(5x - 3y)(25x² + 15xy + 9y²) Step-by-step explanation: 125x³ - 27y³ is a difference of cubes and can be factored as a³ - b³ = (a - b)(a² + ab + b²). Given 125x³ - 27y³ = (5x)³ - (3y)³, it can be written as (5x - 3y)((5x)² + (5x)(3y) + (3y)²) = (5x - 3y)(25x² + 15xy + 9y²).
Total Cost, C = $(16S + 56). Step-by-step explanation: Chris purchases 8 more Ninja Turtles than Star Wars action figures. The cost per Ninja Turtle is $7, while each Star Wars figure costs $9. If we let S represent the number of Star Wars figures bought, then the number of Ninja Turtles becomes S + 8. The cost for S Star Wars figures is $9S. Similarly, for (S + 8) Ninja Turtles, the total cost is $(7S + 56). Therefore, the overall Total Cost is represented by the sum of the costs for both types of figures, leading to the Total Cost being expressed as C = 9S + (7S + 56).
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There are 2π radians in a complete circle.
Now, let's calculate the circumference.
5/2π = 60/circumference.
Next, solve for the circumference.
By multiplying both sides by 2π, we have: 5 * circumference = 120π.
Now divide both sides by 5, and we find: circumference = 24π.
Using the formula c = 2πr,
we set 24π = 2πr.
Dividing both sides by 2π gives us r = 12. Thus, the radius measures 12cm.