Answer:
Here we can only answer A and B.
For a given function f(x), the average rate of change in a given interval [a, b] is given by:
![r = \frac{f(b) - f(a)}{b - a}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D)
A) we have g(x) = 14*x + 6, and the interval [0, 5], the average rate of change is:
![r = \frac{g(5) - g(0)}{5 - 0} = \frac{(14*5 + 6) - (14*0 + 6)}{5} = \frac{14*5}{5} = 14](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bg%285%29%20-%20g%280%29%7D%7B5%20-%200%7D%20%3D%20%5Cfrac%7B%2814%2A5%20%2B%206%29%20-%20%2814%2A0%20%2B%206%29%7D%7B5%7D%20%20%3D%20%5Cfrac%7B14%2A5%7D%7B5%7D%20%3D%2014)
The average rate of change is 14.
B) We have g(x) = 3*(2x) - 6
we can rewrite this as:
g(x) = 3*2*x - 6 = 6x - 6
And we want to find the rate of change in the interval [0, 5]
is:
![r = \frac{g(5) - g(0)}{5 - 0} = \frac{(6*5 - 6) - (6*0 - 6)}{5} = 6](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bg%285%29%20-%20g%280%29%7D%7B5%20-%200%7D%20%3D%20%5Cfrac%7B%286%2A5%20-%206%29%20-%20%286%2A0%20-%206%29%7D%7B5%7D%20%20%3D%206)
Answer:
<u>x = 8/23</u>
Step-by-step explanation:
<u>Adding 3.5 to each side</u>
- -3.5 + 3.5 = -4.6x - 5.1 + 3.5
- -4.6x - 1.6 = 0
<u>Adding 4.6x to each side</u>
- -4.6x - 1.6 + 4.6x = 0 + 4.6x
- 4.6x = -1.6
<u>Dividing each side by 4.6</u>
- 4.6x/4.6 = -1.6/4.6
- <u>x = 8/23</u>
Since they are opposite angles about the intersection of two straight lines they are equal angles....
5x+12=6x-10 subtract 12 from both sides
5x=6x-22 subtract 6x from both sides
-x=-22 divide both sides by -1
x=22°
So those angles are 5*22+12=122°
Now HJI is an adjacent angle so it is 180°-122°=58°
Answer:
541.17ft^2
Step-by-step explanation:
the total area of the garden is the sum of area of rectangle and half of area of circle
area of rectangle=(l)(h)=(23)(18)=414
area of semicircle=1/2pir^2
since r is half of h=1/2(18)=9
area of semicircle=1/2pi(9)^2=127.17
total area of garden=414+127.17=541.17 ft^2