Answer:
D
Step-by-step explanation:
|-6x+3|=0
-6x+3=0
-6x=-3
x=-3/-6
x=1/2
a) The linear function that models the population in t years after 2004 is: P(t) = -200t + 29600.
b) Using the function, the estimate for the population in 2020 is of 26,400.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The initial population in 2004, of 29600, is the y-intercept. In 12 years, the population decayed 2400, hence the slope is:
m = -2400/12 = -200.
Hence the equation is:
P(t) = -200t + 29600.
2020 is 16 years after 2004, hence the estimate is:
P(16) = -200(16) + 29600 = 26,400.
More can be learned about linear functions at brainly.com/question/24808124
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The inequality that represents the given graph is y < x/5 -2 OR 5y < x - 10
<h3>Graph of Inequality</h3>
From the question, we are to determine the inequality that represents the graph
First, we will assume the inequality is a straight line and we will determine the equation of the line
From the graph, we have two points on the line
(0, -2) and (5, -1)
Using the formula for the equation of a line with two given point
(y - y₁)/(x -x₁) = (y₂ - y₁)/ (x₂ - x₁)
x₁ = 0
y₁ = -2
x₂ = 5
y₂ = -1
Thus,
(y - -2)/(x - 0) = (-1 - -2)/ (5 - 0)
(y +2)/(x - 0) = (-1 + 2)/ (5 - 0)
(y +2)/(x ) = 1/ 5
5(y + 2) =1(x)
5y + 10 = x
5y = x - 10
y = 1/5(x) - 2
y = x/5 - 2
Now,
Since the solution is below the line and the line is dotted
The inequality becomes
y < x/5 -2
OR
5y < x - 10
Hence, the inequality that represents the given graph is y < x/5 -2 OR 5y < x - 10
Learn more on Graph of Inequality here: brainly.com/question/17106134
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