Answer:
Step-by-step explanation:
Factor the sum of cubes
a³ + b³ = (a+b)(a² - ab +b²)
= 2a² - 2ab + 2b²
a³ + b³ + 6ab = 2a² + 4ab + 2b²
= 2(a² + 2ab +b²)
= 2(a+b)²
= 8
Y = a(x + 2)(x - 3) : equation of the parabola in factored form 10 = a(5 + 2)(5 - 2) : (5 , 10) is a point on the graph of the parabola and therefore satisfies the equation of the parabola. a = 5/7: solve the above equation for a.
Answer:
Triangles:
10 m, 21 m, 29 m
10 m, 29 m, 37 m
Not triangles:
10 m, 14 m, 29 m
10 m, 29 m, 40 m
Step-by-step explanation:
For a triangle to exist, the sum of any two sides of a triangle must be greater than that of the third side.
Let us check each of the options.
Option 1: 10 m, 14 m, 29 m
The sum of lengths 10 m and 14 m must be greater than 29 m.
10 + 14 = 24 < 29
So, this is not a triangle.
Option 2: 10 m, 21 m, 29 m
10 + 21 = 31 > 29
21 + 29 = 50 > 10
29 + 10 = 39 > 21
Therefore, it is a triangle.
Option 3: 10 m, 29 m, 37 m
10 + 29 = 39 > 37
29 + 37 = 66 > 10
37 + 10 = 47 > 29
Therefore, it is a triangle.
Option 4: 10 m, 29 m, 40 m
10 + 29 =39 < 40
So, this is not a triangle.
