19) B
20) D
21) A
22) B
23) C
24) C
Hj and jk are the same length line segments ( because the midpoint divides a line into two equal parts)
So hj = jk.
hk is the line segment which has the mid point j. It is the double of hj or jk. It can be the sum of hj and jk.
hj + jk = hk
or
2 * hj = hk
or
2 * jk = hk
To start, we're given the range that x lies in: from -1 to 4. We know from the fact that

that -1 will be <em /><em>included</em> in that range, so we mark -1 on the number line with a solid circle. We also know from

that, while x can be any value <em>up to</em> 4, it does not <em>include </em>4. We indicate this by drawing a hollow circle around 4 on the number line. Since x can be <em>any value within this range</em>, we make that fact clear by drawing a bold line between the points -1 and 4 on the number line. I've attached an image of what our final graph would look like.
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
Answer:
Type of drink given to each group
Step-by-step explanation: