8 corners would be the answer
Answer:
6 plus dollars
so 14 dollars
Step-by-step explanation:
That funky circle in the middle is the composition of the function. It asks you to take a function as an input and to yield an output that's another function. It's one of the five function operations, along with adding, subtracting, multiplying, and dividing.
When you compose, you might find the notation w(u(x)) easier to understand. It's saying evaluate u then evaluate w.
For our functions, the compositions are:
u(w(x)) = u(2x²) = -(2x²) - 2 = -2x² - 2
w(u(x)) = w(-x - 2) = 2(-x - 2)² = 2(x² + 4x + 4) = =2x²+ 8x +8
Now we evaluate each composition at 4.
u(w(4)) = -2(4²) - 2 = -2(16) - 2 = -32 -2 = -34
w(u(4)) = -2(2²) +8(2) + 8 = -2(4) + 16 + 8 = -8 + 16 + 8 = 16.
Thus, u(w(4)) = -34 and w(u(4)) = 16.
Answer:
PC = 12 units
AP = 10 units
Step-by-step explanation:
- The centroid of a triangle is the intersection of the three medians of the triangle
- Each median connecting a vertex with the midpoint of the opposite side
- The centroid divides each median into two parts, which are always in the ratio 2: 1 from the vertex
In ΔACE
∵ P is the centroid of it
∴ P divides CF the ratio 2: 1 from C
∴ PC = 2 PF
∵ PF = 6 units
∴ PC = 2(6)
∴ PC = 12 units
∵ P divides AD at the ratio 2: 1 from A
→ That means AD = 2 + 1 = 3 parts, and AP =
AD
∴ AP =
AD
∵ AD = 15 units
∴ AP = AP =
(15)
∴ AP = 10 units