Answer:
carlos will have one brownie left over.
Step-by-step explanation:
im smart
Answer:
x² + y² + 4x - 2y + 1 = 0
Step-by-step explanation:
The equation of a circle is given by the general equation;
(x-a)² + (y-b)² = r² ; where (a,b) is the center of the circle and r is the radius.
In this case; the center is (-2,1)
We can get radius using the formula for magnitude; √((x2-x1)² + (y2-y1)²)
Radius = √((-4- (-2))² + (1-1)²)
= 2
Therefore;
The equation of the circle will be;
(x+2)² + (y-1)² = 2²
(x+2)² + (y-1)² = 4
Expanding the equation;
x² + 4x + 4 + y² -2y + 1 = 4 subtracting 4 from both sides;
x² + 4x + y² - 2y + 4 + 1 -4 = 0
= x² + y² + 4x - 2y + 1 = 0
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:
- 3
- 7
- 7
Step-by-step explanation:
1. In 2 draws, you can get one of each, so a minimum of 3 draws will guarantee at least 2 of one color.
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2. A minimum of 3 socks must be drawn to ensure one pair. A minimum of 2 must be drawn to ensure an additional pair. For three pairs, 7 socks must be drawn.
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3. The first 5 balls drawn could be white, so an additional 2 must be drawn to ensure 2 red balls. To be sure of 2 red balls, 7 balls must be drawn.
