The quadratic function f(x) = 2x² – 44x + 185 is written in vertex form is f(x) = 2(x – 11)² – 57.
<h3>What is a quadratic equation?</h3>
It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
The quadrattic equation is f(x) = 2x² – 44x + 185.
Take common 2 from the equation, we have
Add and subtract 121, we have
And we know that the standard equation
f(x) = a(x - h)² + k
On comparing, we have
The vertex (h, k) is (11, -57).
More about the quadratic equation link is given below.
brainly.com/question/2263981
The sales and expenditures will be $120 and it will take 12 card boxes.
Step-by-step explanation:
Cost of booth = $48
Expenditure per card box = $6
Let,
x be the number of card boxes.
Total cost as a function of x.
T(x)= 48+6x Eqn 1
Selling price of one card box = $10
Total sales as a function of x, where x is the no. of card boxes
S(x) = 10x Eqn 2
For expenditures and sales to be same
T(x) = S(x)
Dividing both sides by 4
Putting x=12 in both Equations
The sales and expenditures will be $120 and it will take 12 card boxes.
Keywords: function, variable
Learn more about functions at:
#LearnwithBrainly
Answer:
A. Considering the environmental impacts of an experiment
Explanation:
Ethics is just a person's brain's choice without any reasoning like your gut answer so Mathematics is the same but it considers the environmental impacts of an experiment.
Short Answer: Current speed = 3 miles per hour.
Givens
Downstream
d = 4.48 miles
t = 0.32 hours.
c = ??
r_boat = ??
Upstream
d = 4.48 miles
t = 0.56 miles
c = ??
r_boat =??
Equations.
Since the distances are the same, you can equate the distances and come back to them later.
d = r*t
(r - c) * 0.56 = (r + c) * 0.32 This will give you r in terms of c. Notice the minus sign on the left. It's there because the current is going against you, slowing you down.
Remove brackets
0.56r - 0.56c = 0.32r + 0.32c Add 0.56c to both sides.
0.56r = 0.32r + 0.32c + 0.56c
0.56r = 0.32r + 0.88c Subtract 0.32r from both sides.
0.56r - 0.32r = 0.88c
0.24r = 88c Divide by 0.24
r = 0.88/0.24 c
r = 3 2/3 c
Now we have enough information to solve for c
4.48/(r + c) = 0.32
4.48 = 0.32 * (r + c) Substitute r = 3 2/3c into this equation.
4.48 = 0.32 * (3 2/3c + c) Add c and 3 2/3c together.
4.48 = 0.32 * (4 2/3c) Change 4 2/3 to 14/3
4.48 = 0.32 * 14/3 c
4.48 = (4.48 / 3 ) * c
4.48 = 1.493333333 c Divide 4.48 by 1.493333333
c = 4.48 / 1.4933333
c = 3 mph <<<<<<<<<<<<<<Answer
It would be B because it makes sense