The answer will be A. 471/11. Hope it help!
Answer:
The value of x and y that satisfy the equations is x = 2 and y = 1
Step-by-step explanation:
Given
2.5(x−3y)−3=−3x+0.5
3(x+6y)+4=9y+19
Required.
Find x and y
We start by opening all brackets
2.5(x−3y)−3=−3x+0.5 becomes
2.5x - 7.5y - 3 = -3x + 0.5
Collect like terms
2.5x + 3x - 7.5y = 3 + 0.5
5.5x - 7.5y = 3.5 ---- Equation 1
In similar vein, 3(x+6y)+4=9y+19 becomes
3x + 18y + 4 = 9y + 19
Collect like terms
3x + 18y - 9y = 19 - 4
3x + 9y = 15
Multiply through by ⅓
⅓ * 3x + ⅓ * 9y = ⅓ * 15
x + 3y = 5
Make x the subject of formula
x = 5 - 3y
Substitute 5 - 3y for x in equation 1
5.5(5 - 3y) - 7.5y = 3.5
27.5 - 16.5y - 7.5y = 3.5
27.5 - 24y = 3.5
Collect like terms
-24y = 3.5 - 27.5
-24y = -24
Divide through by - 24
y = 1
Recall that x = 5 - 3y.
Substitute 1 for y in this equation
x = 5 - 3(1)
x = 5 - 3
x = 2
Hence, x = 2 and y = 1
Answer:
Step-by-step explanation:
50 X 240 = 2700. So you will need 240 packs of 50. They cost 17.95 each, so the multiply. 240 X 17.95 is 4,308. So, 4,308 is your answer.
Answer: 46.90mins
Step-by-step explanation:
The given data:
The diameter of the balloon = 55 feet
The rate of increase of the radius of the balloon when inflated = 1.5 feet/min.
Solution:
dr/dt = 1.5 feet per minute = 1.5 ft/min
V = 4/3·π·r³
The maximum volume of the balloon
= 4/3 × 3.14 × 55³
= 696556.67 ft³
When the volume 2/3 the maximum volume
= 2/3 × 696556.67 ft³
= 464371.11 ft³
The radius, r₂ at the point is
= 4/3·π·r₂³
= 464371.11 ft³
r₂³ = 464371.11 ft³ × 3/4
= 348278.33 ft³
348278.333333
r₂ = ∛(348278.33 ft³) ≈ 70.36 ft
The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)
The time for the radius to increase to the
above length
Time taken for the radius to increase the length.
= is 70.369 ft/(1.5 ft/min)
= 46.90 minutes
46.90mins is the time taken to inflate the balloon.