Which of the following equations is written in vertex form?

At the beginning of an experiment, the number of bacteria in a colony was counted at time t=O. The number of bacteria in the col

yan [13]

Answer:

1092

Step-by-step explanation:

We have been given that the number of bacteria in the colony t minutes after the initial count modeled by the function $B(t)=9(3)^t$ . We are asked to find the average rate of change in the number of bacteria over the first 6 minutes of the experiment.

We will use average rate of change formula to solve our given problem.

$\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}$

Upon substituting our given values, we will get:

$\text{Average rate of change}=\frac{b(6)-b(0)}{6-0}$

$\text{Average rate of change}=\frac{9(3)^6-9(3)^0}{6}$

$\text{Average rate of change}=\frac{9(729)-9(1)}{6}$

$\text{Average rate of change}=\frac{6561-9}{6}$

$\text{Average rate of change}=\frac{6552}{6}$

$\text{Average rate of change}=1092$

Therefore, the average rate of change in the number of bacteria is 1092 bacteria per minute.

8 0

3 years ago

Clarke borrows $16,000 to buy a new car. He pays simple interest at an annual rate of 6% over a period of 3.5 years. How much do

STALIN [3.7K]

Answer:

Step-by-step explanation:

8 0

4 years ago

Julio bought 4 pencils and 3 erasers for $0.37 and David paid $0.33 for 3 pencils and 4 erasers. What is the cost of one pencil?

nirvana33 [79]

Answer:

Each pencil costs $0.07 and each eraser costs $0.03

Step-by-step explanation:

System of linear equations

It refers to the study of systems when n variables are related in m linear equations, each one is not independent from the others. Solving such systems can be done following very diverse approaches.

Let p=the price of each pencil while e is the price each eraser

Julio bought 4 pencils and 3 erasers, spending

$4p+3e=0.37$

David bought 3 pencils and 4 erasers, spending

$3p+4e=0.33$

The system of equations is written in the form

$\left\{\begin{matrix}4p+3e=0.37\\ 3p+4e=0.33\end{matrix}\right$

We'll solve it by reduction. Multiplying the first equation by -3 and the second by 4:

$\left\{\begin{matrix}-12p-9e=-1.11\\ 12p+16e=1.32\end{matrix}\right.$

Adding both equations:

7e=0.21

e=0.03

Multiplying the first one by -4 and the second by 3

$\left\{\begin{matrix}-16p-12e=-1.48\\ 9p+12e=0.99\end{matrix}\right.\end{matrix}\right.$

Adding both equations:

-7p=-0.49

p=0.07

Solution: Each pencil costs $0.07 and each eraser costs $0.03

7 0

3 years ago

What is a number between 364 and 384 that is a multiple of both 3 and 7

masya89 [10]

Answer:

378

Step-by-step explanation:

It will also be a multiple of 21 .

As it is divisible by 3 the first possibility is 366 so:-

364 + n = 21m

where n = 2,5,8,11,14...

Trying each number in turn we get:-

364 + 14 = 21m

21m = 378

m = 18

so the answer is 378

7 0

4 years ago

Look at the top for the directions, and follow it.

mr_godi [17]

Here are all of the fill in the blanks, even the first on,

(-7,-6); (-7,-3); (-5,-3); (-5,-7); (2,-7); (2,-2,); (-1,-2); (-1,4); (-5,4); (-5,6); (-6,6); (-6,1); (2,1); (2,7); (4,7); (4,3); (7,3); (7,6)

you're welcome (:

3 0

3 years ago