Answer:
Zeroes : 1, 4 and -5.
Potential roots:
.
Step-by-step explanation:
The given equation is

It can be written as

Splitting the middle terms, we get



Splitting the middle terms, we get



Using zero product property, we get



Therefore, the zeroes of the equation are 1, 4 and -5.
According to rational root theorem, the potential root of the polynomial are

Constant = 20
Factors of constant ±1, ±2, ±4, ±5, ±10, ±20.
Leading coefficient= 1
Factors of leading coefficient ±1.
Therefore, the potential root of the polynomial are
.
Answer:
g(x) = 
Step-by-step explanation:
f(x) = 3x + 5
f[g(x)] = 3[g(x)] + 5
⇒ 3[g(x)] + 5 = x + 4
⇒ 3[g(x)] = x + 4 - 5
⇒ 3[g(x)] = x - 1
⇒ g(x) = 
In order to calculate the amount, we simply substitute the number of years into x in both equations.
After 3 years:
f(3) = 5(3) + 150
= $165
g(3) = 150 * 1.03⁽³⁾
= $163.90
After 10 years:
f(10) = 5(10) + 150
= $200
g(10) = 150 * 1.03⁽¹⁰⁾
= $201.59
After three years, the first account has more money but after ten years, the second account has more money.
For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

Where:
m: It's the slope
b: It is the cut-off point with the y axis
While the point-slope equation of a line is given by:

Where:
m: It's the slope
It is a point through which the line passes
In this case we have a line through:
(8,4) and (0,2)
Therefore, its slope is:

Its point-slope equation is:

Then, we manipulate the expression to find the equation of the slope-intersection form:

Therefore, the cut-off point with the y-axis is 
ANswer:

Answer:
The point (0, 1) represents the y-intercept.
Hence, the y-intercept (0, 1) is on the same line.
Step-by-step explanation:
We know that the slope-intercept form of the line equation
y = mx+b
where
Given
Using the point-slope form

where
- m is the slope of the line
In our case:
substituting the values m = 2/3 and the point (-6, -3) in the point-slope form



Subtract 3 from both sides



comparing with the slope-intercept form y=mx+b
Here the slope = m = 2/3
Y-intercept b = 1
We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
Given the line

at x = 0, y = 1
Thus, the point (0, 1) represents the y-intercept.
Hence, the y-intercept (0, 1) is on the same line.