The x and the y-intercepts of the function are 8 and 6, respectively
<h3>Intercepts</h3>
The intercepts of a function are the points where the graph of the function crosses the x-axis
<h3>The
function</h3>
The function is given as:
Set y to 0, to calculate the x-intercept
Divide both sides by 3
Set x to 0, to calculate the y-intercept
Divide both sides by 4
Hence, the x and the y-intercepts of the function are 8 and 6, respectively
Read more about intercepts at:
brainly.com/question/26233
Answer:
x(2x + 3) + (x - 3) (x - 4) = 3x²- 4x + 12
Step-by-step explanation:
<em>Expand:</em>
x(2x + 3): 2x² + 3x
2x² + 3x + (x - 3) (x - 4)
<em>Expand</em>:
(x - 3) (x - 4): x²- 7x + 12
2x² + 3x + x²- 7x + 12
<em>Simplify:</em>
2x² + 3x + x² - 7x + 12: 3x² - 4x + 12
= 3x² - 4x +12
To find the solution to the problem, we can divide the number by 1,000.
Because we're trying to find how many 1,000's are there in this 800,000.
800,000 / 1,000 = 800
There are 800 1,000's in that number.
I have to do a little more than I thought
<span>Constraints (in slope-intercept form)
x≥0,
y≥0,
y≤1/3x+3,
y</span>≤ 5 - x
The vertices are the points of intersection between the constraints, or the outer bounds of the area that agrees with the constraints.
We know that x≥0 and y≥0, so there is one vertex at (0,0)
We find the other vertex on the y-axis, plug in 0 for x in the function:
y <span>≤ 1/3x+3
y </span><span>≤1/3(0)+3
y = 3.
There is another vertex at (0,3)
Find where the 2 inequalities intersect by setting them equal to each other
(1/3x+3) = 5-x Simplify Simplify Simplify
x = 3/2
Plugging in 3/2 into y = 5-x: 10/2 - 3/2 = 7/2
y=7/2
There is another vertex at (3/2, 7/2)
There is a final vertex where the line y=5-x crosses the x axis:
0 = 5 -x , x = 5
The final vertex is at point (5, 0)
Therefore, the vertices are:
(0,0), (0,3), (3/2, 7/2), (5, 0)
We want to maximize C = 6x - 4y.
Of all the vertices, we want the one with the largest x and smallest y. We might have to plug in a few to see which gives the greatest C value, but in this case, it's not necessary.
The point (5,0) has the largest x value of all vertices and lowest y value.
Maximum of the function:
C = 6(5) - 4(0)
C = 30</span>
