Answer:
A landscape architect recommends installing a triangular statue with
vertices at (10, −10), (10, −8), and (7, −10).
a. Is the triangle congruent to triangle T ? Justify your answer.
b. Propose a series of rigid motions that justifies your answer to part a.
6. Another landscape architect recommends installing a triangular statue
Step-by-step explanation:A landscape architect recommends installing a triangular statue with
vertices at (10, −10), (10, −8), and (7, −10).
a. Is the triangle congruent to triangle T ? Justify your answer.
b. Propose a series of rigid motions that justifies your answer to part a.
6. Another landscape architect recommends installing a triangular statue
Answer:
Below in bold.
Step-by-step explanation:
Area = 30 + 12x and area is also = to width * length so we need to look for factors of 30 + 12x.
30 + 12x = 6(5 + 2x)
So 6 and 5 + 2x is one possible answer.
3 and 10 + 4x is another.
12 and 2.5 + x is another.
If we multiply these pairs together we see that the result is
30 + 12x in each case.
Answer:
SA = 615.4 yd²
Step-by-step explanation:
The surface area (SA) of a sphere is calculated as
SA = 4πr² ← r is the radius
Here diameter = 14, thus r = 14 ÷ 2 = 7, then
SA = 4π × 7² = 4π × 49 = 196π = 196 × 3.14 ≈ 615.4 yd²
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Answer:
64 × pi m²
Step-by-step explanation:
the formulas needed for the surface area of a cone are :
base area plus the "mantle", the lateral "wall" around it.
the base area is a circle.
so, that formula is Ac = pi×r²
the "wall" formula is Aw = pi×r×s
r = radius
s = slant height = 12
the formula for the surface area of a sphere is
As = 4×pi×r²
we know now, that both surface areas are the same, and also the radius is the same for both objects.
Ac + Aw = As
pi×r² + 12×pi×r = 4×pi×r²
=>
12×pi×r = 3×pi×r²
12×pi = 3×pi×r
12 = 3×r
r = 4 m
now, we only need to use this value of r in our formulas for surface areas, like for the sphere :
4×pi×r² = 4×pi×4² = 4³×pi = 64×pi
