Answer:
-4w + 32
Step-by-step explanation:
4 (-w + 8)
= (-4 × w) + (4 × 8)
= -4w + 32
Hope it helps :)
Please mark my answer as the brainliest
Answer: 32
Step-by-step explanation:
20 mins means the hand moves 120 degrees around the clock.
The formula to find the arc length is 2pi×r×a/360
2×pi×15×1/3=30pi×1/3=10pi
so i think the answer would be 10 pi cm
Answer:
The maximum value of the function = 11, at x = 3 and y = 5
The minimum value of the function = -21, at x = 3 and y = -3
Step-by-step explanation:
Given;
F = 4y - 3x
The function is subject to y ≤ 2x - 1,
y ≥ -2x + 3,
x ≤ 3
y ≤ 2x - 1
- ( y ≥ -2x + 3)
-------------------
0 ≤ 4x - 4
4 ≤ 4x
1 ≤ x
thus, 1 ≤ x ≤ 3
When x = 3
y ≤ 2x - 1 ⇒ y ≤ 2(3) - 1, ⇒ y ≤ 5
y ≥ -2x + 3, ⇒ y ≥ -2(3) + 3, ⇒ y ≥ - 3
thus, -3 ≤ y ≤ 5
When x = 1
y ≤ 2x - 1 ⇒ y ≤ 2(1) - 1, ⇒ y ≤ 1
y ≥ -2x + 3, ⇒ y ≥ -2(1) + 3, ⇒ y ≥ 1
when x = 1 and y = 1
F = 4(1) - 3(1)
F = 1
when y = -3, and x = 3
F = 4(-3) - 3(3)
F = -12 - 9
F = - 21
When y = 5 and x = 3
F = 4(5) - 3(3)
F = 20 - 9
F = 11
Therefore, the maximum value of the function = 11, at x = 3 and y = 5
The minimum value of the function = -21, at x = 3 and y = -3
The answer is 1000 ft, 800 ft, 600 ft.
Let:
a - the longest side
b - the middle side
c - the shortest side
The <span>perimeter of a triangular plot of land is 2400 ft: P = 2400 ft
The perimeter of a triangle is P = a + b + c, thus a + b + c = 2400
</span><span>The longest feet (a) is 200 ft less than twice the shortest (c): a = 2c - 200
</span><span>The middle side (b) is 200 ft less than the longest side (a): b = a - 200
Now, we have the system of three equations:
</span>a + b + c = 2400
a = 2c - 200
b = a - 200
__________
Substitute a from the second equation into the third equation:
b = 2c - 200 - 200 = 2c - 400
__________
Substitute a and b into the first equation:
(2c - 200) + (2c - 400) + c = 2400
2c - 200 + 2c - 400 + c = 2400
2c + 2c + c - 200 - 400 = 2400
5c - 600 = 2400
5c = 2400 + 600
5c = 3000
c = 3000/5
c = 600 ft
_________
Now, use c and substitute into the second and third equation:
a = 2c - 200
a = 2 * 600 - 200
a = 1200 - 200
a = 1000 ft
___
b = a - 200
b = 1000 - 200
b = 800 ft