Answer:
number of gallons of water the family will use every morning = 50 gallons
Step-by-step explanation:
Every minutes 2.5 gallons of water flows from the shower . The amount of water disperse by the shower for every 1 minutes is 2.5 gallons. The family using the shower are 4 in numbers . And each of them spend on average of 5 minutes showering .
Let us find how many gallons of water will flow for 5 minutes since family member spent an average of 5 minutes bathing every morning/. Therefore,
2.5 gallons = 1 minutes
? gallons = 5 minutes
cross multiply
number of gallons of water each family member uses every morning = 2.5 × 5 = 12.5 gallons
They are 4 family members in number since each person uses 12.5 gallons of water , 4 of them will use 4 × 12.5 = 50 gallons
Answer:
The room dimensions for a minimum cost are: sides of 10 feet and height of 8.75 feet.
Step-by-step explanation:
We have a rectangular room with sides x and height y.
The volume of the room is 875 cubic feet, and can be expressed as:
With this equation we can define y in function of x as:
The cost of wall paint is $0.08 per square foot. We have 4 walls which have an area Aw:
The cost of ceiling paint is $0.14 per square foot. We have only one ceiling with an area:
We can express the total cost of painting as:
To calculate the minimum cost, we derive this function C and equal to zero:
The sides of the room have to be x=10 feet.
The height can be calculated as:
The room will have sides of 10 feet and a height of 8.75 feet.
Hi there!
α, β, γ are the zeroes of the polynomial x³ + px² + qx + 2
Then,
• α + β + γ = - p ---(i)
• αβ + βγ + γα = q. ---(ii)
• αβγ = - 2. ---(iii)
We're Given :-
αβ + 1 = 0 Or αβ = - 1
Substitute " αβ = - 1 " in eqn. (iii) :-
(- 1) γ = - 2
γ =
γ = 2
Now. Accr'ding to the question :-
2p + q + 5 = - 2 (α + β + γ) + (αβ + βγ + γα) + 5
= - 2 (α + β + γ) + (αβ + [ γ (β + α) ] + 5
= - 2 (α + β + 2) + [ - 1 + 2 ( α + β ) ] + 5
= - 2α - 2β - 4 - 1 + 2α + 2β + 5
= 5 - 5
= 0
∴ 2p + q + 5 = 0
~ Hope it helps!
Area of the rectangle: {base times height}
4cm x 8cm = 32cm^2
Area of the triangle: {base times height divided by two}
(4cm x 11cm) : 2 = 22cm^2
Total area = 22cm^2 + 32cm^2 = 54cm^2
Using Distributive Property:
Combine and get all the terms in left sides and set it equal to zero and solve for m.
(m-5) (m-1) = -3 //Basic step of distribution.
m(m-1) -5(m-1) = -3
m^2 - m - 5m + 5 = -3 //Combine like terms and add 3 on both sides.
m^2 - 6m + 8 = 0 //Factor
m^2 - 4m - 2m + 8 = 0
m(m-4) -2(m -4) = 0
(m-4)(m-2) = 0 //Solve for m.
Got two equations:
1)m - 4 = 0
m = 4
2) m - 2 = 0
m = 2
Solution: m = 4, 2
//Hope this helps