<h2>
Explanation:</h2>
Hello! Remember you have to write complete questions in order to get good and exact answers. Here I'll assume the graphed function comes from:
So this is the equation of a parabola that opens upward and whose vertex lies on the point:
The graph of this function is shown below. Which is true regarding the graphed function f(x)?
- It is true that the domain is the set of all real numbers because this is a polynomial function.
- It is true that the range is the set of all real numbers such that y ≥ 5
- It is true that this parabola opens upward
- It is true that it doesn't cut the x-axis
To write the function to show the weekly growth rate of population , we first find the weekly growth rate by dividing yearly growth rate by 52 ( as there are 52 weeks in an year)
Given function is ,
or
To convert in weekly growth rate , divide 0.016 by 52
So formula for weekly growth rate of population is
or
And the weekly growth rate = 
The equation of line CD in standard form is: B. 5x - 3y = 30
<h3>How to determine the equation of line CD in standard form?</h3>
Mathematically, the standard form of the equation of a straight line is given by this mathematical expression (linear function);
y = mx + c
Where:
- x and y are the points.
- m represents the slope, gradient, or rate of change.
- c represents the intercept.
Next, we would determine the slope of this line by using this formula:
Slope, m = Δy/Δx
Slope, m = Change in y-axis/Change in x-axis
Slope, m = (0 + 5)/(6 - 3)
Slope, m = 5/3
At point (6, 0), the point-slope equation of the line is given by:
y - y₁ = m(x - x₁)
y - 0 = 5/3(x - 6)
y = 5x/3 - 30/3
y = 5x/3 - 10
Multiplying all through by 3, we have:
3y = 5x - 30
Rearranging the equation, we have:
5x - 3y = 30
Read more on slope here: brainly.com/question/7748981
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6.
4x^2 + 4 = 0
Divide both sides by 4
x^2 + 1 = 0
Use the quadratic formula since this cannot be factored.
x = (-b +- sqrt(b^2 - 4ac))/(2a)
x = +- sqrt(-4(1)(1))/2
x = +- sqrt(-4)/2
x = +- 2i/2
x = +- i
x = i or x = -i
Quicker solution:
If you have x^2 = number, then
x = +- sqrt(number)
Once you get to
x^2 + 1 = 0
Subtract 1 from both sides
x^2 = -1
Apply the quick method
x = +- sqrt(-1)
x = +- i
8.
2x^2 + 50 = 0
Divide both sides by 2
x^2 + 25 = 0
Subtract 25 from both sides
x^2 = -25
Apply quick method
x = +- sqrt(25)
x = +- 5i
x = 5i or x = -5i
The answer is 3.46 meters
You can get the answer by using the pythagorean theorem, since the ladder and the wall form a right triangle.
c^2 = a^2 + b^2
4^2 = 2^2 + b^2
16 = 4 + b^2
12 = b^2
b = sqrt(12) or 3.46 meters
