The two inequalities can be rewritten as
The solution is composed by every point below the graph of the line 
, and above the horizontal line 
To draw the line we can build a little table (only 2 points are required):
So, if you draw the points (0,2) and (1, -2) and connect them, you'll have your line.
To draw the line , simply pick any point with y coordinate -2, for example (0, -2), and draw a horizontal line.
Choose the above/below areas as specified above to solve the system.
Answer:
She went on the slide 8 times and on the roller coaster 4 times
Step-by-step explanation:
We convert each statements to a mathematical equation.
Firstly, let's represent the number of times she went on the coaster with R and the number of times on the slide with S. We know quite well she went on 12 rides. Hence the summation of both number of times yield 12.
Mathematically, R + S = 12. ........(i)
Now we also know her total wait time was 3hours. Since an hour equals 60 minutes, her total wait time would equal 180 minutes.
To get a mathematical representation for the wait time, we multiply the number of roller coaster rides by 25 and that of the slides by 10.
Mathematically, 25R + 10S = 180 .......(ii)
Here we now have two equations that we can solve simultaneously.
From equation 1 we can say R = 12 - S. We can then substitute this into equation 2 to yield the following:
25(12 - s) + 10s = 180
300 - 25s + 10s = 180
300 - 25s + 10s = 180
300 - 15s = 180
15s = 300 - 180
15s = 120
S = 120/15
S = 8
S = 8 , and R = 12 - S = 12 - 8 = 4
Answer:
Step-by-step explanation:
The number of parrots in t years after 2010 can be modeled by the following function:
In which P(0) is the number of parrots in 2010 and r is the growth rate, as a decimal.
608 parrots in the forest in 2010.
This means that 
Then
When the scientists went back 5 years later, they found 4617 parrots.
This means that 
We use this to find 1 + r. So
![1 + r = \sqrt[5]{\frac{4617}{608}}](https://tex.z-dn.net/?f=1%20%2B%20r%20%3D%20%5Csqrt%5B5%5D%7B%5Cfrac%7B4617%7D%7B608%7D%7D)
So
Answer:
12.1
Step-by-step explanation:
The dashed line joining M₁ and M₂ is the hypotenuse of a right triangle as shown in red below.
The base of the triangle is
x₂ - x₁ = 2 - (-3) = 2+ 3 = 5
The height of the triangle is
y₂ - y₁ = 16 - 5 = 11
We can now use Pythagoras' theorem to calculate distance between the two midpoints.
x² = 5² + 11² = 25 + 121 = 146
x = √146 =
12.1
The distance between M₁ and M₂ is 12.1.
