Answer:
A - (2a+0)/2 ; (2b+0)/2 = ( a , b )
B - (-2a+0)/2 ; (2b+0)/2 = ( - a, b )
C - (-2a+0)/2 ; ( -2b+0)/2 = ( - a, - b )
D - (2 a+0)/2 ; (-2b+0)/2 = ( a , - b )
Step-by-step explanation:
Answer:
a) 2
b) s₁ and s₂
c) First linear equation: 5*x₁ + 8*x₂ + 10*x₃ + s₁ = 173
Second linear equation: 5*x₁ + 4*x₂ + 17*x₃ + s₂ = 254
Step-by-step explanation:
The problem statement, establishes two constraints, each one of them will need a slack variable to become a linear equation, so the answer for question
a) 2.
b) The constraints are: s₁ and s₂
c) First constraint
5*x₁ + 8*x₂ + 10*x₃ ≤ 173
We add slack variable s₁ and the inequality becomes
5*x₁ + 8*x₂ + 10*x₃ + s₁ = 173
The second constraint is:
5*x₁ + 4*x₂ + 17*x₃ ≤ 254
We add slack variable s₂ and the inequality becomes
5*x₁ + 4*x₂ + 17*x₃ + s₂ = 254
Answer:
65 in and 39 in respectively
Step-by-step explanation:
Let r be the common ratio; when we multiply both L and R by this common ratio, we'll get the actual length and actual width of the rectangle, Recalling that the formula for the perimeter of a rectangle is P = 2L + 2R, we get:
2(5r) + 2(3r) = 16r = 208 in
Then r = 208/16 = 13
Thus, the actual length is 5(13 in) and the actual width is 3(13 in.),
or 65 in and 39 in respectively.
As a check, calculate 65 in / 39 in; this comes out to 5:3, as required.
Then
