4x - 5y = -3 ⇒ 1st equation
2x + 3z = 4 ⇒ 2nd equation
3y - z = 8 ⇒ 3rd equation
find the value of z.
3y - z = 8
- z = 8 - 3y
z = (8 - 3y) / -1
z = -8 + 3y
Substitute z with its value in the 2nd equation:
2x + 3z = 4
2x + 3(-8 + 3y) = 4
2x - 24 + 9y = 4
2x + 9y = 4 + 24
2x + 9y = 28
find value of x
2x + 9y = 28
2x = 28 - 9y
x = (28 - 9y)/2
x = 14 - 9y/2
Substitute the value of x in 1st equation
4x - 5y = -3
4(14-9y/2) - 5y = -3
56 - 36y/2 - 5y = -3
- 36y/2 - 5y = -3 - 56
- 36y/2 - 5y = - 59
2(-36y/2 - 5y) = 2(-59)
-36y - 10y = -118
-46y = -118
-46y/-46 = -118/-46
y = 2 26/46
y = 2 13/23
x = 14 - 9y/2
x = 14 - 9 (2 13/23) /2
x = 14 - 9 (59/23) / 2
x = 14 - 531/23 / 2
x = 14 - 531/23 * 1/2
x = 14 - 531/23*2
x = 14 - 531/46
x = (14*46/46) - 531/46
x = 644/46 - 531/46
x = (644-531)/46
x = 113/46
x = 2 21/46
z = -8 + 3y
z = -8 + 3(2 13/23)
z = -8 + 3(59/23)
z = -8 + 177/23
z = (-8*23/23) + 177/23
z = -184/23 + 177/23
z = (-184 + 177)/23
z = -7/23
x = 2 21/46 ; y = 2 13/23 ; z = -7/23
4x - 5y = -3
4(113/46) - 5(59/23) = -3
452/46 - 295/23 = -3
9.826 - 12.826 = -3
-3 = -3
2x + 3z = 4
2(113/46) + 3(-7/23) = 4
226/46 - 21/23 = 4
4.913 - 0.913 = 4
4 = 4
3y - z = 8
3(59/23) - (-7/23) = 8
177/23 + 7/23 = 8
7.696 + 0.304 = 8
8 = 8
Answer:
r(t) = 75 kg - (4.5 kg/wk)w
Step-by-step explanation:
Let r(t) represent the amount of rice remaining after w weeks.
Then:
r(t) = 75 kg - (4.5 kg/wk)w
Answer:
The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.
⇒The water level in the pool cannot exceed 14 feet.
Step-by-step explanation:
The question is on inequalities
Given;
Length= x ft
depth= x-6 ft
Width= x-8 ft
volume ≤ 1680 ft³
Forming the inequality to find length x of the pool
Volume= base area × depth
base area × depth ≤ volume
x(x-8) × (x-6) = 1680
(x²-8x )(x-6) = 1680
x(x²-8x) -6 (x²-8x)=1680
x³-8x²-6x²+48x=1680
x³-14x²+48x=1680
x³-14x²+48x-1680 ≤ 0
⇒The water level in the pool cannot exceed 14 feet...why?
taking the value of x at maximum to be 17 according to the graph, then maximum depth will be;
d=x-6 = 17-6=11 ft
⇒11 ft is less than 14ft
A value that doesn't change is a constant.
