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3 years ago

I need some help with quadratic function

Mathematics

1 answer:

Sonja [21]3 years ago

8 0

Y= (x-2)² + 5. We can write it as : y-5 = (x-2)². The general equation of a quadratic function is :

(y-k) = a(x-h)², where h and k are the vertex of the parabola and a, the coefficient which determines whether the parabola opens upward or downward.
So, y-5 = (x-2)²
Having said that we can say that the VERTEX( 2,5) and since a=1 (a>0) the parabola is open upward OR it passes by a MINIMUM (Then the vertex is minimum)
The domain (x- value) is all Real { x|x = -∞ to x=+∞}
The Range (y-value) is all y ≥ 5

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The marginal price per pound (in dollars) at which a coffee store is willing to supply x pounds of Jamaican Blue Mountain coffee

il63 [147K]

Answer:

Thus, the coffee shop is willing to supply 6 pounds per week at a price of $4 per pound.

Step-by-step explanation:

We are given the following information in the question:

The marginal price per pound (in dollars) is given by:

$p'(x) = \displaystyle\frac{208}{(x+7)^2}$

where x is the supply in pounds.

$P(x) = \displaystyle\int p'(x)~dx =\displaystyle\int\displaystyle\frac{208}{(x+7)^2}~dx\\\\P(x) = \frac{-208}{(x+7)} + c\\\\\text{where c is the constant of integration.}$

The coffee shop is willing to supply 9 pounds per week at a price of $7 per pound.

Thus, we are given that

P(9) = 7

Putting the values, we get,

$P(x) = \displaystyle\frac{-208}{(x+7)} + c\\\\P(9) = 7\\\\\displaystyle\frac{-208}{(9+7)} + c = 7\\\\c = 7 + \frac{208}{16} = 20$

$P(x) = \displaystyle\frac{-208}{(x+7)} + 20$

Now, we have to find how many pounds it would be willing to supply at a price of $4 per pound.

P(x) = 4

$P(x) = \displaystyle\frac{-208}{(x+7)} + 20 = 4\\\\\frac{-208}{x+7} = -16\\\\x + 7 = 13\\x = 6$

Thus, the coffee shop is willing to supply 6 pounds per week at a price of $4 per pound.

3 0

3 years ago

In a triangle the measurements of the angles are x°, ( x + 6)°, (2x + 10)°, and the sum of the three angles of a triangle is 180

34kurt

Answer:

largest angle = 92°

Step-by-step explanation:

Since the measurement of the angles are;

x°, ( x + 6)°, (2x + 10)°

And we know that sum of angles in a triangle is 180. Thus;

x + (x + 6) + (2x + 10) = 180

x + x + 6 + 2x + 10 = 180

4x + 16 = 180

4x = 180 - 16

4x = 164

x = 164/4

x = 41°

The other two angles will be;

(41 + 6)° and (2(41) + 10)°

Which gives;

47° and 92°

So,largest angle = 92°

7 0

3 years ago

Which radical expression is equivalent to 3^3/4

OleMash [197]

The numerator of the fraction is the power of the number and the denominator is the root of the number. This is expressed as follows:

⁴√(3)³

8 0

2 years ago

Read 2 more answers

78 divided by 21?:-:

MA_775_DIABLO [31]

Answer:

3.7 or 3.71428571429

Step-by-step explanation:

4 0

2 years ago

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Jason went shopping he bought a watch and a pair of trainers for a total price of £53.55 this price includes 15% loyalty discoun

babymother [125]

Answer: price of the watch before the discount is £23.5825

Step-by-step explanation:

Let x represent the original price of the watch.

Jason went shopping he bought a watch and a pair of trainers for a total price of £53.55. This price includes 15% loyalty discount. The value of the discount is

15/100 × 53.55 = 8.0325

This means that the original cost of both items is

53.55 + 8.0325 = 61.5825

Before the discounts, the trainers were priced at £38. Therefore,

38 + x = 61.5825

x = 61.5825 - 38

x = 23.5825

4 0

3 years ago