Find a value for m and n to make a true statement.
a) mx^2 - 36 = (3x + 6)(3x - 6)
b) (mx + ny)^2 = 4x^2 + 12xy + 9y^2

Correct a) m = 9 ; b) m = 2 and n = 3

Step-by-step explanation:

Given:

a) m x² - 36  = (3 x + 6) (3 x - 6)  ⇒ m = ?

b) (m x + n y)² = 4 x² + 12 x y + 9 y²  ⇒ m, n = ?

a)  m x² - 36 (3 x + 6) (3 x - 6)  

The right side of the equation is the difference of the square, so we will present the left side in the same way:

(√m x)² - 6² = (3 x + 6) (3 x - 6)

(√m x + 6) (√m x - 6) = (3 x + 6) (3 x - 6)

√m = 3 /²  when we square both sides of the equation we get:

m = 9

b)

(m x + n y)² = 4 x² + 12 x y + 9 y²

The left side of the equation is the complete square of the binomial, so we will present the right side in the same way:

(m x + n y)² = (2 x)² + 2 · 2 x · 3 y + (3 y)² = (2 x + 3 y)²

(m x + n y)² = (2 x + 3 y)²  ⇒

m = 2 and n = 3

God is with you!!!

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: