The answer is Difference of Cubes.
Difference of cubes is a³ - b³.
27 can be written as 3³ (= 3 × 3 × 3 = 27). So, a = 3.
8 can be written as 2³ (= 2 × 2 × 2 = 8). So, b = 2.
Difference of cubes can be expressed as:
a³ - b³ = (a - b)(a² + ab + b²)
⇒ 3³ - 2³ = (3 - 2)(3² + 3×2 + 2²) = 1 × (9 + 6 + 4) = 1 × 19 = 19
⇒ 27 - 8 = 19
Answer:
Pounds of raisins = 1.5 lb
Pounds of cashew = 3.5 lb
Step-by-step explanation:
Let
Pounds of raisins = x
Pounds of cashew = y
x + y = 5 (1)
4.50x + 9.50y = 40 (2)
From (1)
x = 5 - y
Substitute x = 5 - y into
4.50x + 9.50y = 40
4.50(5 - y) + 9.50y = 40
22.50 - 4.50y + 9.50y = 40
- 4.50y + 9.50y = 40 - 22.50
5y = 17.5
y = 17.5 / 5
= 3.5
y = 3.5lb
Substitute y = 3.5 into
x + y = 5
x + 3.5 = 5
x = 5 - 3.5
= 1.5
x = 1.5lb
Pounds of raisins = 1.5 lb
Pounds of cashew = 3.5 lb
Answer:
36
Step-by-step explanation:
Since BD is similar to GI, the ratio of the sides of the triangles is 27:3=9:1. This means that BC is 9 times larger than BH, or 4*9=36 units long. Hope this helps!
