Answer:
1) (2,4)
2) (5,-2)
Step-by-step explanation:
those are the points at which the lines cross making them the solutions to the equations
<h3>
Answer: 2x</h3>
Explanation:
Each person is x years old. Adding those unknown ages gets us x+x = 2x
We can think of it like x being one box, so x+x represents having two boxes which shortens to 2x.
Answer:
1. Objective function is a maximum at (16,0), Z = 4x+4y = 4(16) + 4(0) = 64
2. Objective function is at a maximum at (5,3), Z=3x+2y=3(5)+2(3)=21
Step-by-step explanation:
1. Maximize: P = 4x +4y
Subject to: 2x + y ≤ 20
x + 2y ≤ 16
x, y ≥ 0
Plot the constraints and the objective function Z, or P=4x+4y)
Push the objective function to the limit permitted by the feasible region to find the maximum.
Answer: Objective function is a maximum at (16,0),
Z = 4x+4y = 4(16) + 4(0) = 64
2. Maximize P = 3x + 2y
Subject to x + y ≤ 8
2x + y ≤ 13
x ≥ 0, y ≥ 0
Plot the constraints and the objective function Z, or P=3x+2y.
Push the objective function to the limit in the increase + direction permitted by the feasible region to find the maximum intersection.
Answer: Objective function is at a maximum at (5,3),
Z = 3x+2y = 3(5)+2(3) = 21
Nicoles pattern:
1
5
17
53
161
Ian’s pattern:
0
1
3
7
15
Ordered pair:
(1, 0)
(5, 1)
(17, 3)
(53, 7)
(161, 15)
Table 1 -
Sequence 1:
9
11
13
15
17
Sequence 2:
5
8
11
14
17
Ordered pair:
(9, 5)
(11, 8)
(13, 11)
(15, 14)
(17, 17)
Table 2 -
Sequence 1:
20
16
12
8
4
Sequence 2:
20
17
14
11
8
Ordered pair:
(20, 20)
(16, 17)
(12, 14)
(8, 11)
(4, 8)
Table 3 -
Sequence 1:
1
3
7
15
31
Sequence 2:
40
24
16
12
10
Ordered pair:
(1, 40)
(3, 24)
(7, 16)
(15, 12)
(31, 10)
Answer:
x ≥ 0
Step-by-step explanation:
The absolute value of x+8 equals itself, thus x must be a real number (0 or any positive number).