Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola.
equation 1: (x – 3)2 = y – 4
equation 2: y = -x + b
in order for this solution to be reasonable, which qualifications must be met?

a) b must equal 7 and a second solution to the system must be located at the point (2, 5).
b) b must equal 1 and a second solution to the system must be located at the point (4, 5).
c) b must equal 7 and a second solution to the system must be located at the point (1, 8).
d) b must equal 1 and a second solution to the system must be located at the point (3, 4).

Option A is the correct answer.

Step-by-step explanation:

In this question the given parabola is (x - 3)²= y - 4

And the equation is y = -x + b

One solution of these equations lies on vertex.

Therefore we have to find the coordinates of vertex so that value of b can be measured.

We know that if a parabola is in the form of y = (x - h)²+ k

Then the coordinates of the vertex of this parabola will be (h, k).

Now our equation of parabola is y = (x-3)² + 4

Therefore the vertex will be (3, 4).

And it has been given that the vertex is y = -x + b

Therefore by putting x = 3 and y = 4 we can get the value of b.

4 = -3 + b

b = 7.

Now the second solution to the system will be

(x - 3)² = -(x - 7) - 4

x² + 9 - 6x = -x + 7 - 4

x² +9 - 6x = -x + 3

x² - 6x + x + 9 - 3 = 0

x² -5x + 6 = 0

x² - 3x - 2x + 6 = 0

x(x - 3) - 2(x - 3) = 0

(x - 3)(x -2 ) = 0

x = 3, 2

Hence y = (-3 + 7) and y = (-2 + 7)

y = 4, 5

As we know first solution is (3, 4) the second solution will be (2, 5).

Option A is the correct answer.

goog may be able to you find that answer

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get