Greetings.
The answer is y = 2x + 7.
Explanation:
If you are an expert in graph then you are able to find the slope without calculating. (Rise over Run by looking at the graph.)
We can also find the slope by calculating m-value.
---> Rise Over Run
<em>But how are we gonna calculate if we don't have any two given ordered pairs?</em>
The answer is, we can just pick two ordered pairs that are part of the graph, or rather say that the graph passes through.
The graph passes through (-3,1) and (-2,3).
Then we can calculate the slope by using rise/run.
![m=\frac{3-1}{-2-(-3)}\\m=\frac{2}{-2+3}\\m=\frac{2}{1}\\m=2](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3-1%7D%7B-2-%28-3%29%7D%5C%5Cm%3D%5Cfrac%7B2%7D%7B-2%2B3%7D%5C%5Cm%3D%5Cfrac%7B2%7D%7B1%7D%5C%5Cm%3D2)
Thus, the slope is m = 2.
However, we are not done yet. We just only found out the slope. We need to find the y-intercept too.
From Linear Function - ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where m = slope and b = y-intercept.
Since b = y-intercept, we don't need to calculate/substitute x = 0. We simply find which number the graph has y-intercept at.
Which is (0,7), the y-intercept.
Then we substitute b = 7 as y-intercept.
Thus the answer is ![y=2x+7](https://tex.z-dn.net/?f=y%3D2x%2B7)
Answer:
2
Step-by-step explanation:
The "average value of function f(x) on interval [a, b] is given by:
f(b) - f(a)
ave. value = ---------------
b - a
Here f(t)=(t-2)^2.
Thus, f(b) = (b - 2)^2. For b = 6, we get:
f(6) = 6^2 - 4(6) + 4, or f(6) = 36 - 24 + 4 = 16
For a = 0, we get:
f(0) = (0 - 2)^2 = 4
Plugging these results into the ave. value function shown above, we get:
16 - 4
ave. value = ------------ = 12/6 = 2
6 - 0
The average value of the function f(t)=(t-2)^2 on [0,6] is 2.
Answer:
the answer is 22 minutes
Step-by-step explanation:
because when you need to add 2 to get 12:25 and then u add 20 more minutes which then gives takes u to 12:45 then add the time u added and that is the answer, 22 minutes
Answer:
![4x^2 + 22x + 15](https://tex.z-dn.net/?f=4x%5E2%20%2B%2022x%20%2B%2015)
Step-by-step explanation:
The side length of a square is represented by the expression 2x + 5.
The area of a square is given as:
![A = a^2](https://tex.z-dn.net/?f=A%20%3D%20a%5E2)
where a = length of side of the square
The area of the square is therefore:
![A = (2x + 5)^2\\\\A = (2x + 5)(2x + 5)\\\\A = 4x^2 + 20x + 25](https://tex.z-dn.net/?f=A%20%3D%20%282x%20%2B%205%29%5E2%5C%5C%5C%5CA%20%3D%20%282x%20%2B%205%29%282x%20%2B%205%29%5C%5C%5C%5CA%20%3D%204x%5E2%20%2B%2020x%20%2B%2025)
The perimeter of a square is given as:
![P = 4a](https://tex.z-dn.net/?f=P%20%3D%204a)
The perimeter of the square is therefore:
![P = 4(2x + 5) \\\\P = 8x + 10](https://tex.z-dn.net/?f=P%20%3D%204%282x%20%2B%205%29%20%5C%5C%5C%5CP%20%3D%208x%20%2B%2010)
The difference between the area of the square and the perimeter of the square is:
![4x^2 + 30x + 25 - (8x + 10)\\\\4x^2 + 30x + 25 - 8x - 10\\\\4x^2 + 30x - 8x + 25 -10\\\\4x^2 + 22x + 15](https://tex.z-dn.net/?f=4x%5E2%20%2B%2030x%20%2B%2025%20-%20%288x%20%2B%2010%29%5C%5C%5C%5C4x%5E2%20%2B%2030x%20%2B%2025%20-%208x%20-%2010%5C%5C%5C%5C4x%5E2%20%2B%2030x%20-%208x%20%2B%2025%20-10%5C%5C%5C%5C4x%5E2%20%2B%2022x%20%2B%2015)
The expression that represents the difference between the area and the perimeter of the square is:
![4x^2 + 22x + 15](https://tex.z-dn.net/?f=4x%5E2%20%2B%2022x%20%2B%2015)