Answer:
Runner Up Amount=$16,000
Winner Amount=$64,000
Step-by-step explanation:
Amount of the college's scholarship=$80,000
The fund is being divided between the top two contestants so that the winner receives four times as much as the runner-up.
Therefore: we can say it is being divided into 5 parts where the winner gets 4 parts and the runner up gets 1 part, i.e in the ratio 4:1.
Runner Up Amount
Winner Amount
The winner gets $64,000 and the runner up gets $16,000.
Answer:
The range of T is a subspace of W.
Step-by-step explanation:
we have T:V→W
This is a linear transformation from V to W
we are required to prove that the range of T is a subspace of W
0 is a vector in range , u and v are two vectors in range T
T = T(V) = {T(v)║v∈V}
{w∈W≡v∈V such that T(w) = V}
T(0) = T(0ⁿ)
0 is Zero in V
0ⁿ is zero vector in W
T(V) is not an empty subset of W
w₁, w₂ ∈ T(v)
(v₁, v₂ ∈V)
from here we have that
T(v₁) = w₁
T(v₂) = w₂
t(v₁) + t(v₂) = w₁+w₂
v₁,v₂∈V
v₁+v₂∈V
with a scalar ∝
T(∝v) = ∝T(v)
such that
T(∝v) ∈T(v)
so we have that T(v) is a subspace of W. The range of T is a subspace of W.
Answer:
c This is the direct variation
Step-by-step explanation:
The equation for direct variation is y= kx
Solving this for k
y/x =k
So y/x must be a constant
a. 9/3 =3
2/7 does not =3 so this is not a direct variation
b 1/2 = .5
-3/6 = -.5
This is not the same so this is not a direct variation
c. 27/9 =3
18/6 =3
9/3 =3
This is a direct variation with a constant of 3
d 5/-7 = -5/7
1/-3 = -1/3
This is not the same so this is not a direct variation
