PLEASE HELP!! DUE TODAY!! ! 25 POINTS!! Given f (x) = x^4 - 5x^3 - 20x^2 + 60x + 144. Explain how to find the x and y-intercept
1 answer:
You might be interested in
Step-by-step explanation:
I am only sure about the first one but as for the rest I am not really but I tried...if you need explanations to the first one feel free to ask me
<h2>Answer:</h2>
y = x + 3
As shown in the graph, the line is a straight line. Therefore, the general equation of a straight line can be employed to derive the equation of the line.
The general equation of a straight line is given by:
y = mx + c <em>or </em>-------------(i)
y - y₁ = m(x - x₁) -----------------(ii)
Where;
y₁ is the value of a point on the y-axis
x₁ is the value of the same point on the x-axis
m is the slope of the line
c is the y-intercept of the line.
Equation (i) is the slope-intercept form of a line
Steps:
(i) Pick any two points (x₁, y₁) and (x₂, y₂) on the line.
In this case, let;
(x₁, y₁) = (0, 3)
(x₂, y₂) = (4, -2)
(ii) With the chosen points, calculate the slope <em>m</em> given by;
m =
m =
m =
(iii) Substitute the first point (x₁, y₁) = (0, 3) and m = into equation (ii) as follows;
y - 3 = (x - 0)
(iv) Solve for y from (iii)
y - 3 = x
y = x + 3 [This is the slope intercept form of the line]
Where the slope is and the intercept is 3
For the given system of inequalities, x represents the number of brownies and y the number of cookies.
And the graph can be seen in the image below.
<h3>What each variable represents?</h3>Here we have the system of inequalities:
4x + 6y ≥ 200
x + y < 75.
We know that they want to make less than 75 items, that is what the second inequality:
x + y < 75.
Represents.
We also know that each brownie costs $4, and each cookie costs $6, then the expression:
x*4 + y*6
Represents the revenue for selling x brownies and y cookies, and because they want to earn at least $200, the inequality becomes:
x*4 + y*6 ≥ 200
So we conclude that x represents the number of brownies and y the number of cookies.
Now the system is:
4x + 6y ≥ 200
x + y < 75.
To graph it, you just need to graph both the lines and shade the indicated region, we can write the inequalities sa:
y ≥ (200 - 4x)/6
y < 75 + x
Just graph these two lines, for the first one you need to use a solid line and shade the region above the line, for the second, a dashed line and you need to shade the region below the line. The graph can be seen below.
The solutions to the systems are in the region where both shaded parts intersect.
There we can see that the point x = 20 and y = 20 (among a lot of other ones) is a solution to the system.
If you want to learn more about systems of inequalities:
#SPJ1
