Remember
(x^m)(x^n)=x^(m+n)
and difference of 2 perfect squres
(a²-b²)=(a-b)(a+b)
and sum or difference of 2 perfect cubes
so
(x^3)(x^3)(x^3)=x^(3+3+3)=x^9
so
x^9=3*3*x^3
x^9=9x^3
minus 9x^3 both sides
0=x^9-9x^3
factor
0=(x^3)(x^6-9)
factor difference of 2 perfect squraes
0=(x^3)(x^3-3)(x^3+3)
factor differnce or sum of 2 perfect cubes (force 3 into (∛3)³)
0=(x³)(x-∛3)(x²+x∛3+∛9)(x+∛3)(x²-x∛3+∛9)
set each to zero
x³=0
x=0
x-∛3=0
x=∛3
x²+x∛3+∛9=0 has no solution
x+∛3=0
x=-∛3
x²-x∛3+∛9=0 has no solution
so the solutions are
x=-∛3, 0, ∛3
Answer:
x=12
Step-by-step explanation:
Since this is a right triangle we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
9^2 + x^2 = 15^2
81 + x^2 = 225
Subtract 81 from each side
x^2 =225-81
x^2 =144
Take the square root of each side
sqrt(x^2) = sqrt(144)
x=12
Answer:
17
Step-by-step explanation:
Answer:
a is adjacent, b is opposite, c is the hypotenuse
Step-by-step explanation:
A right angled triangle must contain the opposite, the adjacent and the hypotenuse. The opposite is the side that directly faces the angle of interest. The adjacent is the side that is close to the angle of interest.
Given that the angle Y is positioned between X and Z, the point b becomes the opposite of Y. The point a becomes adjacent to angle Y while c remains the hypotenuse of the right angled triangle.
The image below typifies the explanation given above. It shows the relationship between the three sides of the right angled triangle in detail.