193k views
3 votes
can anyone help on these two questions show your work and explain please ​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?

can anyone help on these two questions show your work and explain please ​5. the table-example-1
User Joextodd
by
8.2k points

1 Answer

4 votes

Answer:

(1), (3)

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

User Ezod
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories