Answer:
Option D.
Step-by-step explanation:
The slope of a horizontal line is 0.
It is given that the function 1 is a horizontal line that passing through the y-axis at y = 4.
It means the rate of change of function 1 is 0.
The slope intercept form of a linear function is 1
where, m is slope and b is y-intercept.
The function 2 is 2
On comparing (1) and (2), we get
The rate of change of function 2 is 8.
The difference between rate of change is
The rate of change of function 2 is 8 more than the rate of change of function 1.
Therefore, the correct option is D.
1024 can be factored into
<span>2(512) </span>
<span>=2^2(256) </span>
<span>=2^3(128) </span>
<span>=2^4(64) </span>
<span>=2^5(32) </span>
<span>=2^6(16) </span>
<span>=2^10 </span>
<span>Therefore, </span>
<span>√1024 = √(2^10) = 2^5 = 32</span>
Step 1: Find the slope:
This gives you 
, but we need to find b.
To find b, substitute in one (x,y) pair and it doesn't matter which one. I'll go with (4,-2):
![\begin{aligned}-2&=-\dfrac{3}{2}(4)+b\\[0.5em]-2&=-6+b\\[0.5em]4&=b\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D-2%26%3D-%5Cdfrac%7B3%7D%7B2%7D%284%29%2Bb%5C%5C%5B0.5em%5D-2%26%3D-6%2Bb%5C%5C%5B0.5em%5D4%26%3Db%5Cend%7Baligned%7D)
Now take that b-value and plug in into the slope-intercept form:
It's always a good idea to toss in the other x-value from the other point, to make sure it checks out.
Rearrange to: x^2 + 18x - 25 = 0
Then factorise (I like to do it by completing the square):
(x + 9)^2 -81 -25 = 0
(x + 9)^2 = 106
x + 9 = sqrt(106)
The sol'ns are:
x = -9 + and - sqrt(106)
