The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is the number of photos printed, and f(x) is the amount of profit. part a: determine the vertex. what does this calculation mean in the context of the problem? (5 points) part b: determine the x-intercepts. what do these values mean in the context of the problem? (5 points

For letter A, we are asked to determine the vertex of the given function. First, we need to identify each value such as:
a = -1
b = 20
c = -75
The formula in determining the vertex (h, k) is h = -b / 2a
Solving for h, we have it:
h = - 20/ 2*(-1)
h = -20 /-2
h = 10
Solving for k, we have it:
f(h) = -1*10² + 20*10 - 75
f(h) = -100 + 200 - 75
f(h) = 25
Therefore, the vertex is (10,25)
since value for a is negative, the vertex is the maximum point such as when you have 10 photos, you will get $25 profit

For letter B, solving for x-intercepts, we have it:
0 = -1x² + 20x - 75 , divide both sides by -1
0 = x² - 20x + 75
0 = (x-15) (x-5)
x1 = 15
x2=5
If these values are the number of photos, there will be no profit. Break even.

Something that is true about that is that it has numbers

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12