Answer:

Step-by-step explanation:
To find the equation, use the slope-intercept formula:

m is the slope and b is the y-intercept. Now, it'll really help to draw a line through the points, connecting them. If you look at point (0,2), we can see that this is the y-intercept (where a point sits on the y-axis when x=0). You can insert this into the equation by taking the y value:

Now, take any two points to find the slope. To make it easier, I'll use (1,5) and (0,2). Use the slope formula for when you know two points:

Rise over run is the change in the y-axis over the change in the x-axis. Insert values:

Solve:

Since both are negative, the result is a positive:

Insert this into the equation as m, the slope:

Done.
The inequality
gives the least number of buses, b, needed for the trip. The least number of buses is 9
<u>Solution:</u>
Given that, There are 412 students and 20 teachers taking buses on a trip to a museum.
Each bus can seat a maximum of 48.
We have to find which inequality gives the least number of buses, b, needed for the trip?
Now, there are 412 students and 20 teachers, so in total there are 412 + 20 = 432 travelers
<em><u>The number of buses required “b” is given as:</u></em>


Number of buses required ≥ 9 buses.
But least number will be 9 from the above inequality.
Hence, the inequality
gives least count of busses and least count is 9.
Answer:
The population will reach 34,200 in February of 2146.
Step-by-step explanation:
Population in t years after 2012 is given by:

In what month and year will the population reach 34,200?
We have to find t for which P(t) = 34200. So



Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots
such that
, given by the following formulas:



In this question:

So 
Then



We only take the positive value.
134 years after 2012.
.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.
So the population will reach 34,200 in February of 2146.
Answer:
30.25 & 33.25
Step-by-step explanation:
x² + 11x + (5.5)² = 3+ (5.5)²
x² + 11x + 30.25 = 33.25