Can anyone on these two questions show your work and explain 5. the table below shows the temperature t(m) of a cup of hot chocolate that is allowed to chill over several minutes.) which expression best fit the data for t(m) ) a. 150(0.85)m b. 150(1.15)m c. 150(0.85)m-1 d. 150(1.15)m ) 7. the function f(x)=3x squared +12x+11 can be written as vertex form as what? and what is vertex form?

(1), (3)

Step-by-step explanation:

5.  If m starts at 1, a geometric series has the form a₁ (r)ᵐ⁻¹.

If m starts at 0, a geometric series has the form a₀ (r)ᵐ.

Here, m starts at 0.  The first term, a₀, is 150.  The temperature is decreasing, so we're looking for an r < 1.  Therefore, the answer must be (1) 150 (0.85)ᵐ.

7.  A quadratic written in vertex form is:

y = a(x - h)² + k

We can find the vertex of the parabola using x = -b/(2a).

x = -12 / (2*3)

x = -2

f(-2) = 3(-2)² + 12(-2) + 11

f(-2) = -1

So the vertex (h, k) is at (-2, -1).

Therefore, the answer must be f(x) = 3(x + 2)² - 1

We can also show this by completing the square.

f(x) = 3x² + 12x + 11

f(x) = 3(x² + 4x) + 11

f(x) = 3(x² + 4x + 4) - 3(4) + 11

f(x) = 3(x + 2)² - 1