numbers is eight. if the smaller number exceeds half of the larger number by fourteen, what are the numbers?

x < y

 y - x = 8

x = y/2 + 14

y - (y/2 + 14) = 8

y - .5y -14 = 8

.5y = 22

y=44

x = 44 - 8 = 36



:)

find solution cos(2 arcsin x)=-1

 

rewriting in terms if sine... 

 

simplifying... 

 


x=1 or x=-1 


:)

Write a linear factorization of the function. f(x) = x^4 + 36x^2

There isn't one over the reals. over the complex numbers it is... 

x^4 + 36x^2 = 
x^2(x^2+36)= 
x*x*(x+6i)(x-6i) 

:)