Answer:Rigid transformations preserve segment lengths and angle measures.
A rigid transformation, or a combination of rigid transformations, will produce congruent figures.
In proving SAS, we started with two triangles that had a pair of congruent corresponding sides and congruent corresponding included angles.
We mapped one triangle onto the other by a translation, followed by a rotation, followed by a reflection, to show that the triangles are congruent.
Step-by-step explanation:
Sample Response: Rigid transformations preserve segment lengths and angle measures. If you can find a rigid transformation, or a combination of rigid transformations, to map one triangle onto the other, then the triangles are congruent. To prove SAS, we started with two distinct triangles that had a pair of congruent corresponding sides and a congruent corresponding included angle. Then we performed a translation, followed by a rotation, followed by a reflection, to map one triangle onto the other, proving the SAS congruence theorem.
The volume of the sphere is:
V = 4 / 3πr ^ 3
Deriving we have:
V '= (3) (4/3) (π) (r ^ 2) (r')
From here, we clear the value of r ':
r '= (V') / ((4) (π) (r ^ 2))
Substituting values:
r '= (2π) / ((4) (π) ((5) ^ 2))
r '= (2π) / ((4) (π) (25))
r '= (2π) / (100π)
r '= 1/50
Then, the surface area of the sphere is:
A = 4πr ^ 2
Deriving we have:
A '= 8πrr'
Substituting values:
A '= 8π (5) (1/50)
Rewriting:
A '= (40/50) π
A '= (8/10) π
A '= (4/5) π
Answer:
The surface area of the sphere is decreasing at:
(A) 4pi / 5
Answer:
<h2>−9a³ − a² + 12a</h2>
Step-by-step explanation:
3a(a²-3a+4)-4(3a³-2a²) = 3a³ − 9a² + 12a − 12a³ + 8a²
= (3a³ − 12a³) + (− 9a² + 8a²) + 12a
= −9a³ − a² + 12a
Answer:
a = 3
Step-by-step explanation:
Factorize (x+5)(x-4)(x+2)
(x+5)(x-4)(x+2)
= (x²-4x+5x-20)(x+2)
= (x²+x-20)(x+2)
= (x³+2x²+x²+2x-20x-40)
= x³+3x²-18x -40
Compare with x^3+ax^2
3x² = ax²
3 = a
Rearrange
a = 3
Hence the value of a that makes the expressions identical is 3
Answer:
25
Step-by-step explanation:
12= 0.48x
x=12/0.48
x=25
