Answer:
12-3 lily has 9 cats
Step-by-step explanation:
Simplifying
5x(4y + 3x) = 5x(3x + 4y)
Reorder the terms:
5x(3x + 4y) = 5x(3x + 4y)
(3x * 5x + 4y * 5x) = 5x(3x + 4y)
Reorder the terms:
(20xy + 15x2) = 5x(3x + 4y)
(20xy + 15x2) = 5x(3x + 4y)
20xy + 15x2 = (3x * 5x + 4y * 5x)
Reorder the terms:
20xy + 15x2 = (20xy + 15x2)
20xy + 15x2 = (20xy + 15x2)
Add '-20xy' to each side of the equation.
20xy + -20xy + 15x2 = 20xy + -20xy + 15x2
Combine like terms: 20xy + -20xy = 0
0 + 15x2 = 20xy + -20xy + 15x2
15x2 = 20xy + -20xy + 15x2
Combine like terms: 20xy + -20xy = 0
15x2 = 0 + 15x2
15x2 = 15x2
Add '-15x2' to each side of the equation.
15x2 + -15x2 = 15x2 + -15x2
Combine like terms: 15x2 + -15x2 = 0
0 = 15x2 + -15x2
Combine like terms: 15x2 + -15x2 = 0
0 = 0
Solving
0 = 0
Couldn't find a variable to solve for.
This equation is an identity, all real numbers are solutions.
Answer:
1 + cosa sina
Step-by-step explanation:

cos³a - sin³a ← is a difference of cubes and factors in general as
a³ - b³ = (a - b)(a² + ab + b²) , then
cos³a - sin³a
= (cosa - sina )(cos²a + cosa sina + sin²a)
= (cosa - sina)(1 + cosa sina) [ sin²a + cos²a = 1 ]
Then

=
← cancel (cosa - sina) on numerator/ denominator
= 1 + cosa sina
Yes, these both are direct relationships and can be written like

, where k is the constant of variation.
For the first equation, k = 10. For the second equation, k = -4/3. You find it by rearranging the equation into the form

, and you use the coefficient of x for k.