Answer:
Please check the explanation.
Step-by-step explanation:
Given the function
We know that the domain of the function is the set of input or arguments for which the function is real and defined.
In other words,
- Domain refers to all the possible sets of input values on the x-axis.
Now, determine non-negative values for radicals so that we can sort out the domain values for which the function can be defined.
as x³ - 16x ≥ 0
Thus, identifying the intervals:
Thus,
The domain of the function f(x) is:
![x\left(x+4\right)\left(x-4\right)\ge \:0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-4\le \:x\le \:0\quad \mathrm{or}\quad \:x\ge \:4\:\\ \:\mathrm{Interval\:Notation:}&\:\left[-4,\:0\right]\cup \:[4,\:\infty \:)\end{bmatrix}](https://tex.z-dn.net/?f=x%5Cleft%28x%2B4%5Cright%29%5Cleft%28x-4%5Cright%29%5Cge%20%5C%3A0%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3A-4%5Cle%20%5C%3Ax%5Cle%20%5C%3A0%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Ax%5Cge%20%5C%3A4%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%5B-4%2C%5C%3A0%5Cright%5D%5Ccup%20%5C%3A%5B4%2C%5C%3A%5Cinfty%20%5C%3A%29%5Cend%7Bbmatrix%7D)
And the Least Value of the domain is -4.
<em>-</em><em>6</em><em>0</em><em>+</em><em>(</em><em>3</em><em>0</em><em>0</em><em>)</em><em> </em><em>+</em><em>100</em>
<em>-</em><em>6</em><em>0</em><em>-</em><em>3</em><em>0</em><em>0</em><em>+</em><em>100</em>
<em>=</em><em> </em><em>-</em><em>2</em><em>6</em><em>0</em>
<em>=</em><em>5</em><em>0</em><em>-</em><em>(</em><em>-</em><em>4</em><em>0</em><em>)</em><em>-</em><em>(</em><em>-</em><em>2</em><em>)</em>
<em>=</em><em>5</em><em>0</em><em>+</em><em>4</em><em>0</em><em>+</em><em>2</em>
<em>=</em><em>9</em><em>2</em>
Y int = (0,12)
Bc the y intercept is when X = 0
Slope =
(18-15)/(4-2) =
3/2
Answer:
No. Mike wrote the ratio as the amount of change to the new amount. He should have used the ratio of the amount of change to the original amount, which is 55
55/275
, or 20%.
Answer:
Step-by-step explanation:
We are given a ratio for this problem so we will use the formula for when we are given a ratio (as opposed to the formula for when you are given that the point you're looking for is a fraction of the way from one point to another, like 1/3 of the way from point A to point B. That's a different formula).
The formulas are for the x and y coordinates of the point in question:
and 
where
a = 3 (from the ratio),
b = 1 (from the ratio),
x1 = -4, y1 = 0 (from point J)
x2 = 0, y2 = 4 (from point K). Filling in for x first:
gives us
and now for y:
gives us
Therefore, the coordinates that partition that segment into the ratio of 3:1 are (-1, 3)
