Consider the right triangle HBF. The Pythagorean theorem tells you ...
HF² = HB² + BF²

The lengths HB and BF can be determined by counting grid squares, or by subtracting coordinates. Here, it is fairly convenient to count grid squares. When we do that, we find ...
HB = 2
BF = 5
Using these values in the equation above, we get
HF² = 2² + 5²
HF² = 4 + 25 = 29
Taking the square root gives the length HF.
HF = √29

5 0

3 years ago

The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars ea

Gre4nikov [31]

A) zeroes

P(n) = -250 n^2 + 2500n - 5250

Extract common factor:

P(n)= -250 (n^2 - 10n + 21)

Factor (find two numbers that sum -10 and its product is 21)

P(n) = -250(n - 3)(n - 7)

Zeroes ==> n - 3 = 0 or n -7 = 0
Then n = 3 and n = 7 are the zeros.

They rerpesent that if the promoter sells tickets at 3 or 7 dollars the profit is zero.

B) Maximum profit

Completion of squares

n^2 - 10n + 21 = n^2 - 10n + 25 - 4 = (n^2 - 10n+ 25) - 4 = (n - 5)^2 - 4

P(n) = - 250[(n-5)^2 -4] = -250(n-5)^2 + 1000

Maximum ==> - 250 (n - 5)^2 = 0 ==> n = 5 and P(5) = 1000

Maximum profit =1000 at n = 5

C) Axis of symmetry

Vertex = (h,k) when the equation is in the form A(n-h)^2 + k

Comparing A(n-h)^2 + k with - 250(n - 5)^2 + 1000

Vertex = (5, 1000) and the symmetry axis is n = 5.

8 0

3 years ago

Tina is saving to buy a notebook computer. She has two options. The first option is to put $500 away initially and save $10 ever

Alexxandr [17]

Answer:

Tina would save the same amount using either option after 20 months.

With either option, Tina would save $700.

Step-by-step explanation:

This problem can be modeled by a first order equation:

Where Tina's saved money after n months is:

S(n) = S(0) + rn, where S(0) is the money put away initially and r is how much she saves every month.

The first option is to put $500 away initially and save $10 every month, so: